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1
SHANG, YILUN. "DISTRIBUTION DYNAMICS FOR SIS MODEL ON RANDOM NETWORKS". Journal of Biological Systems 20, n. 02 (giugno 2012): 213–20. http://dx.doi.org/10.1142/s0218339012500076.
Abstract (sommario):
We study the evolution of degree distributions of susceptible-infected-susceptible (SIS) model on random networks, where susceptible nodes are capable of being infected, and infected nodes can spread the disease further. The network of contacts is modeled as a configuration model featuring heterogeneous degree distribution. We derive systematically the (excess) degree distributions among susceptible and infected individuals by using the probability generating function formalism.
2
de La Sen, Manuel, A. Ibeas e S. Alonso-Quesada. "A SIS Epidemic Model with Eventual Impulsive Effects". Applied Mechanics and Materials 393 (settembre 2013): 666–74. http://dx.doi.org/10.4028/www.scientific.net/amm.393.666.
Abstract (sommario):
This paper studies a time-varyingSIS(i.e.containing susceptible and infected populations) propagation disease model exhibiting a nonlinear incidence rate and impulsive eventual culling of both populations so that the individuals recover with no immunity to the disease. The nonlinear incidence rate consists of two time-varying additive terms proportional to the susceptible and infected populations normalized to the total population.
3
Xie, Wenhao, Gongqian Liang, Wei Wang e Yanhong She. "A spatial SIS model with Holling II incidence rate". International Journal of Biomathematics 12, n. 08 (novembre 2019): 1950092. http://dx.doi.org/10.1142/s179352451950092x.
Abstract (sommario):
A diffusive SIS epidemic model with Holling II incidence rate is studied in this paper. We introduce the basic reproduction number [Formula: see text] first. Then the existence of endemic equilibrium (EE) can be determined by the sizes of [Formula: see text] as well as the diffusion rates of susceptible and infected individuals. We also investigate the effect of diffusion rates on asymptotic profile of EE. Our results conclude that the infected population will die out if the diffusion rate of susceptible individuals is small and the total population [Formula: see text] is below a certain level; while the two populations persist eventually if at least one of the diffusion rates of the susceptible and infected individuals is large.
4
Coronel, Aníbal, Fernando Huancas, Ian Hess e Alex Tello. "The diffusion identification in a SIS reaction-diffusion system". Mathematical Biosciences and Engineering 21, n. 1 (2023): 562–81. http://dx.doi.org/10.3934/mbe.2024024.
Abstract (sommario):
<abstract><p>This article is concerned with the determination of the diffusion matrix in the reaction-diffusion mathematical model arising from the spread of an epidemic. The mathematical model that we consider is a susceptible-infected-susceptible model with diffusion, which was deduced by assuming the following hypotheses: The total population can be partitioned into susceptible and infected individuals; a healthy susceptible individual becomes infected through contact with an infected individual; there is no immunity, and infected individuals can become susceptible again; the spread of epidemics arises in a spatially heterogeneous environment; the susceptible and infected individuals implement strategies to avoid each other by staying away. The spread of the dynamics is governed by an initial boundary value problem for a reaction-diffusion system, where the model unknowns are the densities of susceptible and infected individuals and the boundary condition models the fact that there is neither emigration nor immigration through their boundary. The reaction consists of two terms modeling disease transmission and infection recovery, and the diffusion is a space-dependent full diffusion matrix. The determination of the diffusion matrix was conducted by considering that we have experimental data on the infective and susceptible densities at some fixed time and in the overall domain where the population lives. We reformulated the identification problem as an optimal control problem where the cost function is a regularized least squares function. The fundamental contributions of this article are the following: The existence of at least one solution to the optimization problem or, equivalently, the diffusion identification problem; the introduction of first-order necessary optimality conditions; and the necessary conditions that imply a local uniqueness result of the inverse problem. In addition, we considered two numerical examples for the case of parameter identification.</p></abstract>
5
De, A., K. Maity e M. Maiti. "An integrated project of fish and broiler: SIS model with optimal harvesting". International Journal of Biomathematics 09, n. 06 (2 agosto 2016): 1650088. http://dx.doi.org/10.1142/s1793524516500881.
Abstract (sommario):
The paper analyzes the influence of a susceptible–infectious–susceptible (SIS) infectious disease affecting both fish and broiler species. The paper also considers a joint SIS project of fish and broiler in which the growth rates of both species vary with available nutrients and environmental carrying capacities of biomasses. The nutrients for both species are functions of the biomasses of the two species. The harvesting rates of fish and broiler depend linearly on common effort function. It is assumed that the diseases are transmitted to the susceptible populations by direct contact with the infected populations. Using the medicine, some portion of the infected populations are transmitted to the susceptible populations. The existence of steady states and their stability are investigated analytically. The joint profit of the SIS model is maximized using Pontryagin’s maximum principle and corresponding optimum harvesting rates are also obtained. Using Mathematica software, the models are illustrated and the optimum results are obtained and presented in tabular and graphical forms.
6
CHAKRABORTY, ABHIJIT, e S. S. MANNA. "DISEASE SPREADING MODEL WITH PARTIAL ISOLATION". Fractals 21, n. 03n04 (settembre 2013): 1350015. http://dx.doi.org/10.1142/s0218348x13500151.
Abstract (sommario):
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.
7
Drabo, Abdoul Karim, Frédéric Bere e S. P. Clovis Nitiema. "On a Stochastic Approach to Extensions of the Susceptible-Infected-Susceptible (SIS) Model Applied to Malaria". Journal of Applied Mathematics 2024 (30 aprile 2024): 1–16. http://dx.doi.org/10.1155/2024/7555042.
Abstract (sommario):
This work presents a stochastic model of malaria spread. We first calculated the basic reproduction number R0 of the models ShIhRhSh‐SvIv and ShLhIhRhSh‐SvLvIv in order to show that the malaria-free equilibrium is asymptotically stable; then, we used a finite Markov chain model to describe the interactions between the different compartments of the model SeLeIeReSe‐SaLaIaRaSa‐SvIv. We carried out numerical simulations of our results for two types of transmission zones: a zone with low malaria transmission and an endemic zone. Through these simulations, we first determined the invariant stationary distribution π∗ of the model, and then, we found that the use of the indoor residual spraying (IRS) method by regular application of insecticides is more effective for the elimination of malaria than the use of long-acting impregnated mosquito nets (LLINs).
