Статті в журналах: "Susceptible-Infected-Recovered (SIR) model"

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MUTIA UTAMA, NANDA, ARRIVAL RINCE PUTRI, and MAHDHIVAN SYAFWAN. "DINAMIKA MODEL SUSCEPTIBLE INFECTED RECOVERED (SIR) DENGAN STRATEGI VAKSINASI." Jurnal Matematika UNAND 9, no. 4 (February 18, 2021): 357. http://dx.doi.org/10.25077/jmu.9.4.357-365.2020.

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Vaksinasi merupakan salah satu cara untuk mencegah sekaligus mengendalikan penyebaran penyakit menular. Penelitian ini membahas salah satu model penyebaran penyakit menular, yaitu model Susceptible Infected Recovered (SIR). Model SIR yang dibahas mempertimbangkan strategi vaksinasi, yaitu vaksinasi konstan dan vaksinasi berkala, yang diberikan kepada individu rentan terinfeksi penyakit. Kajian analitik dilakukan dengan menganalisis kestabilan model di sekitar titik ekuilibrium berdasarkan nilai eigen dari matriks Jacobian. Kestabilan model dikaitkan juga dengan parameter ambang batas, yaitu parameter yang menentukan apakah suatu populasi bebas atau terinfeksi dari penyakit. Simulasi numerik dilakukan untuk mengkonfirmasi hasil analitik dengan menggunakan parameter dari kasus penyakit Tuberkulosis (TBC) di Provinsi Sumatera Barat tahun 2018. Hasil analitik maupun numerik memperlihatkan bahwa pemberian stategi vaksinasi efektif sebagai pencegahan dan pengendalian penyebaran penyakit, sehingga dapat mengurangi jumlah individu yang terinfeksi.Kata Kunci: Model SIR, Vaksinasi, Kestabilan, Parameter Ambang Batas, Simulasi Numerik

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PUTRI, FARRAS VITASHA, MAHDHIVAN SYAFWAN, and MUHAFZAN MUHAFZAN. "SOLUSI EKSAK MODEL EPIDEMI SUSCEPTIBLE-INFECTED-RECOVERED-DEATH." Jurnal Matematika UNAND 10, no. 3 (July 26, 2021): 293. http://dx.doi.org/10.25077/jmu.10.3.293-300.2021.

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Model epidemi Susceptible-Infected-Recovered-Death (SIRD) adalah pengembangan dari model epidemi Susceptible-Infected-Removed (SIR) yang membagi kompartemen removed menjadi kompartemen recovered dan death. Dalam makalah ini dibahas kembali penurunan model SIRD. Selanjutnya dengan menggunakan persamaan Bernoulli, model tersebut diselesaikan untuk memperoleh solusi eksak dalam bentuk parametrik. Pengujian secara numerik untuk beberapa nilai parameter menunjukkan bahwa solusi numerik persis sama dengan solusi eksak.Kata Kunci: Solusi eksak, model epidemi Susceptible-Infected-Recovered-Death (SIRD), persamaan Bernoulli

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Sifriyani, Sifriyani, and Dedi Rosadi. "SUSCEPTIBLE INFECTED RECOVERED (SIR) MODEL FOR ESTIMATING COVID-19 REPRODUCTION NUMBER IN EAST KALIMANTAN AND SAMARINDA." MEDIA STATISTIKA 13, no. 2 (December 28, 2020): 170–81. http://dx.doi.org/10.14710/medstat.13.2.170-181.

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Modeling and analysis of Covid-19 data, especially on the modeling the spread and the prediction of the total number of cases for Indonesian data, has been conducted by several researchers. However, to the best of our knowledge, it has not been studied specifically for East Kalimantan Province data. The study of the data on the level of provincial and District/City level could help the government in making policies. In this study, we estimate the Covid-19 reproduction number, calculate the rate of recovery, the rate of infection, and the rate of death of East Kalimantan Province and Samarinda City. We also provide a prediction of the peak of the infection cases and forecast the total incidence of Covid-19 cases until the end of 2020. The model used in this research is the Susceptible Infected Recovered (SIR) model and the data used in the study was obtained from the East Kalimantan Public Health Office.

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Suniantara, I. Gusti Ngurah Gede Agung, Nyoman Gunantara, and Made Sudarma. "Analisis Penyebaran Covid 19 Menggunakan Model SIR (Susceptible, Infected, Recovered) Di Provinsi Bali." Majalah Ilmiah Teknologi Elektro 22, no. 1 (June 5, 2023): 39. http://dx.doi.org/10.24843/mite.2023.v22i01.p05.

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Pandemi Corona Virus Disease 2019 (Covid-19) diumumkan oleh WHO (World Health Organization) pada tanggal 11 Maret 2020. WHO menjelaskan Coronavirus merupakan virus yang dapat menyebabkan penyakit pada hewan dan manusia. Penyebaran virus Covid-19 sudah menyebar hingga indonesia dan telah menyebar ke seluruh Provinsi. Penyebaran COVID-19 dapat dimodelkan secara matematis dengan model SIR. Model SIR dibagi menjadi tiga kompartemen, yaitu individu rentan, individu terinfeksi, dan individu sembuh. Estimasi SIR dapat diperiksa tingkat kesalahannya menggunakan metode MAPE. Hasil estimasi SIR di Provinsi Bali menunjukkan pada tanggal 31 Desember 2022 jumlah orang yang terinfeksi virus COVID-19 mencapai 207.220 penduduk. Model SIR ini menghasilkan nilai = 1,393524 yang menandakan bahwa di Provinsi Bali kasus terinfeksi COVID-19 masih akan terus bertambah. Model SIR menghasilkan tingkat error sebesar 21% dengan menggunakan metode MAPE.Kata Kunci— COVID-19; SIR; MAPE.

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Cao, J., H. Han, Y. J. Wang, and T. C. Han. "Optimal logistics scheduling with dynamic information in emergency response: Case studies for humanitarian objectives." Advances in Production Engineering & Management 18, no. 3 (September 30, 2023): 381–95. http://dx.doi.org/10.14743/apem2023.3.480.

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The mathematical model of infectious disease is a typical problem in mathematical modeling, and the common infectious disease models include the susceptible-infected (SI) model, the susceptible-infected-recovered model (SIR), the susceptible-infected-recovered-susceptible model (SIRS) and the susceptible-exposed-infected-recovered (SEIR) model. These models can be used to predict the impact of regional return to work after the epidemic. In this paper, we use the SEIR model to solve the dynamic medicine demand information in humanitarian relief phase. A multistage mixed integer programming model for the humanitarian logistics and transport resource is proposed. The objective functions of the model include delay cost and minimum running time in the time-space network. The model describes that how to distribute and deliver medicine resources from supply locations to demand locations with an efficient and lower-cost way through a transportation network. The linear programming problem is solved by the proposed Benders decomposition algorithm. Finally, we use two cases to calculate model and algorithm. The results of the case prove the validity of the model and algorithm.

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Pasaribu, Donna Mesina Rosadini, Ernawaty Tamba, Muhammad Faturrahman Adani, and Wani Devita Gunardi. "Literature Review: Model Matematika Penyebaran Virus SARS-COV-2 pada Masa Pandemi COVID-19 Tahun 2020." Jurnal Kedokteran Meditek 29, no. 2 (May 22, 2023): 226–35. http://dx.doi.org/10.36452/jkdoktmeditek.v29i2.2607.

