Global stability for SIRS epidemic models with general incidence rate and transfer from infectious to susceptible

2018 ◽  
Vol 25 (3) ◽  
pp. 637-658 ◽  
Author(s):  
Eric J. Avila-Vales ◽  
Ángel G. Cervantes-Pérez
Keyword(s):  
Global Stability ◽  
Incidence Rate ◽  
Epidemic Models ◽  
General Incidence Rate

scholarly journals Global Behaviors of a Class of Discrete SIRS Epidemic Models with Nonlinear Incidence Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Lei Wang ◽  
Zhidong Teng ◽  
Long Zhang
Keyword(s):  
Incidence Rate ◽  
Endemic Equilibrium ◽  
Epidemic Models ◽  
Asymptotically Stable ◽  
Nonlinear Incidence Rate ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
General Incidence Rate ◽  
Special Cases ◽  
Disease Free

We study a class of discrete SIRS epidemic models with nonlinear incidence rateF(S)G(I)and disease-induced mortality. By using analytic techniques and constructing discrete Lyapunov functions, the global stability of disease-free equilibrium and endemic equilibrium is obtained. That is, if basic reproduction numberℛ0<1, then the disease-free equilibrium is globally asymptotically stable, and ifℛ0>1, then the model has a unique endemic equilibrium and when some additional conditions hold the endemic equilibrium also is globally asymptotically stable. By using the theory of persistence in dynamical systems, we further obtain that only whenℛ0>1, the disease in the model is permanent. Some special cases ofF(S)G(I)are discussed. Particularly, whenF(S)G(I)=βSI/(1+λI), it is obtained that the endemic equilibrium is globally asymptotically stable if and only ifℛ0>1. Furthermore, the numerical simulations show that for general incidence rateF(S)G(I)the endemic equilibrium may be globally asymptotically stable only asℛ0>1.

scholarly journals Global stability of a distributed delayed viral model with general incidence rate

2018 ◽  
Vol 16 (1) ◽  
pp. 1374-1389
Author(s):  
Eric Ávila-Vales ◽  
Abraham Canul-Pech ◽  
Erika Rivero-Esquivel
Keyword(s):  
Immune Response ◽  
Viral Infection ◽  
Global Stability ◽  
Numerical Simulations ◽  
Incidence Rate ◽  
Existence And Uniqueness ◽  
Lyapunov Functional ◽  
Infection Model ◽  
General Incidence Rate ◽  
Viral Infection Model

AbstractIn this paper, we discussed a infinitely distributed delayed viral infection model with nonlinear immune response and general incidence rate. We proved the existence and uniqueness of the equilibria. By using the Lyapunov functional and LaSalle invariance principle, we obtained the conditions of global stabilities of the infection-free equilibrium, the immune-exhausted equilibrium and the endemic equilibrium. Numerical simulations are given to verify the analytical results.

scholarly journals Global Stability for Delay SIR and SEIR Epidemic Models with Nonlinear Incidence Rate

2010 ◽  
Vol 72 (5) ◽  
pp. 1192-1207 ◽  
Author(s):  
Gang Huang ◽  
Yasuhiro Takeuchi ◽  
Wanbiao Ma ◽  
Daijun Wei
Keyword(s):  
Global Stability ◽  
Incidence Rate ◽  
Epidemic Models ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence

The global stability of two epidemic models with nonlinear recovery incidence rate

2018 ◽  
Vol 32 (29) ◽  
pp. 1850357
Author(s):  
Yue Pan ◽  
Dechang Pi ◽  
Shuanglong Yao ◽  
Han Meng
Keyword(s):  
Lyapunov Function ◽  
Dynamic System ◽  
Global Stability ◽  
Incidence Rate ◽  
Invariance Principle ◽  
Epidemic Models ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
General Validity ◽  
Nonlinear Condition

In this paper, we present two epidemic models with a nonlinear incidence and transfer from infectious to recovery. For epidemic models, the basic reproductive number is calculated. A dynamic system based on threshold, using LaSalle’s invariance principle and Lyapunov function, is structured completely by the basic reproductive number. By studying the SIR and SIRS models under the nonlinear condition, the general validity of the method is verified.

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