8
Essouifi, Mohamed, e Abdelfattah Achahbar. "A mixed SIR-SIS model to contain a virus spreading through networks with two degrees". International Journal of Modern Physics C 28, n. 09 (settembre 2017): 1750114. http://dx.doi.org/10.1142/s0129183117501145.
Abstract (sommario):
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.
9
Paoluzzi, Matteo, Marco Leoni e M. Cristina Marchetti. "Information and motility exchange in collectives of active particles". Soft Matter 16, n. 27 (2020): 6317–27. http://dx.doi.org/10.1039/d0sm00204f.
Abstract (sommario):
We examine the interplay of motility and information exchange in a model of active particles. Non-motile particles additionally recover their motility at a fixed rate, as in the SIS (Susceptible, Infected, Susceptible) model of epidemic spreading.
10
Ji, Chunyan, e Daqing Jiang. "The asymptotic behavior of a stochastic multigroup SIS model". International Journal of Biomathematics 11, n. 03 (aprile 2018): 1850037. http://dx.doi.org/10.1142/s1793524518500377.
Abstract (sommario):
In this paper, we explore the long time behavior of a multigroup Susceptible–Infected–Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.
11
Lismawati, Eka, Respatiwulan e Purnami Widyaningsih. "Discrete time Markov chains (DTMC) susceptible infected susceptible (SIS) epidemic model with two pathogens in two patches". Journal of Physics: Conference Series 855 (giugno 2017): 012024. http://dx.doi.org/10.1088/1742-6596/855/1/012024.
12
Balzotti, Caterina, Mirko D’Ovidio, Anna Chiara Lai e Paola Loreti. "Effects of Fractional Derivatives with Different Orders in SIS Epidemic Models". Computation 9, n. 8 (8 agosto 2021): 89. http://dx.doi.org/10.3390/computation9080089.
Abstract (sommario):
We study epidemic Susceptible–Infected–Susceptible (SIS) models in the fractional setting. The novelty is to consider models in which the susceptible and infected populations evolve according to different fractional orders. We study a model based on the Caputo derivative, for which we establish existence results of the solutions. Furthermore, we investigate a model based on the Caputo–Fabrizio operator, for which we provide existence of solutions and a study of the equilibria. Both models can be framed in the context of SIS models with time-varying total population, in which the competition between birth and death rates is macroscopically described by the fractional orders of the derivatives. Numerical simulations for both models and a direct numerical comparison are also provided.
13
Zou, Yijiang, Weibing Deng, Wei Li e Xu Cai. "A study of epidemic spreading on activity-driven networks". International Journal of Modern Physics C 27, n. 08 (25 maggio 2016): 1650090. http://dx.doi.org/10.1142/s012918311650090x.
Abstract (sommario):
The epidemic spreading was explored on activity-driven networks (ADNs), accounting for the study of dynamics both on and of the ADN. By employing the susceptible-infected-susceptible (SIS) model, two aspects were considered: (1) the infection rate of susceptible agent (depending on the number of its infected neighbors) evolves due to the temporal structure of ADN, rather than being a constant number; (2) the susceptible and infected agents generate unequal links while being activated, namely, the susceptible agent gets few contacts with others in order to protect itself. Results show that, in both cases, the larger epidemic threshold and smaller outbreak size were obtained.
14
Guo, Dongchao, Libo Jiao, Jian Jiao e Kun Meng. "Variance of the Infection Number of Heterogeneous Malware Spread in Network". Applied Sciences 14, n. 10 (7 maggio 2024): 3972. http://dx.doi.org/10.3390/app14103972.
Abstract (sommario):
The Susceptible–Infected–Susceptible (SIS) model in complex networks is one of the critical models employed in the modeling of virus spread. The study of the heterogeneous SIS model with a non-homogeneous nodal infection rate in finite-size networks has attracted little attention. Investigating the statistical properties of heterogeneous SIS epidemic dynamics in finite networks is thus intriguing. In this paper, we focus on the measure of variability in the number of infected nodes for the heterogeneous SIS epidemic dynamics in finite-size bipartite graphs and star graphs. Specifically, we investigate the metastable-state variance of the number of infected nodes for the SIS epidemic process in finite-size bipartite graphs and star graphs with heterogeneous nodal infection rates. We employ an extended individual-based mean-field approximation to analyze the heterogeneous SIS epidemic process in finite-size bipartite networks and star graphs. We derive the approximation solutions of the variance of the infected number. We verify the proposed theory by simulations. The proposed theory has the potential to help us better understand the fluctuations of SIS models like epidemic dynamics with a non-homogeneous infection rate.
15
Coronel, Aníbal, Fernando Huancas, Esperanza Lozada e Marko Rojas-Medar. "Results for a Control Problem for a SIS Epidemic Reaction–Diffusion Model". Symmetry 15, n. 6 (8 giugno 2023): 1224. http://dx.doi.org/10.3390/sym15061224.
Abstract (sommario):
This article is focused on investigating the mathematical model calibration of a reaction–diffusion system arising in the mathematical model of the spread of an epidemic in a society. We consider that the total population is divided into two classes of individuals, called susceptible and infectious, where a susceptible individual can become infectious, and that upon recovery, an infected individual can become susceptible again. We consider that the population lives in a spatially heterogeneous environment, and that the spread of the dynamics is governed by a reaction–diffusion system consisting of two equations, where the variables of the model are the densities of susceptible and infected individuals. In the reaction term, the coefficients are the rates of disease transmission and the rate of infective recovery. The main contribution of this study is the identification of the reaction coefficients by assuming that the infective and susceptible densities at the end time of the process and on overall spatial domain are observed. We apply the optimal control methodology to prove the main findings: the existence of positive solutions for the state system, the existence of at least one solution for the identification problem, the introduction of first-order necessary conditions, and the local uniqueness of optimal solutions.
16
Coronel, Aníbal, Fernando Huancas e Stefan Berres. "Study of an Epidemiological Model for Plant Virus Diseases with Periodic Coefficients". Applied Sciences 14, n. 1 (31 dicembre 2023): 399. http://dx.doi.org/10.3390/app14010399.
