scholarly journals Asymptotic Dynamics of a Stochastic SIR Epidemic System Affected by Mixed Nonlinear Incidence Rates

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Ping Han ◽  
Zhengbo Chang ◽  
Xinzhu Meng
Keyword(s):  
Stochastic System ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Incidence Rates ◽  
Markov Semigroup ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Nonlinear Incidence Rates ◽  
Asymptotic Dynamics ◽  
Stochastic Sir

This paper considers a stochastic SIR epidemic system affected by mixed nonlinear incidence rates. Using Markov semigroup theory and the Fokker–Planck equation, we explore the asymptotic dynamics of the stochastic system. We first investigate the existence of a positive solution and its uniqueness. Furthermore, we prove that the stochastic system has an asymptotically stable stationary distribution. In addition, the sufficient conditions for disease extinction are also obtained, which imply that the white noise can suppress and control the spread of infectious diseases. Finally, in order to illustrate the analytical results, we give some numerical simulations.

scholarly journals Analysis of a Stochastic SIR Model with Vaccination and Nonlinear Incidence Rate

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Amine El Koufi ◽  
Jihad Adnani ◽  
Abdelkrim Bennar ◽  
Noura Yousfi
Keyword(s):  
Analytical Solution ◽  
Sir Model ◽  
Incidence Rates ◽  
Sir Epidemic Model ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Sir Epidemic ◽  
Nonlinear Incidence Rates ◽  
Stochastic Sir ◽  
Stochastic Sir Model

We expand an SIR epidemic model with vertical and nonlinear incidence rates from a deterministic frame to a stochastic one. The existence of a positive global analytical solution of the proposed stochastic model is shown, and conditions for the extinction and persistence of the disease are established. The presented results are demonstrated by numerical simulations.

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 Stability Analysis of a Multigroup Epidemic Model with General Exposed Distribution and Nonlinear Incidence Rates

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ling Zhang ◽  
Jingmei Pang ◽  
Jinliang Wang
Keyword(s):  
Death Rate ◽  
Sufficient Conditions ◽  
Incidence Rates ◽  
Global Dynamics ◽  
Lyapunov Functionals ◽  
Natural Death ◽  
Nonlinear Incidence ◽  
Nonlinear Incidence Rates ◽  
Basic Production ◽  
Derivatives Of

We investigate a class of multigroup epidemic models with general exposed distribution and nonlinear incidence rates. For a simpler case that assumes an identical natural death rate for all groups, and with a gamma distribution for exposed distribution is considered. Some sufficient conditions are obtained to ensure that the global dynamics are completely determined by the basic production numberR0. The proofs of the main results exploit the method of constructing Lyapunov functionals and a graph-theoretical technique in estimating the derivatives of Lyapunov functionals.

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.

Sign in / Sign up

Export Citation Format

Share Document