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Pandemi COVID-19 dinyatakan sebagai Public Health Emergency of International Concern oleh WHO. Model Matematika penyebaran Susceptible-Infected-Recovered (SIR) dan model Susceptible-Exposed-Infected-Recovered (SEIR) digunakan dalam pemodelan penyakit menular dengan menghitung jumlah orang dalam populasi tertutup. Pemodelan matematika ini merupakan matematika epidemiologi untuk memahami dinamika populasi pada saat pandemi, dan acuan efektivitas kebijakan yang dilakukan selama pandemi. Literatur Riview ini bertujuan untuk mengetahui gambaran situasi pandemi COVID-19 berdasarkan model matematika SIR dan SEIR di beberapa negara tahun 2020. Data yang dipakai pada Literatur Riview ini adalah hasil penelitian, laporan dari lembaga terkait, situs web resmi jurnal dan beberapa situs berita resmi. Model SIR dan SEIR dengan baik menyajikan perubahan data COVID-19 dan model ini dapat memberikan panduan untuk mendapatkan wawasan yang lebih baik tentang evolusi pandemi COVID-19. Model Matematika SIR dan SEIR membantu pemerintah negara di dunia dan badan kesehatan dunia WHO, dalam membuat kebijakan pencegahan penularan dan pengendalian COVID-19.

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CHAKRABORTY, ABHIJIT, and S. S. MANNA. "DISEASE SPREADING MODEL WITH PARTIAL ISOLATION." Fractals 21, no. 03n04 (September 2013): 1350015. http://dx.doi.org/10.1142/s0218348x13500151.

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The effect of partial isolation has been studied in disease spreading processes using the framework of susceptible-infected-susceptible (SIS) and susceptible-infected-recovered (SIR) models. The partial isolation is introduced by imposing a restriction: each infected individual can probabilistically infect up to a maximum number n of his susceptible neighbors, but not all. It has been observed that the critical values of the spreading rates for endemic states are non-zero in both models and decrease as 1/n with n, on all graphs including scale-free graphs. In particular, the SIR model with n = 2 turned out to be a special case, characterized by a new bond percolation threshold on square lattice.

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Okabe, Yutaka, and Akira Shudo. "Microscopic Numerical Simulations of Epidemic Models on Networks." Mathematics 9, no. 9 (April 22, 2021): 932. http://dx.doi.org/10.3390/math9090932.

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Mathematical models of the spread of epidemic diseases are studied, paying special attention to networks. We treat the Susceptible-Infected-Recovered (SIR) model and the Susceptible-Exposed-Infectious-Recovered (SEIR) model described by differential equations. We perform microscopic numerical simulations for corresponding epidemic models on networks. Comparing a random network and a scale-free network for the spread of the infection, we emphasize the role of hubs in a scale-free network. We also present a simple derivation of the exact solution of the SIR model.

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Azirah Amri, Noor, and Yuliani Yuliani. "Analisis Model SIR (Susceptible Infected Recovered) Dalam Penyebaran Penyakit Kanker Serviks Di Kota Palopo." Infinity: Jurnal Matematika dan Aplikasinya 1, no. 1 (August 22, 2020): 22–28. http://dx.doi.org/10.30605/27458326-17.

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Penelitian ini bertujuan untuk mengetaui analisis model SIR (Susceptible infected recovered) dalam penyebaran penyakit kanker serviks di Kota Palopo. Model epidemik SIR membagi populasi menjadi tiga kelompok yaitu, kelompok individu yang sehat tetapi dapat terinfeksi penyakit (susceptible), kelompok individu yang terinfeksi (infected), dan kelompok individu sembuh (recovered). Data yang digunakan adalah data sekunder yaitu mengenai jumlah masyarakat Kota Palopo yang rentan, terinfeksi, dan sembuh dari penyakit kanker serviks. Data diperoleh dari Dinas Kesehatan Kota Palopo. Data yang diperoleh kemudian dianalisis sehingga memperoleh titik keseimbangan dan uji kestabilan titik keseimbangan. Selanjutnya, dilakukan simulasi numerik menggunakan aplikasi MAPLE untuk mengetahui tingkat penularan kanker serviks di Kota Palopo. Dari hasil analisis model SIR penyebaran kanker serviks di Kota Palopo diperoleh 2 titik keseimbangan dimana hanya ada satu titik keseimbangan yang stabil yaitu memiliki sistem yang stabil asimptotik karena seluruh bagian dari nilai eigen bernilai positif. Nilai dari sehingga yang artinya titik keseimbangan bebas penyakit kanker serviks atau penyakit kanker serviks di Kota Palopo dapat sembuh.

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Sharif, Noorzila, Jasmani Bidin, Ku Azlina Ku Akil, and Shasha Fazlisa Mazlan. "Effectiveness of Online Video Marketing on Facebook Using Susceptible-Infected-Recovered (SIR) Model." Journal of Computing Research and Innovation 7, no. 2 (September 30, 2022): 54–65. http://dx.doi.org/10.24191/jcrinn.v7i2.286.

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The advancements in technology and high-speed networks give advantages for entrepreneurs to promote their products and services in various forms of posting through social media platforms such as Facebook, Twitter, Instagram and many more. The effectiveness of the video posting in terms of the virality of the video, the time the video reaches the maximum number of viewers and the flow of video spread are very important inputs for the marketers. Therefore, this preliminary study was designed to differentiate the effectiveness of two selected video posting on Facebook promoting two different popular products among women: shawls and slimming product. Susceptible-Infected-Recovered (SIR) models with demography and without demography was used in analysing the data since the nature of the dissemination of the video is similar to the spread of virus. The variables used in the analysis were the number of Facebook users who exposed to the video (Susceptible), received and shared the video (Infected) and stop sharing the video (Recovered). The finding shows the video promoting the shawl is more viral (R0Â > 1) as compared to the video promoting the slimming product (R0 < 1) based on both SIR Model. Although the earliest number of users who received the shawl video was lower but the number of users who received and shared that videos increased tremendously until it reached the maximum number of 19.6 million viewers in 2 days and after that the number was slowly decreased. For slimming product, it started with higher number of viewers, but reached the maximum number of viewers of 10.3 million in 8 days and later the number was gradually decreased. Further study should be done because there are a lot of possibilities or factors that contribute to these findings.

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Trejo, Imelda, and Nicolas W. Hengartner. "A modified Susceptible-Infected-Recovered model for observed under-reported incidence data." PLOS ONE 17, no. 2 (February 9, 2022): e0263047. http://dx.doi.org/10.1371/journal.pone.0263047.

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Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.

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Kumar, Rajnesh, and Sunil Kumar. "A New Fractional Modelling on Susceptible-Infected-Recovered Equations with Constant Vaccination Rate." Nonlinear Engineering 3, no. 1 (March 1, 2014): 11–19. http://dx.doi.org/10.1515/nleng-2013-0021.

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AbstractIn this article, the authors introduce a fractional order SIR model with constant vaccination rate. The SIR model has been used in the modeling of several epidemiological diseases, biology and medical sciences. Qualitative results show that the model has two equilibria; the disease free equilibrium and the endemic equilibrium points. The local stability of the model for fractional order time derivative is analyzed using fractional Routh-Hurwitz stability criterion. The fractional derivative is described in Caputo sense. The results obtained through numerical procedure show that the method is effective and reliable.

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Nur, Wahyudin, and Nurul Mukhlisah Abdal. "Solusi Numerik Model Umum Epidemik Susceptible, Infected, Recovered (SIR) dengan Menggunakan Metode Modified Milne-Simpson." SAINTIFIK 2, no. 2 (July 2, 2016): 142–46. http://dx.doi.org/10.31605/saintifik.v2i2.159.