Abstract (sommario):
In the present article, we research the existence of the positive periodic solutions for a mathematical model that describes the propagation dynamics of a pathogen living within a vector population over a plant population. We propose a generalized compartment model of the susceptible–infected–susceptible (SIS) type. This model is derived primarily based on four assumptions: (i) the plant population is subdivided into healthy plants, which are susceptible to virus infection, and infected plants; (ii) the vector population is categorized into non-infectious and infectious vectors; (iii) the dynamics of pathogen propagation follow the standard susceptible–infected–susceptible pattern; and (iv) the rates of pathogen propagation are time-dependent functions. The main contribution of this paper is the introduction of a sufficient condition for the existence of positive periodic solutions in the model. The proof of our main results relies on a priori estimates of system solutions and the application of coincidence degree theory. Additionally, we present some numerical examples that demonstrate the periodic behavior of the system.
17
Clancy, Damian. "A stochastic SIS infection model incorporating indirect transmission". Journal of Applied Probability 42, n. 3 (settembre 2005): 726–37. http://dx.doi.org/10.1239/jap/1127322023.
Abstract (sommario):
We describe a stochastic susceptible–infective–susceptible (SIS) model for transmission of infectious disease through a population, incorporating both direct host–host transmission and indirect transmission via free-living infectious stages (e.g. environmental bacteria). Existence of a quasi-stationary distribution conditional upon nonextinction of infection is established. A bivariate Ornstein–Uhlenbeck approximation is used to investigate the long-term behaviour of the process conditional upon nonextinction of infection. We show that indirect transmission leads to lower variability in the number of infected hosts present in quasi-stationarity and, consequently, to a greater tendency of infection to persist, compared with a model with direct transmission only and the same average individual infectivity. Some numerical work illustrating these results is presented.
18
Clancy, Damian. "A stochastic SIS infection model incorporating indirect transmission". Journal of Applied Probability 42, n. 03 (settembre 2005): 726–37. http://dx.doi.org/10.1017/s0021900200000735.
Abstract (sommario):
We describe a stochastic susceptible–infective–susceptible (SIS) model for transmission of infectious disease through a population, incorporating both direct host–host transmission and indirect transmission via free-living infectious stages (e.g. environmental bacteria). Existence of a quasi-stationary distribution conditional upon nonextinction of infection is established. A bivariate Ornstein–Uhlenbeck approximation is used to investigate the long-term behaviour of the process conditional upon nonextinction of infection. We show that indirect transmission leads to lower variability in the number of infected hosts present in quasi-stationarity and, consequently, to a greater tendency of infection to persist, compared with a model with direct transmission only and the same average individual infectivity. Some numerical work illustrating these results is presented.
19
Nzokem, A. H. "SIS Epidemic Model Birth-and-Death Markov Chain Approach". International Journal of Statistics and Probability 10, n. 4 (27 maggio 2021): 10. http://dx.doi.org/10.5539/ijsp.v10n4p10.
Abstract (sommario):
We are interested in describing the dynamics of the infected size of the SIS Epidemic model using the Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) model is defined within a population of constant size $M$; the size is kept constant by replacing each death with a newborn healthy individual. The life span of each individual in the population is modelled by an exponential distribution with parameter $\alpha$; the disease spreads within the population is modelled by a Poisson process with a rate $\lambda_{I}$. $\lambda_{I}=\beta I(1-\frac{I}{M}) $ is similar to the instantaneous rate in the logistic population growth model. The analysis is focused on the disease outbreak, where the reproduction number $R=\frac{\beta} {\alpha} $ is greater than one. As methodology, we use both numerical and analytical approaches. The numerical approach shows that the infected size dynamics converge to a stationary stochastic process. And the analytical results determine the distribution of the stationary stochastic process as a normal distribution with mean $(1-\frac{1}{R}) M$ and Variance $\frac{M}{R} $ when $M$ becomes larger.
20
Kessler, David A. "Epidemic Size in the SIS Model of Endemic Infections". Journal of Applied Probability 45, n. 3 (settembre 2008): 757–78. http://dx.doi.org/10.1239/jap/1222441828.
Abstract (sommario):
We study the susceptible-infected-susceptible model of the spread of an endemic infection. We calculate an exact expression for the mean number of transmissions for all values of the population size (N) and the infectivity. We derive the large-N asymptotic behavior for the infectivitiy below, above, and in the critical region. We obtain an analytical expression for the probability distribution of the number of transmissions, n, in the critical region. We show that this distribution has an n-3/2 singularity for small n and decays exponentially for large n. The exponent decreases with the distance from the threshold, diverging to ∞ far below and approaching 0 far above.
21
Kessler, David A. "Epidemic Size in the SIS Model of Endemic Infections". Journal of Applied Probability 45, n. 03 (settembre 2008): 757–78. http://dx.doi.org/10.1017/s0021900200004691.
Abstract (sommario):
We study the susceptible-infected-susceptible model of the spread of an endemic infection. We calculate an exact expression for the mean number of transmissions for all values of the population size (N) and the infectivity. We derive the large-N asymptotic behavior for the infectivitiy below, above, and in the critical region. We obtain an analytical expression for the probability distribution of the number of transmissions, n, in the critical region. We show that this distribution has an n -3/2 singularity for small n and decays exponentially for large n. The exponent decreases with the distance from the threshold, diverging to ∞ far below and approaching 0 far above.
22
Ponce, Joan, e Horst R. Thieme. "Can infectious diseases eradicate host species? The effect of infection-age structure". Mathematical Biosciences and Engineering 20, n. 10 (2023): 18717–60. http://dx.doi.org/10.3934/mbe.2023830.
Abstract (sommario):
<abstract><p>It is a fundamental question in mathematical epidemiology whether deadly infectious diseases only lead to a mere decline of their host populations or whether they can cause their complete disappearance. Upper density-dependent incidences do not lead to host extinction in simple, deterministic SI or SIS (susceptible-infectious) epidemic models. Infection-age structure is introduced into SIS models because of the biological accuracy offered by considering arbitrarily distributed infectious periods. In an SIS model with infection-age structure, survival of the susceptible host population is established for incidences that depend on the infection-age density in a general way. This confirms previous host persistence results without infection-age for incidence functions that are not generalizations of frequency-dependent transmission. For certain power incidences, hosts persist if some infected individuals leave the infected class and become susceptible again and the return rate dominates the infection-age dependent infectivity in a sufficient way. The hosts may be driven into extinction by the infectious disease if there is no return into the susceptible class at all.</p></abstract>
23
Gong, Guang Wu, e Da Min Zhang. "An SIS Epidemic Model with Feedback Mechanism in Scale-Free Networks". Advanced Materials Research 204-210 (febbraio 2011): 354–58. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.354.
