Academic literature on the topic 'Susceptible-Infected-Recovered (SIR) model'
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Journal articles on the topic "Susceptible-Infected-Recovered (SIR) model":
1
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.
Abstract:
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
2
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.
Abstract:
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
3
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.
Abstract:
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.
4
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.
Abstract:
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.
5
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.
Abstract:
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.
Abstract:
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.
Abstract:
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.
Abstract:
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.
Abstract:
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.
Abstract:
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.
Dissertations / Theses on the topic "Susceptible-Infected-Recovered (SIR) model":
1
Lindamulage, de Silva Olivier. "On the Efficiency of Decentralized Epidemic Management and Competitive Viral Marketing." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0145.
Abstract:
Cette thèse explore la prise de décision décentralisée dans les dynamiques épidémiques et de marketing viral en utilisant la théorie des jeux afin d'évaluer son efficacité. La thèse commence par une revue des outils mathématiques, mettant l'accent sur la théorie des graphes/jeux. Dans la suite de ce manuscrit, l'analyse de jeu épidémiologique et de compétition en marketing viral est établie. Notamment, dans le chapitre 2 où il est présenté un jeu épidémique en réseau dans lequel chaque joueur (région ou pays) cherche à trouver un compromis entre les pertes socio-économiques et sanitaires, tout en prenant en compte des contraintes telles que la disponibilité des unités de soins intensifs (USI). L'équilibre de Nash et l'équilibre de Nash généralisé sont analysés, et l'impact de la décentralisation sur l'efficacité est mesuré à l'aide de paramètres tels que le prix de l'anarchie (PoA) et le prix de la connectivité (PoC). Une application pratique du jeu à un scénario de Covid-19 est également illustrée. Le chapitre 3 étend l'analyse du chapitre 2 en incorporant la dynamique des opinions dans le contrôle décentralisé d'une épidémie en réseau. L'analyse se concentre sur l'existence et l'unicité de l'équilibre de Nash généralisé (GNE), et un algorithme pour atteindre le GNE est proposé. Les simulations identifient les scénarios où la décentralisation est acceptable en termes d'efficacité globale et soulignent l'importance de la dynamique des opinions dans les processus de prise de décision. Finalement, le chapitre 4 explore un modèle de duopole de Stackelberg dans le contexte des campagnes de marketing viral. L'objectif est de caractériser la stratégie d'allocation optimale des budgets publicitaires entre les régions pour maximiser la part de marché. Des stratégies d'équilibre sont déduites et des conditions pour un résultat de type "le gagnant rafle tout" sont établies. Les résultats théoriques sont complétés par des simulations numériques et un exemple illustrant la caractérisation de l'équilibre. Cette thèse offre des perspectives précieuses sur l'efficacité de la prise de décision décentralisée dans les dynamiques épidémiques et de marketing viral. Les résultats ont des implications pour la gestion des soins de santé, la concurrence commerciale et d'autres domaines connexesThis thesis investigates decentralized decision-making in epidemic and viral marketing dynamics. The mathematical framework of game theory is exploited to design and assess the effectiveness of decentralized strategies. The thesis begins with a review of mathematical tools, emphasizing graph theory and game theory. Chapter 2 presents a networked epidemic game where each player (region or country) seeks to implement a tradeoff between socio-economic and health looses, incorporating constraints such as intensive care unit (ICU) availability. Nash equilibrium and Generalized Nash equilibrium are analyzed, and the influence of decentralization on global efficiency is measured using metrics like the Price of Anarchy (PoA) and the Price of Connectedness (PoC). The practical application of the game to a Covid-19 scenario is illustrated. Chapter 3 extends the analysis of Chapter 2 by incorporating opinion dynamics into the decentralized control of a networked epidemic. A new game model is introduced, where players represent geographical aera balancing socio-economic and health losses; the game is built to implement features of practical interests and to possess some mathematical properties (e.g., posynomiality) which makes its analysis tractable. The analysis focuses on the existence and uniqueness of the Generalized Nash Equilibrium (GNE), and an algorithm for computing the GNE is proposed. Numerical simulations quantify the efficiency loss induced by decentralization in the presence and absence of opinion dynamics. The results identify scenarios where decentralization is acceptable in terms of global efficiency measures and highlight the importance of opinion dynamics in decision-making processes. Chapter 4 explores a Stackelberg duopoly model in the context of viral marketing campaigns. The objective is to characterize the optimal allocation strategy of advertising budgets across regions to maximize market share. A relatively simple Equilibrium strategies are derived, and conditions for a "winner takes all" outcome are established. Theoretical findings are complemented by numerical simulations and an example illustrating equilibrium characterization.This thesis offers valuable insights into the effectiveness of decentralized decision-making in the context of epidemic and viral marketing dynamics. The findings have implications for healthcare management, business competition, and related fields
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Gerardi, Davi de Oliveira. "Previsão de séries temporais epidemiológicas usando autômatos celulares e algoritmos genéticos." Universidade Presbiteriana Mackenzie, 2010. http://tede.mackenzie.br/jspui/handle/tede/1386.
