Global stability for a multi-group SIRS epidemic model with varying population sizes

2013 ◽  
Vol 14 (3) ◽  
pp. 1693-1704 ◽  
Author(s):  
Yoshiaki Muroya ◽  
Yoichi Enatsu ◽  
Toshikazu Kuniya
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Sirs Epidemic Model ◽  
Population Sizes ◽  
Varying Population

scholarly journals Dynamical Models for Infectious Diseases with Varying Population Size and Vaccinations

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Peilin Shi ◽  
Lingzhen Dong
Keyword(s):  
Infectious Diseases ◽  
Global Stability ◽  
Periodic Solutions ◽  
Dynamical Models ◽  
Bifurcation Theorem ◽  
Time Period ◽  
Population Sizes ◽  
Variable Population ◽  
Disease Free ◽  
Varying Population

We formulate and discuss models for the spread of infectious diseases with variable population sizes and vaccinations on the susceptible individuals. First, we assume that the susceptible individuals are vaccinated continuously. We establish the threshold-like results for the existence and global stability of the disease-free and the endemic equilibriums for these systems. Especially, we prove the global stability of the endemic equilibriums by converting the systems into integrodifferential equations. Second, we suppose that vaccinations occur once per time period. We obtain the existence and global stability of the disease-free periodic solutions for such systems with impulsive effects. By a useful bifurcation theorem, we acquire the existence of the endemic periodic solutions when the disease-related deaths do not occur. At last, we compare the results with vaccinations and without vaccinations and illustrate our results by numerical simulations.

GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

2006 ◽  
Vol 26 (2) ◽  
pp. 291-306 ◽  
Author(s):  
Jin Zhen ◽  
Zhien Ma ◽  
Maoan Han
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Sirs Epidemic Model

scholarly journals Global Stability of Multigroup SIRS Epidemic Model with Varying Population Sizes and Stochastic Perturbation around Equilibrium

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoming Fan
Keyword(s):  
Deterministic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Endemic Equilibrium ◽  
Random Perturbations ◽  
Sirs Epidemic Model ◽  
Population Sizes ◽  
Time Average ◽  
The Difference ◽  
Varying Population

We discuss multigroup SIRS (susceptible, infectious, and recovered) epidemic models with random perturbations. We carry out a detailed analysis on the asymptotic behavior of the stochastic model; when reproduction numberℛ0>1, we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average. Numerical methods are employed to illustrate the dynamic behavior of the model and simulate the system of equations developed. The effect of the rate of immunity loss on susceptible and recovered individuals is also analyzed in the deterministic model.

Sign in / Sign up

Export Citation Format

Share Document