Abstract (sommario):
A new susceptible-infected-susceptible model with feedback mechanism is proposed. The dynamic behavior of the epidemic model with feedback mechanism in scale-free networks is researched by theoretical analysis and computer simulation. The results show that feedback mechanism can reduce the stable infective ratio of system; however, it can not influence the epidemic threshold of system. The results can help us to understand rightly epidemic spreading process in reality networks and guide people to design effective epidemic preventive and controlling measures when epidemic outbreaks.
24
Mahata, Animesh, Sankar Prasad Mondal, Ali Ahmadian, Fudiah Ismail, Shariful Alam e Soheil Salahshour. "Different Solution Strategies for Solving Epidemic Model in Imprecise Environment". Complexity 2018 (2018): 1–18. http://dx.doi.org/10.1155/2018/4902142.
Abstract (sommario):
We study the different solution strategy for solving epidemic model in different imprecise environment, that is, a Susceptible-Infected-Susceptible (SIS) model in imprecise environment. The imprecise parameter is also taken as fuzzy and interval environment. Three different solution procedures for solving governing fuzzy differential equation, that is, fuzzy differential inclusion method, extension principle method, and fuzzy derivative approaches, are considered. The interval differential equation is also solved. The numerical results are discussed for all approaches in different imprecise environment.
25
Peranginangin, Andreas Perdamenta. "Education and Mathematics Models (A Case Study of Epidemiology of Virus Spread)". Bulletin of Science Education 3, n. 3 (29 dicembre 2023): 330. http://dx.doi.org/10.51278/bse.v3i3.940.
Abstract (sommario):
Viruses are the cause of diseases that affect the human body and can lead to pandemics and epidemics in various countries. No new content has been added beyond the original text. Viruses are the cause of diseases that affect the human body and can lead to pandemics and epidemics in various countries. The language used is clear, objective, and value-neutral, with a formal register and precise word choice. The text adheres to conventional structure and format, with consistent citation and footnote style. The text is free from grammatical errors, spelling mistakes, and punctuation errors. The purpose of this research is to determine the SIS model for the spread of viral diseases, such as Covid-19 and bird flu, and their resolution behavior. The model is formed by creating a flow diagram of the disease spread using the SIS (Susceptible, Infected, Susceptible) model. The sentences and paragraphs create a logical flow of information with causal connections between statements. The study revealed two equilibrium points: the disease-free equilibrium point and the endemic equilibrium point. To analyze the stability of the disease-free equilibrium point, linearization around the equilibrium point was used. The disease-free equilibrium point is asymptotically stable if the basic reproduction number is less than one, indicating that the disease will disappear after a certain period of time. Numerical simulations were conducted to analyze the behavior of the disease model.
Keywords: Education Models, Mathematics Models, SIS (Susceptible, Infected, Susceptible)
26
XU, XIN-JIAN, ZHI-XI WU, YONG CHEN e YING-HAI WANG. "STEADY STATES OF EPIDEMIC SPREADING IN SMALL-WORLD NETWORKS". International Journal of Modern Physics C 15, n. 10 (dicembre 2004): 1471–77. http://dx.doi.org/10.1142/s0129183104006881.
Abstract (sommario):
We consider a standard susceptible–infected–susceptible (SIS) model to study the behaviors of steady states of epidemic spreading in small-world networks. Using analytical methods and large scale simulations, we recover the usual epidemic behavior with a critical threshold λc below which infectious diseases die out. For the spreading rate λ far above λc, it was found that the density of infected individuals ρ as a function of λ has the property ρ≈f(K)( ln λ- ln λc).
27
Gao, Daozhou, Chengxia Lei, Rui Peng e Benben Zhang. "A diffusive SIS epidemic model with saturated incidence function in a heterogeneous environment *". Nonlinearity 37, n. 2 (22 dicembre 2023): 025002. http://dx.doi.org/10.1088/1361-6544/ad1495.
Abstract (sommario):
Abstract In this paper, we propose a diffusive susceptible-infected-susceptible epidemic model in a spatiotemporally heterogeneous environment. We consider a saturated incidence function of the form S I m + S + I , where m is a nonnegative function. When there is a positive disease-induced mortality rate everywhere, we demonstrate that the disease will always become extinct and the susceptible population will stabilize at zero or a positive constant. In the case where the disease-induced mortality rate is negligible, we examine the model in a time-periodic and spatially heterogeneous environment and establish the threshold dynamics between disease extinction and persistence in terms of the basic reproduction number. Under certain conditions, we show the global attractivity of both the disease-free equilibrium and endemic equilibrium by constructing appropriate Lyapunov functions. Moreover, we determine the spatial distribution of the disease when the diffusion rate of the susceptible or infected population (or both) is sufficiently small. Our findings suggest that the presence of a saturation effect reduces the transmission risk, allows for the total population size to have a substantial impact on disease dynamics, and may significantly alter the spatial distribution of the disease under certain circumstances.
28
Darmawati, Darmawati, e Wahyudin Nur. "Model SIS Stokastik pada Penyakit Malaria Berdasarkan Distribusi Data Pasien". SAINTIFIK 5, n. 1 (4 febbraio 2019): 53–57. http://dx.doi.org/10.31605/saintifik.v5i1.198.
