A note on the dynamics analysis of a diffusive cholera epidemic model with nonlinear incidence rate

2020 ◽  
Vol 106 ◽  
pp. 106356 ◽  
Author(s):  
Lian Duan ◽  
Zili Xu
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Dynamics Analysis ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Cholera Epidemic

Pulse Vaccination Strategy in an SIVS Epidemic Model with General Nonlinear Incidence Rate

2016 ◽  
Vol 1 (2) ◽  
Author(s):  
Dan Yu ◽  
◽  
Shujing Gao ◽  
Youquan Luo ◽  
Feiping Xie ◽  
...  
Keyword(s):  
Incidence Rate ◽  
Epidemic Model ◽  
Vaccination Strategy ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Pulse Vaccination

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

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.

Dynamics Analysis of an SEIQS Model with a Nonlinear Incidence Rate

2012 ◽  
Vol 157-158 ◽  
pp. 1220-1223
Author(s):  
Ning Cui ◽  
Jun Hong Li ◽  
Jiao Qu ◽  
Hong Dan Xue
Keyword(s):  
Lyapunov Function ◽  
Incidence Rate ◽  
Matrix Theory ◽  
Invariant Set ◽  
Dynamics Analysis ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Asymptotical Stable ◽  
Compound Matrix ◽  
Disease Free

This paper considers an SEIQS model with nonlinear incidence rate. By means of Lyapunov function and LaSalle’s invariant set theorem, we proved the global asymptotical stable results of the disease-free equilibrium. It is then obtained the sufficent conditions for the global stability of the endemic equilibrium by the compound matrix theory. In addition, we also study the phenomena of limit cycle of the systems with the numerical simulations.

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