Abstract:
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Davi de Oliveira Gerardi.pdf: 2216694 bytes, checksum: 5c92a695124c5b7d9e20de8329020701 (MD5)
Previous issue date: 2010-08-02SIS (susceptible-infected-susceptible) and SIR (susceptible-infectedremoved) epidemiological models based on probabilistic cellular automaton (PCA) are used in order to simulate the temporal evolution of the number of people infected by dengue in the city of Rio de Janeiro in 2007, and to predict the cases of infection in 2008. In the PCA, three different sizes of lattices and two kinds of neighborhoods are utilized, and each time step of simulation is equivalent to one week of real time. A genetic algorithm (GA) is employed to identify the probabilities of the state transition S→I, in order to reproduce the historical series of 2007 related to this disease propagation. These probabilities depend on the number of infected neighbors. Time-varying and constant probabilities are taken into account. These models based on PCA and GA were able of satisfactorily fitting the data from 2007 and making a good prediction for 2008 (mainly about the total number of cases registered during 2008).
Usam-se modelos epidemiológicos SIS (suscetível-infectado-suscetível) e SIR (suscetível-infectado-removido) baseados em autômato celular probabilista (ACP) a fim de simular a evolução temporal do número de pessoas infectadas por dengue, na cidade do Rio de Janeiro em 2007, e de prever os casos de infecção em 2008. No ACP, utilizam-se reticulados de três tamanhos diferentes e dois tipos de vizinhanças, e cada passo de tempo da simulação equivale a uma semana de tempo real. Emprega-se um algoritmo genético (AG) para identificar os valores das probabilidades da transição de estados S→I, de modo a reproduzir a série histórica de 2007 relacionada à propagação dessa doença. Essas probabilidades dependem do número de vizinhos infectados. Probabilidades variantes e invariantes no tempo são consideradas. Esses modelos baseados em ACP e AG foram capazes de fazer um ajuste satisfatório dos dados de 2007 e de fornecerem uma boa previsão para 2008, (principalmente no que diz respeito ao número total de casos registrados em 2008).
3
Kandhway, Kundan. "Optimal Control of Information Epidemics in Homogeneously And Heterogeneously Mixed Populations." Thesis, 2016. http://etd.iisc.ac.in/handle/2005/2670.
Abstract:
Social networks play an important role in disseminating a piece of information in a population. Companies advertising a newly launched product, movie promotion, political campaigns, social awareness campaigns by governments, charity campaigns by NGOs and crowd funding campaigns by entrepreneurs are a few examples where an entity is interested in disseminating a piece of information in a target population, possibly under resource constraints.
In this thesis we model information diffusion in a population using various epidemic models and study optimal campaigning strategies to maximize the reach of information. In the different problems considered in this thesis, information epidemics are modeled as the Susceptible-Infected, Susceptible-Infected-Susceptible, Susceptible-Infected-Recovered and Maki Thompson epidemic processes; however, we modify the models to incorporate the intervention made by the campaigner to enhance information propagation. Direct recruitment of individuals as spreaders and providing word-of-mouth incentives to the spreaders are considered as two intervention strategies (controls) to enhance the speed of information propagation. These controls can be implemented by placing advertisements in the mass media, announcing referral/cash back rewards for introducing friends to a product or service being advertised etc.
