Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age

AbstractIn this paper, we study a novel deterministic and stochastic SIR epidemic model with vertical transmission and media coverage. For the deterministic model, we give the basic reproduction number $R_{0}$ R 0 which determines the extinction or prevalence of the disease. In addition, for the stochastic model, we prove existence and uniqueness of the positive solution, and extinction and persistence in mean. Furthermore, we give numerical simulations to verify our results.

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Dynamics of an infection age-space structured cholera model with Neumann boundary condition

European Journal of Applied Mathematics ◽

10.1017/s095679252100005x ◽

2021 ◽

pp. 1-30

Author(s):

WEIWEI LIU ◽

JINLIANG WANG ◽

RAN ZHANG

Keyword(s):

Vibrio Cholerae ◽

Disease Transmission ◽

Global Attractivity ◽

Neumann Boundary ◽

Reaction Diffusion ◽

Human Populations ◽

Global Dynamics ◽

Infection Age ◽

Reaction Diffusion Model ◽

Disease Persistence

This paper investigates global dynamics of an infection age-space structured cholera model. The model describes the vibrio cholerae transmission in human population, where infection-age structure of vibrio cholerae and infectious individuals are incorporated to measure the infectivity during the different stage of disease transmission. The model is described by reaction–diffusion models involving the spatial dispersal of vibrios and the mobility of human populations in the same domain Ω ⊂ ℝ n . We first give the well-posedness of the model by converting the model to a reaction–diffusion model and two Volterra integral equations and obtain two constant equilibria. Our result suggest that the basic reproduction number determines the dichotomy of disease persistence and extinction, which is achieved by studying the local stability of equilibria, disease persistence and global attractivity of equilibria.

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Stability and Hopf Bifurcation for a Delayed SIR Epidemic Model with Logistic Growth

Abstract and Applied Analysis ◽

10.1155/2013/916130 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 3

Author(s):

Yakui Xue ◽

Tiantian Li

Keyword(s):

Incidence Rate ◽

Epidemic Model ◽

Threshold Value ◽

Endemic Equilibrium ◽

Logistic Growth ◽

Global Dynamics ◽

Asymptotically Stable ◽

Sir Epidemic Model ◽

Globally Asymptotically Stable ◽

Sir Epidemic

We study a delayed SIR epidemic model and get the threshold value which determines the global dynamics and outcome of the disease. First of all, for anyτ, we show that the disease-free equilibrium is globally asymptotically stable; whenR0<1, the disease will die out. Directly afterwards, we prove that the endemic equilibrium is locally asymptotically stable for anyτ=0; whenR0>1, the disease will persist. However, for anyτ≠0, the existence conditions for Hopf bifurcations at the endemic equilibrium are obtained. Besides, we compare the delayed SIR epidemic model with nonlinear incidence rate to the one with bilinear incidence rate. At last, numerical simulations are performed to illustrate and verify the conclusions.

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