Dynamical analysis of a stochastic SIS epidemic model with nonlinear incidence rate and double epidemic hypothesis

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.

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Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate

Abstract and Applied Analysis ◽

10.1155/2013/127321 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Qixing Han ◽

Daqing Jiang ◽

Chengjun Yuan

Keyword(s):

Incidence Rate ◽

Nonnegative Solution ◽

Ergodic Property ◽

Nonlinear Incidence Rate ◽

Sis Model ◽

Nonlinear Incidence ◽

Sis Epidemic Model ◽

Stochastic Sis Epidemic Model ◽

Sis Epidemic ◽

Stochastic Sis Model

We investigate a stochastic SIS model with nonlinear incidence rate. We show that there exists a unique nonnegative solution to the system, and condition for the infectious individualsI(t)to be extinct is given. Moreover, we prove that the system has ergodic property. Finally, computer simulations are carried out to verify our results.

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Local stability of a fractional order sis epidemic model with specific nonlinear incidence rate and time delay

Communications in Mathematical Biology and Neuroscience ◽

10.28919/cmbn/4409 ◽

2021 ◽

Keyword(s):

Time Delay ◽

Incidence Rate ◽

Fractional Order ◽

Epidemic Model ◽

Local Stability ◽

Nonlinear Incidence Rate ◽

Nonlinear Incidence ◽

Sis Epidemic Model ◽

Sis Epidemic

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Dynamical analysis of a reaction–diffusion SEI epidemic model with nonlinear incidence rate

International Journal of Biomathematics ◽

10.1142/s1793524521500418 ◽

2021 ◽

pp. 2150041

Author(s):

Jianpeng Wang ◽

Binxiang Dai

Keyword(s):

Steady State ◽

Incidence Rate ◽

Epidemic Model ◽

Reaction Diffusion ◽

Dynamical Analysis ◽

Asymptotically Stable ◽

Nonlinear Incidence Rate ◽

Globally Asymptotically Stable ◽

Nonlinear Incidence ◽

Positive Steady State

In this paper, a reaction–diffusion SEI epidemic model with nonlinear incidence rate is proposed. The well-posedness of solutions is studied, including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions. The basic reproduction numbers are given in both heterogeneous and homogeneous environments. For spatially heterogeneous environment, by the comparison principle of the diffusion system, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] if [Formula: see text], the system will be persistent and admit at least one positive steady state. For spatially homogenous environment, by constructing a Lyapunov function, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if [Formula: see text]. Finally, two examples are given via numerical simulations, and then some control strategies are also presented by the sensitive analysis.

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Analysis of a Deterministic and a Stochastic SIS Epidemic Model with Double Epidemic Hypothesis and Specific Functional Response

Discrete Dynamics in Nature and Society ◽

10.1155/2020/5362716 ◽

2020 ◽

Vol 2020 ◽

pp. 1-11

Author(s):

Mouhcine Naim ◽

Fouad Lahmidi

Keyword(s):

Epidemic Model ◽

Deterministic Model ◽

Sufficient Condition ◽

Nonlinear Incidence Rate ◽

Local Asymptotic Stability ◽

Sis Epidemic Model ◽

The Stability ◽

Stochastic Sis Epidemic Model ◽

Disease Free ◽

Sis Epidemic

The purpose of this paper is to investigate the stability of a deterministic and stochastic SIS epidemic model with double epidemic hypothesis and specific nonlinear incidence rate. We prove the local asymptotic stability of the equilibria of the deterministic model. Moreover, by constructing a suitable Lyapunov function, we obtain a sufficient condition for the global stability of the disease-free equilibrium. For the stochastic model, we establish global existence and positivity of the solution. Thereafter, stochastic stability of the disease-free equilibrium in almost sure exponential and pth moment exponential is investigated. Finally, numerical examples are presented.

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The Dynamical Behaviors in a Stochastic SIS Epidemic Model with Nonlinear Incidence

Computational and Mathematical Methods in Medicine ◽

10.1155/2016/5218163 ◽

2016 ◽

Vol 2016 ◽

pp. 1-14 ◽

Cited By ~ 4

Author(s):

Ramziya Rifhat ◽

Qing Ge ◽

Zhidong Teng

Keyword(s):

Epidemic Model ◽

Stochastic Perturbation ◽

Threshold Value ◽

Open Problems ◽

Nonlinear Incidence ◽

Sis Epidemic Model ◽

Dynamical Behaviors ◽

The Mean ◽

Stochastic Sis Epidemic Model ◽

Sis Epidemic

A stochastic SIS-type epidemic model with general nonlinear incidence and disease-induced mortality is investigated. It is proved that the dynamical behaviors of the model are determined by a certain threshold valueR~0. That is, whenR~0<1and together with an additional condition, the disease is extinct with probability one, and whenR~0>1, the disease is permanent in the mean in probability, and when there is not disease-related death, the disease oscillates stochastically about a positive number. Furthermore, whenR~0>1, the model admits positive recurrence and a unique stationary distribution. Particularly, the effects of the intensities of stochastic perturbation for the dynamical behaviors of the model are discussed in detail, and the dynamical behaviors for the stochastic SIS epidemic model with standard incidence are established. Finally, the numerical simulations are presented to illustrate the proposed open problems.

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