Stability and extinction of SEIR epidemic models with generalized nonlinear incidence

Wei, Fengying; Xue, Rui

doi:10.1016/j.matcom.2018.09.029

Cited by 53 publications

(23 citation statements)

References 14 publications

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“…In reality, epidemic models are unavoidably influenced by environmental white noise which is an vital component in nature, since it can give an extra degree of reality compared to their undisturbed counterparts. Numerous researchers have examined the impact of stochasticity on epidemic models [27] , [28] , [29] , [30] , [31] . Stochastic perturbation variables have a considerable affect on the disease drive of all sorts of virus infections to humans.…”

Section: Stochastic Epidemic Model With Time-delaysmentioning

confidence: 99%

Dynamics of a stochastic delay differential model for COVID-19 infection with asymptomatic infected and interacting people: Case study in the UAE

Rihan

Alsakaji

2021

Results in Physics

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Public health science is increasingly focusing on understanding how COVID-19 spreads among humans. For the dynamics of COVID-19, we propose a stochastic epidemic model, with time-delays, Susceptible-Infected-Asymptomatic-Quarantined-Recovered (SIAQR). One global positive solution exists with probability one in the model. As a threshold condition of persistence and existence of an ergodic stationary distribution, we deduce a generalized stochastic threshold . To estimate the percentages of people who must be vaccinated to achieve herd immunity, least-squares approaches were used to estimate from real observations in the UAE. Our results suggest that when , a proportion of the population needs to be immunized/vaccinated during the pandemic wave. Numerical simulations show that the proposed stochastic delay differential model is consistent with the physical sensitivity and fluctuation of the real observations.

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Section: Stochastic Epidemic Model With Time-delaysmentioning

confidence: 99%

Dynamics of a stochastic delay differential model for COVID-19 infection with asymptomatic infected and interacting people: Case study in the UAE

Rihan

Alsakaji

2021

Results in Physics

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“…Kemudian Soufiane dan Abdelilah juga melakukan analisis fungsi pengobatan non-linier pada fase infected [5]. Lebih lanjut, telah dikembangkan model SEIR yang menggunakan fungsi insiden nonlinier dalam [6] yang dikembangkan berdasarkan fungsi insiden linier. Meskipun fungsi insiden non-linier tersebut tidak diterapkan dalam artikel ini, namun topik tersebut menarik untuk dikaji pada penelitian lanjutan di masa mendatang.…”

Section: Pendahuluanunclassified

Analisis Kestabilan Model Penyebaran Penyakit Tuberkulosis Dengan Laju Infeksi Tersaturasi (Stability Analysis of Tubercolosis Spread Diseases Model Considering Saturated Infection Rate)

Saputra

Sutimin

Sutrisno

2020

JMT

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This paper deals with the analysis of tuberculosis disease spread model with saturated infection rate and the treatment effect. We analyze the dynamical behavior of the model to observe the stability peroperty of the model’s equilibrium points. The Routh-Hurwitz Theorem is used to analyze the local stability peroperty of the free disease equilibrium point whereas Transcritical Bifurcation principle is used to analyze the local stability property of the endemic equilibrium pont. The result show that the local stability property of the equilibrium points is depending on the basic reproduction number value calculated by the next generation matrix (NGM). When the basic reproduction number is less than 1, the free disease equilibrium point is locally asymptotically stable, and when it is greater than 1, the endemic equilibrium point is locally asymptotically stable. Numeric simulation results were presented to describe the evolution of the dynamical behavior and to understand the treatment effectiveness for the tuberculosis disease of the population. From the simulation results, it was derived that the treatment in the infected subpopulation had a better result than the one in latent.

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“…Recently, quite a number of significant works about SEIR models have been achieved. The key issues are calculation of basic reproduction number, stability of disease‐free equilibrium, extinction of disease, existence and stability of endemic equilibrium, persistence of disease, and existence and stability of bifurcation phenomena (see, e.g., previous works 1–11 and references cited therein). In addition, we see that the SEIR models have been successfully applied to investigate and forecast the dynamical behaviors of many fatal infectious disease in reality, e.g., Ebola, Zika, and measles (see previous studies 12–20 ).…”

Section: Introductionmentioning

confidence: 99%

Global dynamics of a nonautonomous SEIRS epidemic model with vaccination and nonlinear incidence

Zhang

Fan

Teng

2021

Math Methods in App Sciences

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In this paper, a class of nonautonomous SEIRS epidemic models with vaccination and nonlinear incidence is investigated. Under some quite weak assumptions, a couple of new threshold values in the form of integral, i.e., R1, R1∗, R2, and R2∗ on the extinction and permanence of disease for the model, are established. As special cases of our model, the autonomous, periodic, and almost periodic circumstances are discussed. The nearly necessary and sufficient criteria of threshold on the extinction and permanence of disease for above cases are obtained as well. Numerical examples and simulations are presented to illustrate the analytic results.

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Stability and extinction of SEIR epidemic models with generalized nonlinear incidence

Cited by 53 publications

References 14 publications

Dynamics of a stochastic delay differential model for COVID-19 infection with asymptomatic infected and interacting people: Case study in the UAE

Dynamics of a stochastic delay differential model for COVID-19 infection with asymptomatic infected and interacting people: Case study in the UAE

Analisis Kestabilan Model Penyebaran Penyakit Tuberkulosis Dengan Laju Infeksi Tersaturasi (Stability Analysis of Tubercolosis Spread Diseases Model Considering Saturated Infection Rate)

Global dynamics of a nonautonomous SEIRS epidemic model with vaccination and nonlinear incidence

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