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Model Epidemik Susceptible, Infected, Recovered (SIR) merupakan salah satu metode yang paling banyak digunakan untuk memodelkan penyebaran penyakit. Model ini biasa digunakan untuk simulasi dan ptediksi jumlah kasus penyakit tertentu. Dalam artikel ini penulis melakukan simulasi dan mencari solusi numerik model umum epidemik SIR dengan menggunakan MMetode Modified Milne Simpson yang dipadukan dengan metode Runge Kutta Orde 4. Metode ini merupakan salah satu metode prediktor korektor yang biasa digunakan untuk mencari solusi numerik persamaan diferensial. Dengan menggunakan parameter miu=0,1;lamda=0,0098; gamma=0,5 diperoleh r0=0,016333<1. Kurva kelas Infected menuju nol dan setimbang dititik nol. Hal ini menandakan, dengan pemilihan parameter seperti itu, kelas Infected akan menghilang dari populasi. Berdasarkan hasil simulasi, dapat disipulkan bahwa metode Milne Simpson layak digunakan untuk menentukan solusi numerik model umum epidemik SIR.Kata kunci: Model SIR, Modified Milnw Simpson, Runge Kutta Orde 4

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Okabe, Yutaka, and Akira Shudo. "A Mathematical Model of Epidemics—A Tutorial for Students." Mathematics 8, no. 7 (July 17, 2020): 1174. http://dx.doi.org/10.3390/math8071174.

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This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

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Inez, Lucas Martins, Carlos Eduardo Rambalducci Dalla, Wellington Betencurte da Silva, Julio Cesar Sampaio Dutra, and José Mir Justino da Costa. "Selection of models and parameter estimation for monitoring the COVID-19 epidemic in Brazil via Bayesian inference." Ciência e Natura 45, esp. 3 (December 1, 2023): e73812. http://dx.doi.org/10.5902/2179460x73812.

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In 2019, a new strain of coronavirus led to an outbreak of disease cases named COVID-19, evolving rapidly into a pandemic. In Brazil, delayed decision making and lack of knowledge have resulted in an alarming increase in daily transmission and deaths. In this context, researchers used mathematical models to assist in determining the parameters that act in the spread of diseases, revealing containment measures. However, numerous mathematical models exist in the literature, each with specific parameters to be specified, leading to an important question about which model best represents the pandemic behavior. In this regard, this work aims to apply the Approximate Bayesian Computation method to select the best model and simultaneously estimate the parameters to resolve the abovementioned issue. The models adopted were susceptible-infected-recovered (SIR), susceptible-exposed-infected-recovered (SEIR), susceptible-infected-recovered-susceptible (SIRS), and susceptible-exposed-infected-recovered-susceptible (SEIRS). Approximate Bayesian Computation Monte Carlo Sequencing (ABC-SMC) was used to select among four competing models to represent the number of infected individuals and to estimate the model parameters based on three periods of Brazil COVID-19 data. A forecasting test was performed to test the ABC-SMC algorithm and the selected models for two months. The result was compared with the actual number of infected that were reported. Among the teste models, it was found that the ABC-SMC algorithm had a promising performance, since the data were noisy and the models could not predict all parameters.

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Hidayati, Noer, Eminugroho Ratna Sari, and Nur Hadi Waryanto. "Mathematical model of cholera spread based on SIR: Optimal control." PYTHAGORAS Jurnal Pendidikan Matematika 16, no. 1 (September 23, 2021): 70–83. http://dx.doi.org/10.21831/pg.v16i1.35729.

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The bacterium Vibrio cholerae is the cause of cholera. Cholera is spread through the feces of an infected individual in a population. From a mathematical point of view, this problem can be brought into a mathematical model in the form of Susceptible-Infected-Recovered (SIR), which considers the birth rate. Because outbreaks that occur easily spread if not treated immediately, it is necessary to control the susceptible individual population by vaccination. The vaccine used is Oral Vibrio cholera. For this reason, the purposes of this study were to establish a model for the spread of cholera without vaccination, analyze the stability of the model around the equilibrium point, form a model for the spread of cholera with vaccination control, and describe the simulation results of numerical model completion. Based on the analysis of the stability of the equilibrium point of the model, it indicates that if the contact rate is smaller than the sum of the birth rate and the recovery rate, cholera will disappear over time. If the contact rate is greater than the sum of the birth rate and the recovery rate, then cholera is still present, or in other words, the disease can still spread. Because the spread is endemic, optimal control of the population of susceptible individuals is needed, in this case, control by vaccination, so that the population of susceptible individuals becomes minimum and the population of recovered individuals increases.

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Wahyudi, Bambang Ari, and Irma Palupi. "Prediction of the peak Covid-19 pandemic in Indonesia using SIR model." Jurnal Teknologi dan Sistem Komputer 9, no. 1 (December 7, 2020): 49–55. http://dx.doi.org/10.14710/jtsiskom.2020.13877.

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This research implements the Susceptible, Infected, and Removed (SIR) model to predict the Covid-19 outbreak in Indonesia. The government official data, consisting of infected, dead, and recovered, are used as actual data to interpolate the model through matching data with minimum mean squared error (MSE). The study uses one of the Quasi-Newton search methods, the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) algorithm, to determine the interaction coefficient's optimal value in the model with the minimum MSE value. Based on data as of July 18, 2020, it predicts that the peak of the infected number will be in October 2020 with around 14 % of the total population infected, and the MSE of 18.42 is relative to the period of the actual data. Meanwhile, the basic reproduction rate is calculated to be 2.035 from the model, where it is underestimated about 29 % compared to the relative basic reproduction rate from the provided actual data.

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Pertiwi, Julia Indah, Arrival Rince Putri, and Efendi Efendi. "ANALISIS PERILAKU MODEL SIR TANPA DAN DENGAN VAKSINASI." BAREKENG: Jurnal Ilmu Matematika dan Terapan 14, no. 2 (September 7, 2020): 223–32. http://dx.doi.org/10.30598/barekengvol14iss2pp223-232.

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Vaksinasi adalah salah satu cara untuk mengendalikan sekaligus mencegah penyebaran penyakit menular. Tingkat vaksinasi yang diberikan kepada individu dalam suatu populasi, menentukan apakah populasi tersebut tahan atau tidak terhadap penyakit. Penelitian ini mengembangkan model SIR (susceptible, infected, recovered) tanpa dan dengan vaksinasi. Perilaku solusi dari kedua model dianalisis melalui analisis kestabilan di sekitar titik-titik ekuilibriumnya. Kestabilan tersebut juga dikaitkan dengan nilai ambang batas yang menandakan apakah ppopulasi bebas atau terinfeksi penyakit. Hasil analitik dikonfirmasi dengan hasil numerik.

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Essouifi, Mohamed, and Abdelfattah Achahbar. "A mixed SIR-SIS model to contain a virus spreading through networks with two degrees." International Journal of Modern Physics C 28, no. 09 (September 2017): 1750114. http://dx.doi.org/10.1142/s0129183117501145.