Abstract (sommario):
Penyakit Malaria merupakan salah satu penyakit yang paling sering mewabah di daerah beriklim tropis seperti Indonesia, khususnya daerah Sulawesi Barat. Salah satu faktor pendukung dari wabah penyakit ini adalah banyaknya daerah rawa yang merupakan habitat alami perkembang biakan dari vektor, yaitu nyamuk Anopheles spp yang menularkan Parasit Plasmodium spp ke tubuh inang yakni manusia. Dalam penelitian ini kami menggunakan model Susceptible Infected Susceptible (SIS) untuk mengkaji model infeksi penyakit Malaria, dimana laju infeksi penyakitnya dimodelkan oleh Distribusi Poisson dengan berdasarkan pada model distribusi pasien. Data jumlah pasien akan diperiksa model distribusinya untuk mengetahui model stokastik yang akan digunakan dalam memodelkan laju infeksi, yang kemudian akan diaplikasikan dalam model SIS Stokastik infeksi Malaria di daerah Kabupaten Majene, Sulawesi Barat. Tujuan dari penelitian ini adalah untuk mendapatkan model dan analisis matematika untuk menanggulangi infeksi Malaria, agar tidak kembali mewabah. Hasil yang diperoleh menunjukkan bahwa model matematika yang dibentuk dapat menunjukkan dinamik dari penyakit Malaria tersebut.Kata kunci: Malaria, Model SIS, Distribusi Poisson
29
Liu, Ming, e Yihong Xiao. "Modeling and Analysis of Epidemic Diffusion with Population Migration". Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/583648.
Abstract (sommario):
An improved Susceptible-Infected-Susceptible (SIS) epidemic diffusion model with population migration between two cities is modeled. Global stability conditions for both the disease-free equilibrium and the endemic equilibrium are analyzed and proved. The main contribution of this paper is reflected in epidemic modeling and analysis which considers unequal migration rates, and only susceptible individuals can migrate between the two cities. Numerical simulation shows when the epidemic diffusion system is stable, number of infected individuals in one city can reach zero, while the number of infected individuals in the other city is still positive. On the other hand, decreasing population migration in only one city seems not as effective as improving the recovery rate for controlling the epidemic diffusion.
30
Darmawati, Darmawati, Wahyudin Nur e Musafira Musafira. "Penaksiran Parameter Model SIS Stokastik Penyebaran Penyakit Malaria Dengan Metode Stepest Descent". SAINTIFIK 5, n. 2 (31 luglio 2019): 145–46. http://dx.doi.org/10.31605/saintifik.v5i2.297.
Abstract (sommario):
Simulasi numerik dilakukan untuk memperoleh solusi dan gambaran penyebaran penyakit malaria dengan model Susceptible Infected Susceptible (SIS) Stokastik. Laju infeksi penyakitnya dimodelkan mengikuti Distribusi Poisson. Simulasi dilakukan dengan menggunakan data jumlah pasien malaria di kabupaten Majene., Sulawesi Barat. Untuk simulasi numerik, peneliti menaksir parameter model yang mengikuti distribusi poisson dengan menggunakan maksimum likelihood estimator. Untuk menaksir parameter yang memaksimumkan fungsi log likelihoodnya, peneliti menggunakan metode stepest descent. Hasil yang diperoleh adalah Metode Stepest Descent merupakan metode yang sangat cocok digunakan untuk menaksir parameter model karena kecilnya kemungkinan nilai fungsi log likelihood menuju . Selain itu, metode Stepest Descent lebih memudahkan dalam penentuan parameter awal.
31
Wen, Luosheng, Bin Long, Xin Liang e Fengling Zeng. "The Global Behavior of a Periodic Epidemic Model with Travel between Patches". Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/295060.
Abstract (sommario):
We establish an SIS (susceptible-infected-susceptible) epidemic model, in which the travel between patches and the periodic transmission rate are considered. As an example, the global behavior of the model with two patches is investigated. We present the expression of basic reproduction ratioR0and two theorems on the global behavior: ifR0< 1 the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then it is unstable; ifR0> 1, the disease is uniform persistence. Finally, two numerical examples are given to clarify the theoretical results.
32
Liu, Maoxing, Xinjie Fu, Jie Zhang e Donghua Zhao. "Global Dynamics of an SIS Model on Metapopulation Networks with Demographics". Complexity 2021 (20 settembre 2021): 1–9. http://dx.doi.org/10.1155/2021/8884236.
Abstract (sommario):
In this paper, we propose a susceptible-infected-susceptible (SIS) epidemic model with demographics on heterogeneous metapopulation networks. We analytically derive the basic reproduction number, which determines not only the existence of endemic equilibrium but also the global dynamics of the model. The model always has the disease-free equilibrium, which is globally asymptotically stable when the basic reproduction number is less than unity and otherwise unstable. We also provide sufficient conditions on the global stability of the unique endemic equilibrium. Numerical simulations are performed to illustrate the theoretical results and the effects of the connectivity and diffusion. Furthermore, we find that diffusion rates play an active role in controlling the spread of infectious diseases.
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Cifuentes-Faura, Javier, Ursula Faura-Martínez e Matilde Lafuente-Lechuga. "Mathematical Modeling and the Use of Network Models as Epidemiological Tools". Mathematics 10, n. 18 (15 settembre 2022): 3347. http://dx.doi.org/10.3390/math10183347.
Abstract (sommario):
Mathematical modeling has served as an epidemiological tool to enhance the modeling efforts of the social and economic impacts of the pandemic. This article reviews epidemiological network models, which are conceived as a flexible way of representing objects and their relationships. Many studies have used these models over the years, and they have also been used to explain COVID-19. Based on the information provided by the Web of Science database, exploratory, descriptive research based on the techniques and tools of bibliometric analysis of scientific production on epidemiological network models was carried out. The epidemiological models used in the papers are diverse, highlighting those using the SIS (Susceptible-Infected-Susceptible), SIR (Susceptible-Infected-Recovered) and SEIR (Susceptible-Exposed-Infected-Removed) models. No model can perfectly predict the future, but they provide a sufficiently accurate approximation for policy makers to determine the actions needed to curb the pandemic. This review will allow any researcher or specialist in epidemiological modeling to know the evolution and development of related work on this topic.
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Zhang, Xu, Yurong Song, Haiyan Wang e Guo-Ping Jiang. "Epidemic Spreading Combined with Age and Region in Complex Networks". Mathematical Problems in Engineering 2020 (22 giugno 2020): 1–7. http://dx.doi.org/10.1155/2020/6753798.
Abstract (sommario):
In social networks, the age and the region of individuals are the two most important factors in modeling infectious diseases. In this paper, a spatial susceptible-infected-susceptible (SIS) model is proposed to describe epidemic spreading over a network with region and age by establishing several partial differential equations. Numerical simulations are performed, and the simulation of the proposed model agrees well with real influenza-like illness (ILI) in the USA reported by the Centers for Disease Control (CDC). Moreover, the proposed model can be used to predict the infected density of individuals. The results show that our model can be used as a tool to analyze influenza cases in the real world.
