Multigroup deterministic and stochasticSEIRIepidemic models with nonlinear incidence rates and distributed delays: A stability analysis

2017 ◽  
Vol 40 (18) ◽  
pp. 6254-6275 ◽  
Author(s):  
Hong Zhang ◽  
Juan Xia ◽  
Paul Georgescu
Keyword(s):  
Stability Analysis ◽  
Incidence Rates ◽  
Distributed Delays ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates

scholarly journals Stability analysis of delayed SIR epidemic models with a class of nonlinear incidence rates

2012 ◽  
Vol 218 (9) ◽  
pp. 5327-5336 ◽  
Author(s):  
Yoichi Enatsu ◽  
Eleonora Messina ◽  
Yoshiaki Muroya ◽  
Yukihiko Nakata ◽  
Elvira Russo ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Incidence Rates ◽  
Epidemic Models ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Nonlinear Incidence Rates ◽  
Sir Epidemic Models

scholarly journals Analysis of Pine Wilt Disease Model with Nonlinear Incidence and Horizontal Transmission

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Ozair
Keyword(s):  
Global Analysis ◽  
Horizontal Transmission ◽  
Disease Model ◽  
Pine Wilt Disease ◽  
Incidence Rates ◽  
Reproductive Number ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Pine Wilt ◽  
Nonlinear Incidence Rates

The deterministic pine wilt model with vital dynamics to determine the equilibria and their stability by considering nonlinear incidence rates with horizontal transmission is analyzed. The complete global analysis for the equilibria of the model is discussed. The explicit formula for the reproductive number is obtained and it is shown that the “disease-free” equilibrium always exists and is globally asymptotically stable wheneverR0≤1. Furthermore, the disease persists at an “endemic” level when the reproductive number exceeds unity.

scholarly journals Asymptotic Behavior of Multigroup SEIR Model with Nonlinear Incidence Rates under Stochastic Perturbations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Feng Wang ◽  
Shan Wang ◽  
Youhua Peng
Keyword(s):  
Asymptotic Behavior ◽  
Stochastic Perturbation ◽  
Incidence Rates ◽  
Nonlinear Incidence Rate ◽  
Stochastic Perturbations ◽  
Seir Model ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates ◽  
Uniqueness Of The Solution ◽  
Rate Functions

In this paper, the asymptotic behavior of a multigroup SEIR model with stochastic perturbations and nonlinear incidence rate functions is studied. First, the existence and uniqueness of the solution to the model we discuss are given. Then, the global asymptotical stability in probability of the model with R0<1 is established by constructing Lyapunov functions. Next, we prove that the disease can die out exponentially under certain stochastic perturbation while it is persistent in the deterministic case when R0>1. Finally, several examples and numerical simulations are provided to illustrate the dynamic behavior of the model and verify our analytical results.

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