In the different problems considered in this thesis, social contacts are modeled with varying levels of complexity---population is homogeneously mixed or follows heterogeneous mixing. The solutions to the problems which consider homogeneous mixing of individuals identify the most important periods in the campaign duration which should be allocated more resources to maximize the reach of the message, depending on the system parameters of the epidemic model (e.g., epidemics with high and low virulence). When a heterogeneous model is considered, apart from this, the solution identifies the important classes of individuals which should be allocated more resources depending upon the network considered (e.g. Erdos-Renyi, scale-free) and model parameters. These classes may be carved out based on various centrality measures in the network. If multiple strategies are available for campaigning, the solution also identifies the relative importance of the strategies depending on the network type.
We study variants of the optimal campaigning problem where we optimize different objective functions. For some of the formulated problems, we discuss the existence and uniqueness of the solution. Sometimes our formulations call for novel techniques to prove the existence of a solution.
4
Kandhway, Kundan. "Optimal Control of Information Epidemics in Homogeneously And Heterogeneously Mixed Populations." Thesis, 2016. http://etd.iisc.ernet.in/handle/2005/2670.
Abstract:
Social networks play an important role in disseminating a piece of information in a population. Companies advertising a newly launched product, movie promotion, political campaigns, social awareness campaigns by governments, charity campaigns by NGOs and crowd funding campaigns by entrepreneurs are a few examples where an entity is interested in disseminating a piece of information in a target population, possibly under resource constraints.
In this thesis we model information diffusion in a population using various epidemic models and study optimal campaigning strategies to maximize the reach of information. In the different problems considered in this thesis, information epidemics are modeled as the Susceptible-Infected, Susceptible-Infected-Susceptible, Susceptible-Infected-Recovered and Maki Thompson epidemic processes; however, we modify the models to incorporate the intervention made by the campaigner to enhance information propagation. Direct recruitment of individuals as spreaders and providing word-of-mouth incentives to the spreaders are considered as two intervention strategies (controls) to enhance the speed of information propagation. These controls can be implemented by placing advertisements in the mass media, announcing referral/cash back rewards for introducing friends to a product or service being advertised etc.
In the different problems considered in this thesis, social contacts are modeled with varying levels of complexity---population is homogeneously mixed or follows heterogeneous mixing. The solutions to the problems which consider homogeneous mixing of individuals identify the most important periods in the campaign duration which should be allocated more resources to maximize the reach of the message, depending on the system parameters of the epidemic model (e.g., epidemics with high and low virulence). When a heterogeneous model is considered, apart from this, the solution identifies the important classes of individuals which should be allocated more resources depending upon the network considered (e.g. Erdos-Renyi, scale-free) and model parameters. These classes may be carved out based on various centrality measures in the network. If multiple strategies are available for campaigning, the solution also identifies the relative importance of the strategies depending on the network type.
We study variants of the optimal campaigning problem where we optimize different objective functions. For some of the formulated problems, we discuss the existence and uniqueness of the solution. Sometimes our formulations call for novel techniques to prove the existence of a solution.
Book chapters on the topic "Susceptible-Infected-Recovered (SIR) model":
1
Kalachev, Leonid, Erin L. Landguth, and Jonathan Graham. "Data-Driven Approach to Analysis of SIR (Susceptible-Infected-Removed/ Recovered)-Type Models: The Principle of Parsimony Applied to Epidemics Modeling in the Age of COVID-19." In Handbook of Visual, Experimental and Computational Mathematics, 1–38. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-030-93954-0_1-1.
2
K. Befekadu, Getachew. "Rare Event Simulation in a Dynamical Model Describing the Spread of Traffic Congestions in Urban Network Systems." In A Collection of Papers on Chaos Theory and Its Applications. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.95789.
Abstract:
In this chapter, we present a mathematical framework that provides a new insight for understanding the spread of traffic congestions in an urban network system. In particular, we consider a dynamical model, based on the well-known susceptible-infected-recovered (SIR) model from mathematical epidemiology, with small random perturbations, that describes the process of traffic congestion propagation and dissipation in an urban network system. Here, we provide the asymptotic probability estimate based on the Freidlin-Wentzell theory of large deviations for certain rare events that are difficult to observe in the simulation of urban traffic network dynamics. Moreover, the framework provides a computational algorithm for constructing efficient importance sampling estimators for rare event simulations of certain events associated with the spread of traffic congestions in the dynamics of the traffic network.