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XU, XIN-JIAN, WEN-XU WANG, TAO ZHOU e GUANRONG CHEN. "GEOGRAPHICAL EFFECTS ON EPIDEMIC SPREADING IN SCALE-FREE NETWORKS". International Journal of Modern Physics C 17, n. 12 (dicembre 2006): 1815–22. http://dx.doi.org/10.1142/s0129183106010194.
Abstract (sommario):
Many real networks are embedded in a metric space: the interactions among individuals depend on their spatial distances and usually take place among their nearest neighbors. In this paper, we introduce a modified susceptible-infected-susceptible (SIS) model to study geographical effects on the spread of diseases by assuming that the probability of a healthy individual infected by an infectious one is inversely proportional to the Euclidean distance between them. It is found that geography plays a more important role than hubs in disease spreading: the more geographically constrained the network is, the more highly the epidemic prevails.
36
Pratama, Suryadi Harto, Irma Suryani e Wartono Wartono. "Kestabilan Titik Ekuilibrium Endemik Pada Model SIS Transmisi Human Papillomavirus (HPV) Dengan Populasi Berbeda". KUBIK: Jurnal Publikasi Ilmiah Matematika 6, n. 1 (31 agosto 2021): 36–43. http://dx.doi.org/10.15575/kubik.v6i1.9189.
Abstract (sommario):
Paper ini membahas model matematika tentang kestabilan titik ekuilibrium endemik terhadap Human Papillomavirus (HPV) pada model SIS dengan populasi berbeda. Model SIS Terdiri dari dua kompartemen, yaitu kompartemen rentan (Susceptible) dan kompartemen yang terinfeksi (Infected) dengan populasi yaitu subpopulasi perempuan dan subpopulasi laki-laki . Titik ekuilibrium endemik pada model SIS ini dapat dilakukan dengan melakukan substitusi atau manipulasi aljabar terhadap asumsi-asumsi pada model SIS Human Papillomavirus (HPV). Selanjutnya, kestabilan endemik dinyatakan stabil asimtotik dapat di uji menggunakan matriks Jacobian dengan syarat terpenuhi. Kemudian, model SIS Human Papillomavirus (HPV) dianalisis dengan simulasi numerik dengan hasil kestabilan titik ekuilibrium endemik itu stabil asimtotik jika . Dan ini menjelaskan bahwa subpopulasi terinfeksi akan memungkinkan menginfeksi atau menularkan virus kepada subpopulasi rentan. Artinya virus masih ada dalam populasi.
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Bilge, Ayse Humeyra, Arif Selcuk Ogrenci e Onder Pekcan. "Mathematical models for phase transitions in biogels". Modern Physics Letters B 33, n. 09 (30 marzo 2019): 1950111. http://dx.doi.org/10.1142/s0217984919501112.
Abstract (sommario):
It has been shown that reversible and irreversible phase transitions of biogels can be represented by epidemic models. The irreversible chemical sol–gel transitions are modeled by the Susceptible-Exposed-Infected-Removed (SEIR) or Susceptible-Infected-Removed (SIR) epidemic systems whereas reversible physical gels are modeled by a modification of the Susceptible-Infected-Susceptible (SIS) system. Measured sol–gel and gel–sol transition data have been fitted to the solutions of the epidemic models, either by solving the differential equations directly (SIR and SEIR models) or by nonlinear regression (SIS model). The gel point is represented as the “critical point of sigmoid,” defined as the limit point of the locations of the extreme values of its derivatives. Then, the parameters of the sigmoidal curve representing the gelation process are used to predict the gel point and its relative position with respect to the transition point, that is, the maximum of the first derivative with respect to time. For chemical gels, the gel point is always located before the maximum of the first derivative and moves backward in time as the strength of the activation increases. For physical gels, the critical point for the sol–gel transition occurs before the maximum of the first derivative with respect to time, that is, it is located at the right of this maximum with respect to temperature. For gel–sol transitions, the critical point is close to the transition point; the critical point occurs after the maximum of the first derivative for low concentrations whereas the critical point occurs after the maximum of the first derivative for higher concentrations.
38
Zhu, Qingyi, Xuhang Luo e Yuhang Liu. "Modeling and Analysis of the Spread of Malware with the Influence of User Awareness". Complexity 2021 (1 novembre 2021): 1–9. http://dx.doi.org/10.1155/2021/6639632.
Abstract (sommario):
By incorporating the security awareness of computer users into the susceptible-infected-susceptible (SIS) model, this study proposes a new malware propagation model, named the SID model, where D compartment denotes the group of nodes with user awareness. Through qualitative analysis, the basic reproductive number R 0 is given. Furthermore, it is proved that the virus-free equilibrium is globally asymptotically stable if R 0 is less than one, whereas the viral equilibrium is globally asymptotically stable if R 0 is greater than one. Then, some numerical examples are given to demonstrate the analytical results. Finally, we put forward some efficient control measures according to the theoretical and experimental analysis.
39
LI, HUICONG, RUI PENG e TIAN XIANG. "Dynamics and asymptotic profiles of endemic equilibrium for two frequency-dependent SIS epidemic models with cross-diffusion". European Journal of Applied Mathematics 31, n. 1 (18 settembre 2018): 26–56. http://dx.doi.org/10.1017/s0956792518000463.
Abstract (sommario):
This paper is concerned with two frequency-dependent susceptible–infected–susceptible epidemic reaction–diffusion models in heterogeneous environment, with a cross-diffusion term modelling the effect that susceptible individuals tend to move away from higher concentration of infected individuals. It is first shown that the corresponding Neumann initial-boundary value problem in an n-dimensional bounded smooth domain possesses a unique global classical solution which is uniformly in-time bounded regardless of the strength of the cross-diffusion and the spatial dimension n. It is further shown that, even in the presence of cross-diffusion, the models still admit threshold-type dynamics in terms of the basic reproduction number $\mathcal {R}_0$ – i.e. the unique disease-free equilibrium is globally stable if $\mathcal {R}_0\lt1$, while if $\mathcal {R}_0\gt1$, the disease is uniformly persistent and there is an endemic equilibrium (EE), which is globally stable in some special cases with weak chemotactic sensitivity. Our results on the asymptotic profiles of EE illustrate that restricting the motility of susceptible population may eliminate the infectious disease entirely for the first model with constant total population but fails for the second model with varying total population. In particular, this implies that such cross-diffusion does not contribute to the elimination of the infectious disease modelled by the second one.