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Due to the fact that the “nodes” and “links” of real networks are heterogeneous, to model computer viruses prevalence throughout the Internet, we borrow the idea of the reduced scale free network which was introduced recently. The purpose of this paper is to extend the previous deterministic two subchains of Susceptible-Infected-Susceptible (SIS) model into a mixed Susceptible-Infected-Recovered and Susceptible-Infected-Susceptible (SIR–SIS) model to contain the computer virus spreading over networks with two degrees. Moreover, we develop its stochastic counterpart. Due to the high protection and security taken for hubs class, we suggest to treat it by using SIR epidemic model rather than the SIS one. The analytical study reveals that the proposed model admits a stable viral equilibrium. Thus, it is shown numerically that the mean dynamic behavior of the stochastic model is in agreement with the deterministic one. Unlike the infection densities [Formula: see text] and [Formula: see text] which both tend to a viral equilibrium for both approaches as in the previous study, [Formula: see text] tends to the virus-free equilibrium. Furthermore, since a proportion of infectives are recovered, the global infection density [Formula: see text] is minimized. Therefore, the permanent presence of viruses in the network due to the lower-degree nodes class. Many suggestions are put forward for containing viruses propagation and minimizing their damages.

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Hidayati, Aulia Maulani Syifa Nur, Respatiwulan Respatiwulan, and Sri Subanti. "Model Simulation of Continuous Time Markov Chain Susceptible Infected Recovered-Bacterial Population for Cholera Disease." Indonesian Journal of Applied Statistics 6, no. 1 (January 18, 2024): 1. http://dx.doi.org/10.13057/ijas.v6i1.71801.

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Epidemic is an outbreak of an infectious disease rapidly in a population at a certain place and time. Epidemic models are used to explains the spread pattern of disease. The continuous time Markov chain susceptible infected recovered-bacterial population in the aquatic reservoir (CTMC SIR-B) model is a stochastic model, which considers the effect of bacterial population. The human population are classified into 3 groups. There are susceptible, infected, and recovered groups. Then, there are bacterial population which can infectious the cholera disease to human. CTMC SIR-B model considers treatment and water sanitation parameters. The spread of cholera disease can be modeled as CTMC SIR-B. Cholera is an acute intestinal infectious disease caused by the bacterium Vibrio cholerae. Cholera can be transmitted through the human digestive system. The symptoms of cholera disease are diarrhea, vomiting, and dehydration. The dehydration if not handled properly, may cause death. The aims of this research are to build and simulate the CTMC SIR-B model for cholera disease. The result of the model simulation shows that there is no significant difference between various values of treatment and water sanitation parameters. The pattern of the cholera disease spread describes that the transmission of cholera can occur from human to human even though there is no population of bacteria in the aquatic reservoir.Keywords: cholera; ctmc sir-b; epidemic model; stochastic.

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Zrieq, Rafat, Sahbi Boubaker, Souad Kamel, Mohamed Alzain, and Fahad D. Algahtani. "Analysis and modeling of COVID-19 epidemic dynamics in Saudi Arabia using SIR-PSO and machine learning approaches." Journal of Infection in Developing Countries 16, no. 01 (January 31, 2022): 90–100. http://dx.doi.org/10.3855/jidc.15004.

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Introduction: COVID-19 has become a global concern because it has extensive damage to health, social and economic systems worldwide. Consequently, there is an urgent need to develop tools to understand, analyze, monitor and control further outbreaks of the disease. Methodology: The Susceptible Infected Recovered-Particle SwarmOptimization model and the feed-forward artificial neural network model were separately developed to model COVID-19 dynamics based on daily time-series data reported by the Saudi authorities from March 2, 2020 to February 21, 2021. The collected data were divided into training and validation datasets. The effectiveness of the investigated models was evaluated by using various performance metrics. The Susceptible-Infected-Recovered-Particle-Swarm-Optimization model was found to well predict the cumulative infected and recovered cases and to optimally tune the contact rate and the characteristic duration of the illness. The feed-forward artificial neural network model was found to be efficient in modeling daily new and cumulative infections, recoveries and deaths. Results: The forecasts provided by the investigated models had high coefficient of determination values of more than 0.97 and low mean absolute percentage errors (around 7% on average). Conclusions: Both the Susceptible-Infected-Recovered-Particle-Swarm-Optimization and feed-forward artificial neural network models were efficient in modeling COVID-19 dynamics in Saudi Arabia. The results produced by the models can help the Saudi health authorities to analyze the virus dynamics and prepare efficient measures to control any future occurrence of the epidemic.

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Baran, V. I., and E. P. Baran. "SIMULATION OF PANDEMIC DEVELOPMENT PROCESSES." Vestnik of the Russian University of Cooperation, no. 3(45) (October 10, 2021): 9–13. http://dx.doi.org/10.52623/2227-4383-3-45-2.

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The study is devoted to the development of mathematical models for predicting the incidence of COVID-19 using simulation tools. Methods of modeling the spread of infectious diseases have been studied since the beginning of the twentieth century. In the classical SIR model, the entire population was divided into three parts: «susceptible – infected – recovered». In the 1980s, the intermediate state – «infected, but not yet infectious» was added to the classical model. This model is called SEIR. The spread of the epidemic in both models is described by a system of differential equations, which is solved using numerical methods. Significantly new simulation modelling approaches are necessary to forecast evolution of the coronavirus pandemic. This study based on the classical SEIR model («susceptible – infected but not yet infectious – infected – recovered») suggests several methods for developing models: with a long plateau, with two or more waves. The modern tool used for the simulation is Anylogic 8.

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BOLUMA MANGATA, Bopatriciat, Odette Sangupamba Mwilu, Patience Ryan Tebua Tene, and Gilgen Mate Landry. "Evaluation of two biometric access control systems using the Susceptible-Infected-Recovered model." Journal of Electronics, Electromedical Engineering, and Medical Informatics 5, no. 2 (April 30, 2023): 119–24. http://dx.doi.org/10.35882/jeemi.v5i2.288.

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This paper evaluates the effectiveness of decisions made on two single-mode biometric systems based on facial recognition and fingerprints for access control. To achieve this, we first implemented an embedded system under Arduino to allow us to open and close doors, then we programmed two biometric recognition systems, namely facial recognition and fingerprint recognition, and finally we exploited the Susceptible-Infected-Covered model without demographics to evaluate the efficiency of these two access control systems. The variables used in the analysis were the number of individuals enrolled in the biometric system to be subject to access control (Susceptible), the number of individuals enrolled in the biometric system and denied access by the system, as well as the number of individuals not enrolled in the biometric system and allowed access by the system (Infected), and the number of false acceptance rates and false rejection rates at time t in the systems (Retrieved). In a sample of 600 individuals, of which 300 were enrolled and 300 were not, our two simple modal access control systems each obtained the following results: 270 true positives, 30 false negatives, 48 false positives and 252 true negatives for the facial recognition system, compared to 288 true positives, 12 false negatives, 24 false positives and 276 true negatives for the fingerprint recognition system, which constitute our confusion matrix. Based on this confusion matrix, we were able to exploit the false rejection rates and false acceptance rates to correct for these inconveniences using the SIR model, i.e. 78 infected individuals for the facial recognition system, compared to 36 infected individuals for the fingerprint recognition system over a period of 216 days. The results show that the fingerprint recognition system is more efficient than the facial recognition system, according to the SIR model without demographic formulation.

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Rohimasanti, Wulan, Respatiwulan Respatiwulan, and Hasih Pratiwi. "MODEL EPIDEMI STOKASTIK SIR RANTAI BINOMIAL." Seminar Nasional Official Statistics 2020, no. 1 (January 5, 2021): 1239–46. http://dx.doi.org/10.34123/semnasoffstat.v2020i1.674.