3
Schmid-Hempel, Paul. "Between-host dynamics (Epidemiology)." In Evolutionary Parasitology, 281–316. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198832140.003.0011.
Abstract:
Epidemiology is the population dynamics of host–parasite systems. The spread of an infective disease is analysed with several tools. The SIR model (susceptible, infected, recovered hosts) is a standard model, with the basic reproductive number (R 0) as a characteristic. Diseases, in general, spread if R 0 > 1, which suggests a threshold size for host populations, and also for endemic maintenance or periodic outbreaks. Furthermore, spatial heterogeneity or the distribution of infections among hosts affects an epidemic. Individual-based models can follow the fate of infections more closely. Network analysis provides insights into transmission and contact rates. Models also describe the epidemics of vectored diseases, or of macroparasitic infections. Molecular epidemiology uses genetic markers or genomes to follow the spread of an infectious disease; phylodynamics reconstructs transmission chains, especially for viral diseases. Immunoepidemiology studies how immune defences affect an epidemic and identifies immunological markers for the study of infectious disease dynamics.
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Rosli, Norhayati, Noryanti Muhammad, and Muhammad Fahmi Ahmad Zuber. "PREDICTIVE ANALYTICS OF THE COVID-19 OUTBREAK UNDER UNCERTAINTY OF THE DISEASE SPREADING." In Emerging Technologies During the Era of Covid-19 Pandemic. PENERBIT UNIVERSITI MALAYSIA PAHANG, 2023. http://dx.doi.org/10.15282/pandemic.2023.03.
Abstract:
COVID-19 pandemic was identified in Wuhan, China in 2019 and has spread at a tremendous rate affecting all countries over the world. Understanding the spreading disease is crucial; hence, the dynamic behaviour of the disease can be predicted. This paper is aimed to model the COVID-19 outbreak by extending the deterministic susceptible-infected-recovered-death (DSIRD) into a stochastic SIRD (SSIRD) model. Infectious rate parameter of the DSIRD model is perturbed with Brownian motion to reflect the uncertainty of the COVID-19 outbreak. Fourth order stochastic Runge-Kutta (SRK4) method is used to simulate the model. Parameter estimation is estimated using the Markov Chain Monte Carlo (MCMC) method. The simulated results for three ASEAN countries of Malaysia, Indonesia and Singapore indicate that SSIRD model is consistent with the infected COVID-19 data;hence, shows the model is adequate in explaining the behaviour of the infectious disease.
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Cardoso, Anamaria de Oliveira, Renato Fleury Cardoso, Alex Garcez Utsumi, and Nádia Guimarães Sousa. "Wearing Masks in COVID-19 pandemic: Mathematical model and simulation for evaluating the impact of non-pharmaceutical intervention strategy associated with social distancing on pandemic behavior in Minas Gerais/Brazil." In DEVELOPMENT AND ITS APPLICATIONS IN SCIENTIFIC KNOWLEDGE. Seven Editora, 2023. http://dx.doi.org/10.56238/devopinterscie-205.
Abstract:
The COVID-19 pandemic has caused health system collapse and led governments to implement non-pharmaceutical interventions, such as wearing a mask and social distancing. In this study, the SEIR (susceptible-exposed-infected-recovered) model is proposed for assessing the effects of social distancing and wearing a mask on the prediction of COVID-19 transmission dynamic in Minas Gerais – Brazil. This work presents a theoretical-computational study and the mathematical modeling simulations of COVID-19 transmission dynamics. The model describes eight population groups: susceptible, confined, exposed, asymptomatic, symptomatic, hospitalized, recovered, and dead. The mask-wearing is inferred by the following parameters: mask aerosol reduction (M_red ), mask availability (M_ava), and proper mask-wearing (M_cov). Different scenarios are simulated for evaluating the effect of the parameters on the pandemic evolution. Simulations demonstrate a reduction of around 99% compared to the no-mask-wearing scenario when masks are available for 80% of the population. Professional masks, such as N95 and FFP2 (M_red=97%), reduce by 98,9% of the number of deaths. The proper mask-wearing shows a significant impact on pandemic development, by reducing considerably M_cov it could even overcome the total number of deaths and infections than those in a no-mask-wearing scenario, if the social distancing measures were not intensified. Wearing a mask is extremely efficient and required in the fight against the COVID-19 pandemic. A combination of social distancing and wearing a mask, if properly performed, allows controlling the pandemic more efficiently, minimizing the total and the daily number of deaths and infections, and avoiding a greater health system overload.