40
KANG, HUIYAN, YIJUN LOU, GUANRONG CHEN, SEN CHU e XINCHU FU. "EPIDEMIC SPREADING AND GLOBAL STABILITY OF A NEW SIS MODEL WITH DELAY ON HETEROGENEOUS NETWORKS". Journal of Biological Systems 23, n. 04 (30 novembre 2015): 1550029. http://dx.doi.org/10.1142/s0218339015500291.
Abstract (sommario):
In this paper, we study a susceptible-infected-susceptible (SIS) model with time delay on complex heterogeneous networks. Here, the delay describes the incubation period in the vector population. We calculate the epidemic threshold by using a Lyapunov functional and some analytical methods, and find that adding delay increases the epidemic threshold. Then, we prove the global stability of disease-free and endemic equilibria by using the theory of functional differential equations. Furthermore, we show numerically that the epidemic threshold of the new model may change along with other factors, such as the infectivity function, the heterogeneity of the network, and the degrees of nodes. Finally, we find numerically that the delay can affect the convergence speed at which the disease reaches equilibria.
41
COEN, P. G., A. G. LUCKINS, H. C. DAVISON e M. E. J. WOOLHOUSE. "Trypanosoma evansi in Indonesian buffaloes: evaluation of simple models of natural immunity to infection". Epidemiology and Infection 126, n. 1 (febbraio 2001): 111–18. http://dx.doi.org/10.1017/s0950268801004964.
Abstract (sommario):
Deterministic models were employed to investigate the biology of Trypanosoma evansi infection in the Indonesian buffalo. Models were fitted to two age-structured data sets of infection. The Susceptible–Infected–Susceptible (SIS) model was the best supported description of this infection, although the results of the analysis depended on the serological test used: the Tr7 Ag-ELISA was judged the most reliable indicator of infection. Estimated forces of infection increase with age from 1·2 to 2·0 acquisitions per buffalo per year. The buffaloes would clear infection in an estimated mean time period of 16·8 months (95% CIs: 12·5–25·9 months) since acquisition, either by drug treatment by owners or self-cure. A general discussion on the role of immunity in protozoan infections includes consideration that the fitted SIS model would be consistent with strain-specific immunity. The model may become a useful tool for the evaluation of control programmes.
42
HUI, ZI, XU CAI, JEAN-MARC GRENECHE e QIUPING A. WANG. "IMPACTS OF SPATIAL STRUCTURE ON EPIDEMIC SPREADING". International Journal of Modern Physics C 23, n. 12 (dicembre 2012): 1250082. http://dx.doi.org/10.1142/s0129183112500829.
Abstract (sommario):
The epidemic spreading on spatial-driven network is studied with the spatial susceptible-infected-susceptible (SIS) model. The network is constructed by random addition of nodes on the plan. The probability for a previous node to be connected to the new one is inversely proportional to their spatial distance to the power α. The spreading rate between two nodes is inversely proportional to their spatial distance. The effective spreading time increases with the increasing of α. The proportional coefficient is found to have a α-dependent threshold with a maximum situated in the interval 1.5 < α < 2.
43
Wu, Qingchu, e Wenfang Zhu. "Toward a generalized theory of epidemic awareness in social networks". International Journal of Modern Physics C 28, n. 05 (21 marzo 2017): 1750070. http://dx.doi.org/10.1142/s012918311750070x.
Abstract (sommario):
We discuss the dynamics of a susceptible-infected-susceptible (SIS) model with local awareness in networks. Individual awareness to the infectious disease is characterized by a general function of epidemic information in its neighborhood. We build a high-accuracy approximate equation governing the spreading dynamics and derive an approximate epidemic threshold above which the epidemic spreads over the whole network. Our results extend the previous work and show that the epidemic threshold is dependent on the awareness function in terms of one infectious neighbor. Interestingly, when a pow-law awareness function is chosen, the epidemic threshold can emerge in infinite networks.
44
Chen, Shanshan, Yijun Ran, Hebo Huang, Zhenzhen Wang e Ke-ke Shang. "Epidemic Dynamics of Two-Pathogen Spreading for Pairwise Models". Mathematics 10, n. 11 (2 giugno 2022): 1906. http://dx.doi.org/10.3390/math10111906.
Abstract (sommario):
In the real world, pathogens do not exist in isolation. The transmission of one pathogen may be affected by the presence of other pathogens, and certain pathogens generate multiple strains with different spreading features. Hence, the behavior of multi-pathogen transmission has attracted much attention in epidemiological research. In this paper, we use the pairwise approximation method to formulate two-pathogen models capturing cross-immunity, super-infection, and co-infection phenomena, in which each pathogen follows a susceptible-infected-susceptible (SIS) mechanism. For each model, we calculate the basic reproduction number and analyze the stability of equilibria, and discuss the differences from the mean-field approach. We demonstrate that simulations are in good agreement with the analytical results.
45
Zhang, Haiyan, Yufei Teng, Josep M. Guerrero, Pierluigi Siano e Xiaorong Sun. "Analysis of Failure Propagation in Cyber-Physical Power Systems Based on an Epidemic Model". Energies 16, n. 6 (10 marzo 2023): 2624. http://dx.doi.org/10.3390/en16062624.
Abstract (sommario):
From the perspective of propagation dynamics in complex networks, failure propagation in cyber-physical power systems is analogous to the spread of diseases; subsequently, the cyber nodes and power nodes are regarded as individuals in each of their groups. In this study, a two-layer interdependent network model of the cyber-physical power system is proposed, where each subnetwork adopts the Susceptible-Infected-Susceptible (SIS) epidemic-spreading model. On this basis, we construct a failure cooperation propagation model of cyber-physical power systems. Furthermore, we introduce the node protection mechanism to ensure the normal operation of key nodes. The generated scale-free cyber network and IEEE118-bus power system are used for simulation to analyze the influence of the coupling effect between them on the final failure scale.
46
Leng, Hui, Yi Zhao, Jianfeng Luo e Yong Ye. "Simplicial epidemic model with birth and death". Chaos: An Interdisciplinary Journal of Nonlinear Science 32, n. 9 (settembre 2022): 093144. http://dx.doi.org/10.1063/5.0092489.