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Epidemi adalah kejadian berjangkitnya suatu penyakit menular dalam masyarakat dengan jumlah penderitanya meningkat secara nyata pada waktu dan daerah tertentu. Model Susceptible Infected Recovered (SIR) merupakan suatu model epidemi yang menggambarkan proses penyebaran penyakit dengan karakteristik setiap individu sembuh memiliki kekebalan tubuh permanen. Jumlah individu yang terinfeksi diasumsikan berdistribusi binomial dengan periode penyembuhan bagi individu yang terinfeksi berhingga (ℜ<∞), sehingga individu yang terinfeksi hanya dapat menginfeksi individu lain pada periode ini. Periode penyembuhan (ℜ) adalah waktu yang diperlukan individu terinfeksi untuk sembuh dan menjadi kelompok recovered. Kondisi ini dapat pula disebut waktu penularan karena pada kondisi ini individu yang terinfeksi dapat menularkan penyakit pada individu lainnya. Tujuan penelitian ini adalah menurunkan model epidemi stokastik SIR dengan infeksi yang menyebar dalam populasi membentuk rantai penularan yang ditentukan oleh distribusi binomial dan periode penyembuhan bervariasi kemudian dilakukan simulasi model dan memberikan interpretasi. Pada penelitian ini, periode penyembuhan mempengaruhi durasi epidemi. Penelitian dilakukan dengan mengkaji terlebih dahulu asumsi SIR rantai binomial, probabilitas transisi dan melakukan simulasi model. Selanjutnya memberikan

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AlQadi, Hadeel, and Majid Bani-Yaghoub. "Incorporating global dynamics to improve the accuracy of disease models: Example of a COVID-19 SIR model." PLOS ONE 17, no. 4 (April 8, 2022): e0265815. http://dx.doi.org/10.1371/journal.pone.0265815.

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Mathematical models of infectious diseases exhibit robust dynamics, such as stable endemic, disease-free equilibriums or convergence of the solutions to periodic epidemic waves. The present work shows that the accuracy of such dynamics can be significantly improved by including global effects of host movements in disease models. To demonstrate improved accuracy, we extended a standard Susceptible-Infected-Recovered (SIR) model by incorporating the global dynamics of the COVID-19 pandemic. The extended SIR model assumes three possibilities for susceptible individuals traveling outside of their community: • They can return to the community without any exposure to the infection. • They can be exposed and develop symptoms after returning to the community. • They can be tested positively during the trip and remain quarantined until fully recovered. To examine the predictive accuracy of the extended SIR model, we studied the prevalence of the COVID-19 infection in six randomly selected cities and states in the United States: Kansas City, Saint Louis, San Francisco, Missouri, Illinois, and Arizona. The extended SIR model was parameterized using a two-step model-fitting algorithm. The extended SIR model significantly outperformed the standard SIR model and revealed oscillatory behaviors with an increasing trend of infected individuals. In conclusion, the analytics and predictive accuracy of disease models can be significantly improved by incorporating the global dynamics of the infection.

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Bartoszek, Krzysztof, Wojciech Bartoszek, and Michał Krzemiński. "Simple SIR models with Markovian control." Japanese Journal of Statistics and Data Science 4, no. 1 (February 16, 2021): 731–62. http://dx.doi.org/10.1007/s42081-021-00107-1.

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AbstractWe consider a random dynamical system, where the deterministic dynamics are driven by a finite-state space Markov chain. We provide a comprehensive introduction to the required mathematical apparatus and then turn to a special focus on the susceptible-infected-recovered epidemiological model with random steering. Through simulations we visualize the behaviour of the system and the effect of the high-frequency limit of the driving Markov chain. We formulate some questions and conjectures of a purely theoretical nature.

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Sagar, Surendra Kumar. "SIR-SI Mathematical Model for Zika Virus Progression Dynamics in India: A Case Study." Journal of Communicable Diseases 53, no. 02 (June 30, 2021): 100–104. http://dx.doi.org/10.24321/0019.5138.202132.

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Viral diseases are very hazardous for humanity because in the case of most viral diseases, drugs are not effective. At present, the whole world is living with the fear of COVID-19. From time to time, several viral diseases have been troubling human life. In this article, we have tried to capture the progression dynamics of Zika Virus (ZIKV) infection in the Indian scenario. A constructed model is based on compartment modelling. In the model, Susceptible-Infected-Recovered (SIR) structure is used for the human population and Susceptible-Infected (SI) structure is used for mosquito population. The value of the basic reproduction number (R0) is computed 0.36 at baseline values of parameters involved in the model. The lower value of R0 suggests that infection was unable to spread in the human population. Sensitive analysis for R0 revealed that the most accountable parameter in the spread of infection was mosquito biting rate. The modelling technique might be useful for other diseases also.

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Bakare, Emmanuel A., Snehashish Chakraverty, and Radovan Potucek. "Numerical Solution of an Interval-Based Uncertain SIR (Susceptible–Infected–Recovered) Epidemic Model by Homotopy Analysis Method." Axioms 10, no. 2 (June 6, 2021): 114. http://dx.doi.org/10.3390/axioms10020114.

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This work proposes an interval-based uncertain Susceptible–Infected–Recovered (SIR) epidemic model. The interval model has been numerically solved by the homotopy analysis method (HAM). The SIR epidemic model is proposed and solved under different uncertain intervals by the HAM to obtain the numerical solution of the model. Furthermore, the SIR ODE model was transformed into a stochastic differential equation (SDE) model and the results of the stochastic and deterministic models were compared using numerical simulations. The results obtained were compared with the numerical solution and found to be in good agreement. Finally, various simulations were done to discuss the solution.

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Wilkinson, Robert R., Frank G. Ball, and Kieran J. Sharkey. "The deterministic Kermack‒McKendrick model bounds the general stochastic epidemic." Journal of Applied Probability 53, no. 4 (December 2016): 1031–40. http://dx.doi.org/10.1017/jpr.2016.62.

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Abstract We prove that, for Poisson transmission and recovery processes, the classic susceptible→infected→recovered (SIR) epidemic model of Kermack and McKendrick provides, for any given time t>0, a strict lower bound on the expected number of susceptibles and a strict upper bound on the expected number of recoveries in the general stochastic SIR epidemic. The proof is based on the recent message passing representation of SIR epidemics applied to a complete graph.

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Burmakina, Valeria V., Dmitriy V. Pomazkin, and Ivan D. Prokhorov. "Methods for constructing an assessment of the development of the coronavirus pandemic." Population and Economics 4, no. 2 (May 18, 2020): 96–102. http://dx.doi.org/10.3897/popecon.4.e53686.

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Ji, Shenggong, Linyuan Lü, Chi Ho Yeung, and Yanqing Hu. "Effective spreading from multiple leaders identified by percolation in the susceptible-infected-recovered (SIR) model." New Journal of Physics 19, no. 7 (July 20, 2017): 073020. http://dx.doi.org/10.1088/1367-2630/aa76b0.

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Azis, Dorrah, La Zakaria, Tiryono Ruby, and Muhammad Is’ad Arifaldi. "THE DEVELOPMENT OF COVID-19 USING OUTBREAK THE SUSCEPTIBLE, INFECTED, AND RECOVERED (SIR) MODEL WITH VACCINATION." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 3 (September 30, 2023): 1325–40. http://dx.doi.org/10.30598/barekengvol17iss3pp1325-1340.