Conference papers on the topic "Susceptible-Infected-Recovered (SIR) model":
1
Ismail, Siti Suhaila, Ku Azlina Ku Akil, Majdah Chulan, and Noorzila Sharif. "The susceptible-infected-recovered (SIR) model for viral marketing." In PROCEEDINGS OF THE 13TH IMT-GT INTERNATIONAL CONFERENCE ON MATHEMATICS, STATISTICS AND THEIR APPLICATIONS (ICMSA2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5012164.
2
Mahasmara, Jane Lola, Respatiwulan, and Yuliana Susanti. "Final size distribution of stochastic susceptible infected recovered (SIR) epidemic model." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039277.
3
Mawarni, Murtantina Dyahayu, and Dwi Lestari. "The SIR fuzzy epidemic model (Susceptible, Infected, Recovered) on spreading tuberculosis disease." In PROCEEDINGS OF THE 4TH INTERNATIONAL SEMINAR ON INNOVATION IN MATHEMATICS AND MATHEMATICS EDUCATION (ISIMMED) 2020: Rethinking the role of statistics, mathematics and mathematics education in society 5.0: Theory, research, and practice. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0108518.
4
Sedaghat, Ahmad, Shahab Band, Amir Mosavi, and Laszlo Nadai. "COVID-19 (Coronavirus Disease) Outbreak Prediction Using a Susceptible-Exposed-Symptomatic Infected-Recovered-Super Spreaders-Asymptomatic Infected-Deceased-Critical (SEIR-PADC) Dynamic Model." In 2020 IEEE 3rd International Conference and Workshop in Óbuda on Electrical and Power Engineering (CANDO-EPE). IEEE, 2020. http://dx.doi.org/10.1109/cando-epe51100.2020.9337775.
5
Arotaritei, Dragos, George Constantin, and Calin Corciova. "MATHEMATICAL MODELS OF MEASLES BY DIFFERENTIAL EQUATIONS IN VIRTUAL EDUCATION." In eLSE 2018. Carol I National Defence University Publishing House, 2018. http://dx.doi.org/10.12753/2066-026x-18-197.
Abstract:
Compartmental models have proven to be useful in various forms of epidemics: Ebola, dengue fever, swine fever, flu, avian flu, etc. Such models have experienced a great development especially because of the multitude of practical applications, but also due to the many possibilities of software implementation. Although there are a few software tools, for example, EpiModel, they have limitations in modelling and use of language employed in the simulation. Measles can be described as a model with 4 compartments, SEIR, but for a better knowledge of all geographic implications in terms of vaccination, we propose a MSEIR model (S = susceptible, I = infected, R = recovered, vaccinated, E = exposed, M = maternally immune). The educational software created in MATLAB, can generate a graphical system, with specific interactions between compartments, starting with initial values set by the user as a result of specific epidemiological studies. After defining the compartments and their links, a generator will build the system of equations which models the compartmental system, solvable through numerical methods specific to measles. Optionally, the user will be able to view the system of differential equations using symbolic calculation. The solutions will be displayed graphically and will allow the user to compare the epidemic evolution with or without vaccine, as well as optimal policy for vaccination using the Jacobian matrix for determination of the endemic equilibrium. Graphical user interface is intuitive, educational, with the possibility of amending the transfer rate between compartments, parameters and initial values. The reproduction number R0 can be defined to be used in order to analyse the influence of it for fit the model with experimental data. The main novelty in this paper is composed mainly by a graphical interface an easy-to-use by student and researcher for in create abilities to use a compartmental model and at the same time, able to provide sufficient arguments in the decision making process and health policies. The other innovative approach is the possibility to define by user a symbolic equation for a compartmental model meanwhile the too will translate in mathematical one that can be solved by differential equation using numerical methods.