The threshold behavior and periodic solution of stochastic SIR epidemic model with saturated incidence
نویسندگان
چکیده
In this article, we investigate degenerate stochastic SIR epidemic model with saturated incidence. For the constant coefficients case, we achieve a threshold which determines the extinction and persistence of the epidemic by utilizing Markov semigroup theory. Furthermore, we conclude that environmental white noise plays a positive effect in the control of infectious disease in some sense comparing to the corresponding deterministic system. For the stochastic non-autonomous system, we prove the existence of periodic solution.
منابع مشابه
Dynamics of a Delayed Epidemic Model with Beddington-DeAngelis Incidence Rate and a Constant Infectious Period
In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...
متن کاملMathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asym...
متن کاملStability and Bifurcation of an SIS Epidemic Model with Saturated Incidence Rate and Treatment Function
In this paper an SIS epidemic model with saturated incidence rate and treatment func- tion is proposed and studied. The existence of all feasible equilibrium points is discussed. The local stability conditions of the disease free equilibrium point and endemic equilibrium point are established with the help of basic reproduction number.However the global stabili- ty conditions of these eq...
متن کاملThe Dynamics of the Pulse Birth in an SIR Epidemic Model with Standard Incidence
An SIR epidemic model with pulse birth and standard incidence is presented. The dynamics of the epidemic model is analyzed. The basic reproductive number R∗ is defined. It is proved that the infection-free periodic solution is global asymptotically stable if R∗ < 1. The infection-free periodic solution is unstable and the disease is uniform persistent if R∗ > 1. Our theoretical results are conf...
متن کاملExistence and uniqueness of periodic solution for a discrete-time SIR epidemic model with time delays and impulses
In this paper, a discrete-time SIR epidemic model with nonlinear incidence rate, time delays and impulses is investigated. Sufficient conditions for the existence and uniqueness of periodic solutions are obtained by using contraction theorem and inequality techniques. An example is employed to illustrate our results. Keywords—Discrete-time SIR epidemic model, Time delay, Nonlinear incidence rat...
متن کامل