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The Covid-19 pandemic in 2020 has caused severe problems in Indonesia. The Covid-19 virus epidemic can be modeled using the Susceptible, Infected, and Recovered (SIR) model. This modeling aims to look at the dynamics of Covid-19 to predict when disease-free and endemic disease occurs and to find the basic reproduction number ( ) for policy making in suppressing the spread of Covid-19. In this article, we describe and solve a research result on the SIR model with an assumption. The assumption in the model is that there is vaccination for the population. There are live stages of research conducted. The first is creating the SIR model and determining the equilibrium points on disease-free and disease-endemic. The Second is getting the basic reproduction number. The third is determining the stability around the equilibrium points using the Routh-Hurwitz criteria. Fourth, create a diagram for the subpopulations state at a specific time using Wolfram Mathematica software. As an implementation of the model created, COVID-19 data at the Batanghari Community Health Center Inpatient UPTD was used. Finally, determine the model error percentage with MAPE. The SIR Covid-19 model was made using eight parameters, namely , which are all positive. The results showed that the disease-free and disease-endemic equilibrium points were locally asymptotically stable after being analyzed using the Routh-Hurwitz stability criteria. The model trial using data from UPTD Puskesmas Batanghari obtained a stable condition for up to 100 months with a MAPE of 2.8%. From this study, obtained an . This means that if you want to reduce the rate of spread, then reduce the number of people who are easily infected ( ) and reduce contacts ( ), and increase the healing rate ( ).

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Katuwal, Khagendra, Manab Prakash, Naveen Adhikari, Nirmal Kumar Raut, and Shiva Raj Adhikari. "An Assessment of the Macroeconomic Implications of COVID-19 in Nepal: Evidence from SIR –Macro Model Analysis." Economic Journal of Nepal 44, no. 1-2 (June 30, 2021): 1–18. http://dx.doi.org/10.3126/ejon.v44i1-2.55024.

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This paper assesses the macroeconomic implications of COVID-19 in the context of Nepal. The study uses a susceptible, infected, and recovered macro model (SIR-Macro model) where epidemiological variables are interacted with macroeconomic variables namely consumption and working hours to simulate the implication. The model estimates show that the containment measures of the government reduced the spread of the disease by 17 percent. However, the COVID-19 pandemic had a significant negative impact on macroeconomic outputs. On average, both consumption and working hours declined by 20 percent which otherwise would be more serious if no containment measures were adopted. In addition, the study also finds that the impact has been heterogeneous across susceptible, infected, and recovered population. Interestingly, the study also indicates that the individual utility lowered while societal utility improved with containment policies.

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Khader, M. M., and M. Adel. "Numerical Treatment of the Fractional Modeling on Susceptible-Infected-Recovered Equations with a Constant Vaccination Rate by Using GEM." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 1 (February 23, 2019): 69–75. http://dx.doi.org/10.1515/ijnsns-2018-0187.

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AbstractHere, we introduce a numerical solution by using the generalized Euler method for the (Caputo sense) fractional Susceptible-Infected-Recovered (SIR) model with a constant vaccination rate. We compare the obtained numerical solutions with those solutions by using the RK4. Hence, the obtained numerical results of the SIR model show the simplicity and the efficiency of the proposed method.

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Juhari, Juhari, Olivia Karinina, Abdul Aziz, and Evawati Alisah. "Global Stability Analysis of Susceptible, Infected, Recovered (S, I, R) Model Measles Vaccination Based on Age." InPrime: Indonesian Journal of Pure and Applied Mathematics 5, no. 2 (November 20, 2023): 144–60. http://dx.doi.org/10.15408/inprime.v5i2.32318.

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AbstractThis study discusses the behavioral analysis model of the Susceptible-Infected-Recovered (SIR) epidemic of the spread of measles based on age structure. The total population of measles is grouped into four age groups, namely the first age group (0-4 years), the second age group (5-9 years), the third age group (10-14 years) and the fourth age group (> 15 years). The steps in modeling behavior can be done by determining the equilibrium point, and the basic reproduction number and performing a global stability analysis by building the Lyapunov function. This research contributes to providing information both to the government and the community.Keywords: Epidemic Model; SIR; Lyapunov function; Measles. AbstrakPenelitian ini membahas model analisis perilaku epidemi Susceptible-Infected-Recovered (SIR) penyebaran campak berdasarkan struktur umur. Jumlah penduduk yang terkena campak dikelompokkan menjadi empat kelompok umur, yaitu kelompok umur pertama (0-4 tahun), kelompok umur kedua (5-9 tahun), kelompok umur ketiga (10-14 tahun) dan kelompok umur keempat. (> 15 tahun). Langkah-langkah dalam pemodelan perilaku dapat dilakukan dengan menentukan titik ekuilibrium, bilangan reproduksi dasar dan melakukan analisis stabilitas global dengan membangun fungsi Lyapunov. Penelitian ini memberikan kontribusi untuk memberikan informasi baik kepada pemerintah maupun masyarakat.Kata Kunci: Model Epidemi; PAK; fungsi Lyapunov; Campak. 2020MSC: 00A71.

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Albidah, Abdulrahman B. "A Proposed Analytical and Numerical Treatment for the Nonlinear SIR Model via a Hybrid Approach." Mathematics 11, no. 12 (June 17, 2023): 2749. http://dx.doi.org/10.3390/math11122749.

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This paper re-analyzes the nonlinear Susceptible–Infected–Recovered (SIR) model using a hybrid approach based on the Laplace–Padé technique. The proposed approach is successfully applied to extract several analytic approximations for the infected and recovered individuals. The domains of applicability of such analytic approximations are addressed. In addition, the present results are validated through various comparisons with the Runge–Kutta numerical method. The obtained analytical results agree with the numerical ones for a wide range of numbers of contacts featured in the studied model. The efficiency of the present analysis reveals that it can be implemented to deal with other systems describing real-life phenomena.

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Lamzabi, S., S. Lazfi, A. Rachadi, H. Ez-Zahraouy, and A. Benyoussef. "Modeling the spread of virus in packets on scale free network." International Journal of Modern Physics C 27, no. 06 (May 13, 2016): 1650068. http://dx.doi.org/10.1142/s0129183116500686.

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In this paper, we propose a new model for computer virus attacks and recovery at the level of information packets. The model we propose is based on one hand on the susceptible-infected (SI) and susceptible-infected-recovered (SIR) stochastic epidemic models for computer virus propagation and on the other hand on the time-discrete Markov chain of the minimal traffic routing protocol. We have applied this model to the scale free Barabasi–Albert network to determine how the dynamics of virus propagation is affected by the traffic flow in both the free-flow and the congested phases. The numerical results show essentially that the proportion of infected and recovered packets increases when the rate of infection [Formula: see text] and the recovery rate [Formula: see text] increase in the free-flow phase while in the congested phase, the number of infected (recovered) packets presents a maximum (minimum) at certain critical value of [Formula: see text] characterizing a certain competition between the infection and the recovery rates.

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Xue, Chunrong. "Study on the Global Stability for a Generalized SEIR Epidemic Model." Computational Intelligence and Neuroscience 2022 (August 8, 2022): 1–6. http://dx.doi.org/10.1155/2022/8215214.

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In the current study, a generalized SEIR epidemic model is studied. The generalized fractional-order SEIR model (susceptible-infected-recovered (SIR) epidemic) model differentiated the population into susceptible population, exposure population, infected population, and rehabilitation population and has fundamental mentoring importance for the forecast of the probable outburst of infectious ailments. The fundamental duplicated quantity R 0 is inferred. When R 0 < 1 , the disease-free equilibrium (DFE) is particular and tending towards stability. When R 0 > 1 , the endemic equilibrium is sole. In addition, certain circumstances are set up to make sure the local progressive stability of disease-free and endemic equilibrium. Considering the influence of the individual behavior, a broader SEIR epidemic model is raised, which classified the population into susceptible, exposure, infected, and rehabilitation. What is more, the basic reproduction number, that regulates whether the infection will die out or not, is obtained by the spectral radius of the next-generation matrix; moreover, the global stability of DFE and endemic equilibrium are analyzed by a geometry method.