Abstract (sommario):
In this paper, we propose a simplicial susceptible-infected-susceptible (SIS) epidemic model with birth and death to describe epidemic spreading based on group interactions, accompanying with birth and death. The site-based evolutions are formulated by the quenched mean-field probability equations for each site, which is a high-dimensional differential system. To facilitate a theoretical analysis of the influence of system parameters on dynamics, we adopt the mean-field method for our model to reduce the dimension. As a consequence, it suggests that birth and death rates influence the existence and stability of equilibria, as well as the appearance of a bistable state (the coexistence of the stable disease-free and endemic states), which is then confirmed by extensive simulations on empirical and synthetic networks. Furthermore, we find that another type of the bistable state in which a stable periodic outbreak state coexists with a steady disease-free state also emerges when birth and death rates and other parameters satisfy the certain conditions. Finally, we illustrate how the birth and death rates shift the density of infected nodes in the stationary state and the outbreak threshold, which is also verified by sensitivity analysis for the proposed model.
47
Zhang, June, José M. F. Moura e June Zhang. "Contact process with exogenous infection and the scaled SIS process". Journal of Complex Networks 5, n. 5 (15 maggio 2017): 712–33. http://dx.doi.org/10.1093/comnet/cnx003.
Abstract (sommario):
Abstract Propagation of contagion in networks depends on the graph topology. This article is concerned with studying the time-asymptotic behaviour of the extended contact processes on static, undirected, finite-size networks. This is a contact process with nonzero exogenous infection rate (also known as the $\epsilon$-susceptible-infected-susceptible model). The only known analytical characterization of the equilibrium distribution of this process is for complete networks. For large networks with arbitrary topology, it is infeasible to numerically solve for the equilibrium distribution since it requires solving the eigenvalue-eigenvector problem of a matrix that is exponential in $N$, the size of the network. We derive a condition on the infection rates under which, depending on the degree distribution of the network, the equilibrium distribution of extended contact processes on arbitrary, finite-size networks is well approximated by a closed-form formulation. We confirm the goodness of the approximation with small networks answering inference questions like the distribution of the percentage of infected individuals and the most-probable equilibrium configuration. We then use the approximation to analyse the equilibrium distribution of the extended contact process on the 4941-node US Western power grid.
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Pakes, Anthony G. "A SIR Epidemic Model Allowing Recovery". Axioms 13, n. 2 (8 febbraio 2024): 115. http://dx.doi.org/10.3390/axioms13020115.
Abstract (sommario):
The deterministic SIR model for disease spread in a closed population is extended to allow infected individuals to recover to the susceptible state. This extension preserves the second constant of motion, i.e., a functional relationship of susceptible and removed numbers, S(t) and R(t), respectively. This feature allows a substantially complete elucidation of qualitative properties. The model exhibits three modes of behaviour classified in terms of the sign of −S′(0), the initial value of the epidemic curve. Model behaviour is similar to that of the SIS model if S′(0)>0 and to the SIR model if S′(0)<0. The separating case is completely soluble and S(t) is constant-valued. Long-term outcomes are determined for all cases, together with determination of the rate of convergence. Determining the shape of the epidemic curve motivates an investigation of curvature properties of all three state functions and quite complete results are obtained that are new, even for the SIR model. Finally, the second threshold theorem for the SIR model is extended in refined and generalised forms.
49
Jia, Cai, Shuyan Zheng, Hanqiang Qian, Bingxin Cao e Kaiting Zhang. "Analysis of Crowded Propagation on the Metro Network". Sustainability 14, n. 16 (9 agosto 2022): 9829. http://dx.doi.org/10.3390/su14169829.
Abstract (sommario):
The crowd in a metro system can cause inconvenience and even safety problems to passengers. The study of crowded propagation in metro systems can identify where and when crowds occur, ensuring travel quality and safety. Based on this, a modified susceptible–infected-susceptible (SIS) crowded propagation model is proposed to estimate the risk probability of crowding (RPC) in the metro network. Each station’s real transport capacity is considered. Infection rate and the recovery rate are proposed considering the traffic difference between stations. Using the Beijing metro network as a case study, the spatial and temporal patterns of crowded propagation are analyzed, and the types of nodes suitable for regulation are further discussed. This proposed model can provide a reference for RPC identification and regulation and promote sustainable development of metro operations.
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Mahmudah, Ana Rizki, Muhammad Ahsar Karim e Yuni Yulida. "ANALISIS KESTABILAN MODEL SI UNTUK PENYAKIT MENULAR DENGAN ADANYA TRANSMISI VERTIKAL DAN TINGKAT KEJADIAN JENUH". EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN 17, n. 2 (30 novembre 2023): 210. http://dx.doi.org/10.20527/epsilon.v17i2.10826.
Abstract (sommario):
The transmission of infectious diseases can occur through two pathways: horizontal and vertical. Horizontal transmission occurs through direct or indirect physical contact with the infectious agent, while vertical transmission takes place when an infected mother transmits the disease to a fetus or a newborn. Within the context of disease transmission models, a critical feature is the saturation incidence rate, which refers to the impact of interventions that can reduce the rate of disease transmission among susceptible and infected individuals. This research aims to elucidate the formation of a model, determine equilibrium points, and calculate the basic reproduction number using the Next Generation Matrix method. The analysis involves assessing local stability through linearization methods and global stability using Lyapunov functions. Sensitivity analysis is conducted on the basic reproduction number, and numerical simulations are performed using the fourth-order Runge-Kutta method. The research findings indicate the establishment of an SIS (Susceptible-Infected) model for infectious diseases with vertical transmission and saturation incidence. This model depicts the spread of the disease in a population, where individuals can exist in susceptible or infected conditions. Equilibrium points include a disease-free equilibrium that is locally and globally stable when the basic reproduction number is less than one, and an endemic equilibrium that is locally and globally stable when the basic reproduction number exceeds one. Sensitivity analysis reveals that each parameter has varying influences on the basic reproduction number. An increase in the saturation incidence rate leads to a decrease in the number of infected subpopulations, while an increase in the vertical transmission rate results in a similar decline. Numerical simulations support stability analyses at equilibrium points. These findings provide a deeper understanding of the factors influencing the spread of diseases within a population.