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Devi, Rima, and Balendra Kumar Dev Choudhury. "Analysis of SIR Mathematical Model for Malaria Disease: A Study in Assam, India." Jurnal ILMU DASAR 24, no. 2 (July 25, 2023): 169. http://dx.doi.org/10.19184/jid.v24i2.38917.

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The global outbreak of covid-19 pandemic is still affecting people around the globe very badly. Before the covid-19 pandemic outbreak, several research works were done for the detection and prevention of various infectious diseases using different mathematical modeling. Implementing mathematical modeling to resolve problems in Biology and physiology is generally called Mathematical Biology, an extremely interdisciplinary area. The applications of mathematical modeling in the analysis of infectious diseases help to concentrate on the necessary processes associated with forming the infectious disease epidemiology and specifications estimation. The compartmental mathematical model can be either SI, SIS, SIR, SIRS, or SEIR where S, I, R, and E denote susceptible, infected, recovered, and exposed respectively. Malaria is an infectious disease that has a large economic and health impact on society. This study aims to predict the estimation of suspected, infected and recovered people using the SIR mathematical model of the Barama area of Baksa District in Assam, India. Here we analyzed the Basic Reproductive Ratio of the SIR model for malaria disease and examined if malaria is epidemic or endemic in that area.

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Side, Syafruddin, Wahidah Sanusi, and Nur Khaerati Rustan. "Model Matematika SIR Sebagai Solusi Kecanduan Penggunaan Media Sosial." Journal of Mathematics, Computations, and Statistics 3, no. 2 (October 31, 2020): 126. http://dx.doi.org/10.35580/jmathcos.v3i2.20124.

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Penelitian ini bertujuan untuk membangun model SIR (Susceptible – Infected – Recovered) sebagai solusi kecanduan penggunaan media sosial dengan asumsi bahwa mahasiswa yang sembuh dari kecanduan media sosial karena memiliki kontrol diri tinggi. Model ini dibagi menjadi tiga kelas yaitu kelas mahasiswa yang berpotensi menggunakan media sosial, kelas mahasiswa yang kecanduan media sosial, dan kelas mahasiswa yang memiliki kontrol diri tinggi. Data yang digunakan adalah data primer yang diperoleh dengan membagikan kuesioner kepada 145 mahasiswa Jurusan Matematika FMIPA UNM angkatan 2017, 2018, dan 2019. Hasil data riil model tipe SIR menghasilkan bilangan reproduksi dasar (R0) sebesar yang berarti bahwa jumlah mahasiswa yang kecanduan penggunaan media sosial akan meningkat dalam kurun waktu tertentu.Kata Kunci: Titik Ekuilibrium, Bilangan Reproduksi Dasar, Media Sosial, Kontrol Diri, Model SIRThis study aims to build the SIR (Susceptible - Infected - Recovered) model as a solution of social media addiction with the assumption that students who recover from addiction of social media because they have high selfcontrol. This model is divided into three classes: namely class of students who have potential to use social media, class of students who are addicted to social media, and class of students who have high selfcontrol. The data used are primary data that was obtained by distributing questionnaires to 145 students of mathematics departement FMIPA UNM class of 2017, 2018, and 2019. The simulation results of the SIR type model produce a basic reproduction number (R0) of 1.451136 which means that the number of students who are addicted to the use of social media will increase in a certain period of time.Keywords: Equilibrium Points, Basic Reproduction Numbers, Social Media, Selfcontrol, SIR Model

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De la Sen, Manuel, Asier Ibeas, and Ravi P. Agarwal. "On Confinement and Quarantine Concerns on an SEIAR Epidemic Model with Simulated Parameterizations for the COVID-19 Pandemic." Symmetry 12, no. 10 (October 7, 2020): 1646. http://dx.doi.org/10.3390/sym12101646.

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This paper firstly studies an SIR (susceptible-infectious-recovered) epidemic model without demography and with no disease mortality under both total and under partial quarantine of the susceptible subpopulation or of both the susceptible and the infectious ones in order to satisfy the hospital availability requirements on bed disposal and other necessary treatment means for the seriously infectious subpopulations. The seriously infectious individuals are assumed to be a part of the total infectious being described by a time-varying proportional function. A time-varying upper-bound of those seriously infected individuals has to be satisfied as objective by either a total confinement or partial quarantine intervention of the susceptible subpopulation. Afterwards, a new extended SEIR (susceptible-exposed-infectious-recovered) epidemic model, which is referred to as an SEIAR (susceptible-exposed-symptomatic infectious-asymptomatic infectious-recovered) epidemic model with demography and disease mortality is given and focused on so as to extend the above developed ideas on the SIR model. A proportionally gain in the model parameterization is assumed to distribute the transition from the exposed to the infectious into the two infectious individuals (namely, symptomatic and asymptomatic individuals). Such a model is evaluated under total or partial quarantines of all or of some of the subpopulations which have the effect of decreasing the number of contagions. Simulated numerical examples are also discussed related to model parameterizations of usefulness related to the current COVID-19 pandemic outbreaks.

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Bano, Elinora Naikteas, Adriana Leltakaeb, and Leonardus Frengky Obe. "ANALISIS KESTABILAN MODEL PENYEBARAN PENYAKIT DEMAM BERDARAH DENGUE (DBD) TIPE SIR MEMAKAI LARVASIDA." STATMAT : JURNAL STATISTIKA DAN MATEMATIKA 4, no. 1 (January 31, 2022): 9–27. http://dx.doi.org/10.32493/sm.v4i1.17529.

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Demam Berdarah Dengue (DBD) menjadi salah satu masalah kesehatan masyarakat di Indonesia yang masih membutuhkan penanganan hingga saat ini. Salah satunya yakni memberantas larva nyamuk DBD memakai larvasida. Penelitian ini membahas mengenai model penyebaran penyakit DBD tipe SIR, kelompok populasi manusia (host) dipilah menjadi tiga kelas, yaitu Susceptible, Infected, dan Recovered, sedangkan populasi nyamuk (vektor) juga dalam tiga kelas, yakni ASI (Aquatic, Susceptible, dan Infected). Selanjutnya dari model ditentukan titik kesetimbangan, bilangan reproduksi dasar, analisis kestabilan terhadap titik kesetimbangan bebas penyakit dan simulasi. Hasil analisis menunjukkan bahwa pada kondisi â„›0 < 1 titik kesetimbangan tanpa penyakit stabil asimtotik. Hasil simulasi pengaruh penggunaan larvasida terhadap penyebaran penyakit DBD juga menunjukkan bahwa semakin meningkatnya jumlah kematian larva karena pengaruh penggunaan larvasida menyebabkan bilangan reproduksi dasar semakin menurun bahkan sangat kecil sehingga hal ini dapat membantu menekan laju penyebaran penyakit DBD tersebut dalam populasi.

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Rosyid, Ilham Asyifa Maulana, Respatiwulan Respatiwulan, and Sri Sulistijowati Handajani. "Model Penyebaran Penyakit SIR Tipe Rantai Binomial dengan Kontak Random dan Waktu Penyembuhan Bernilai Tak Hingga." Indonesian Journal of Applied Statistics 3, no. 2 (January 23, 2021): 132. http://dx.doi.org/10.13057/ijas.v3i2.44307.

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Susceptible-Infected-Recovered (SIR) epidemic model is an epidemic model that illustrates the pattern of disease spread with the characteristics of individuals who have recovered cannot be re-infected and have a permanent immune system. The binomial chain type epidemic model assumes that infection spreads in discrete time units and the number of the infected individuals follows a binomial distribution. This research aims to discuss binomial chain type SIR epidemic model by simulating the model. The transition probability depends on the number of infected individuals in the period the number of individuals encountered, and the transmission probability. This model also assumes an infinite recovery time ( = ∞). This situation illustrates that infected individuals remain contagious during the period of spread of the disease. This situation can arise when the causative agent of the disease has a long life. Then simulations are performed by giving different transmission probability The results show that the greater transmission probability will cause the probability of a new individual being infected in the next period to be greater.Keywords : SIR epidemic model, binomial chain, infinite recovery time

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Olu, Ogunlade Temitope, Ogunmiloro Oluwatayo Michael, Fadugba Sunday Emmanuel, Oginni Omoniyi Israel, Oluwayemi Matthew Olanrewaju, Okoro Joshua Otonritse, and Olatunji Sunday Olufemi. "Numerical Implementation of a Susceptible - Infected - Recovered (SIR) Mathematical Model of Covid-19 Disease in Nigeria." WSEAS TRANSACTIONS ON BIOLOGY AND BIOMEDICINE 21 (February 27, 2024): 65–74. http://dx.doi.org/10.37394/23208.2024.21.7.

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In this study, we examine the dynamics of the Susceptible Infected Recovered (SIR) model in the context of the COVID-19 outbreak in Nigeria during the year 2020. The model is validated by fitting it to data on the prevalence and active cases of COVID-19, sourced from a government agency responsible for disease control. Utilizing the parameters associated with the disease prevalence, we calculate the basic reproduction number 𝑅𝑐𝑟, revealing its approximate value as 10.84. This suggests an average infection rate of around 10 human individuals, indicating the endemic nature of the disease in Nigeria. The impact of variation of recovery rate via treatment is examined, demonstrating its effectiveness in reducing disease prevalence when 𝑅𝑐𝑟 is below or above unity. To numerically implement the model, we employ the Sumudu Decomposition Method (SDM) and compare its results with the widely used Runge–Kutta fourth-order (RK4) method, implemented through the Maple software. Our findings indicate a mutual efficiency and convergence between the two methods, providing a comprehensive understanding of the COVID-19 dynamics in Nigeria.

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Firmansyah, Rasyid, and Yuli Bangun Nursanti. "ANALISIS EFEKTIVITAS PENERAPAN PEMBATASAN SOSIAL BERSKALA BESAR (PSBB) DI INDONESIA DENGAN MODEL SUSCEPTIBLE-INFECTED-RECOVERED (SIR)." JATI (Jurnal Mahasiswa Teknik Informatika) 8, no. 2 (April 3, 2024): 1724–30. http://dx.doi.org/10.36040/jati.v8i2.9097.

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COVID-19 telah menjadi perhatian masyrakat dunia sejak kemunculannya. Virus ini menyebar dengan sangat mudah dan sangat cepat. Oleh karena itu, dalam upaya memutus rantai penyebarakn virus tersebut, pemerintah Indonesia mengeluarkan kebijakan Pembatasan Sosial Berskala Besar (PSBB). Akibat dari diberlakukannya kebijakan, yaitu muncul pro dan kontra yang mempertanyakan tentang efektivitas pemberlakukan kebijakan tersebut. Pada penelitian ini penulis membahas tentang pengukuran terhadap efektivitas penerapan kebijakan Pembatasan Sosial Berskala Besar (PSBB) di Indonesia menggunakan teori differensial matematika, yaitu model Susceptible-Infected-Recovered (SIR). Dalam melakukan penelitian ini penulis menggunakan metode penelitian systematic literature review. Dari penelitian yang telah dilakukan didapatkan hasil bahwa penerapan kebijakan Pembatasan Sosial Berskala Besar (PSBB) di Indonesia terbukti efektif dalam memutus rantai penyebaran COVID-19.

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Dubey, Balram, Preeti Dubey, and Uma S. Dubey. "Role of media and treatment on an SIR model." Nonlinear Analysis: Modelling and Control 21, no. 2 (March 25, 2016): 185–200. http://dx.doi.org/10.15388/na.2016.2.3.

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n this paper, the impact of awareness programs as well as treatment on an SIR model has been investigated. We assume that the whole population is divided into four compartments, named as susceptible (S), infected (I), aware susceptible (Sa) and recovered (R). Analytical findings and numerical simulations of the model show that if the exposure to the awareness program is high and adequate treatment is available, then the infection can be eliminated. Analysis of the model also depicts that if treatment is not available, then infection is high even if enough awareness is present. But in absence of awareness an infection can not be eliminated inspite of adequate treatment. Effective treatment can led to a diminished level of infection. Stability analysis of the model is investigated by using stability theory of differential equations. Further, numerical simulations are carried out to validate the analytical results.

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Biswas, Abhik. "Bayesian MCMC Approach to Learning About the SIR Model." International Journal for Research in Applied Science and Engineering Technology 10, no. 6 (June 30, 2022): 540–53. http://dx.doi.org/10.22214/ijraset.2022.43818.

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Abstract: This project aims to study the parameters of the Deterministic SIR(Susceptible → Infected → Recovered) model of COVID-19 in a Bayesian MCMC framework. Several deterministic mathematical models are being developed everyday to forecast the spread of COVID-19 correctly. Here, I have tried to model and study the parameters of the SIR Infectious disease model using the Bayesian Framework and Markov-Chain Monte-Carlo (MCMC) techniques. I have used Bayesian Inference to predict the Basic Reproductive Rate ࢚ࡾ in real time using and following this, demonstrated the process of how the parameters of the SIR Model can be estimated using Bayesian Statistics and Markov-Chain Monte-Carlo Methods. Keywords: COVID-19, Bayesian Inference, Dynamical Systems, SIR Model, Basic Reproductive Rate, Markov-Chain MonteCarlo(MCMC)

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Harko, Tiberiu, Francisco S. N. Lobo, and M. K. Mak. "Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates." Applied Mathematics and Computation 236 (June 2014): 184–94. http://dx.doi.org/10.1016/j.amc.2014.03.030.

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Li, Hanwen, and Yong Deng. "Local volume dimension: A novel approach for important nodes identification in complex networks." International Journal of Modern Physics B 35, no. 05 (February 19, 2021): 2150069. http://dx.doi.org/10.1142/s0217979221500697.

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How to identify important nodes in complex networks? It is still an open problem. Many methods have been proposed to tackle this problem. The main contribution of this paper is to propose a method to identify important nodes based on local volume dimension (LVD). If the LVD of the node is lower, the node is more important. Promising results of experiments on four real-world networks compared with six methods under both Susceptible–Infected (SI) model and Susceptible–Infected–Recovered (SIR) model validate and demonstrate the effectiveness of the proposed method.

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Flayyih, Hadeer S. "Stability Analysis of Fractional SIR Model Related to Delay in State and Control Variables." BASRA JOURNAL OF SCIENCE 39, no. 2 (April 1, 2021): 204–20. http://dx.doi.org/10.29072/basjs.202123.

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The study of a nonlinear mathematical fractional SIR (Susceptible - Infected - Recovered) epidemiological model related to the delay in state and control variables in terms of time is the focus of this paper. The existence of a bounded solution for the fractional SIR epidemic model has been demonstrated, and it is unique. A new set of infection-free equilibrium points has been discovered, and their local stability has been investigated. In addition, using the next-generation matrix method, the basic reproductive number Ro was calculated

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