The persistence and extinction of a stochastic SIS epidemic model with Logistic growth

The persistence and extinction of a stochastic SIS epidemic model with Logistic growth

The dynamical properties of a stochastic susceptible-infected epidemic model with Logistic growth are investigated in this paper. We show that the stochastic model admits a nonnegative solution by using the Lyapunov function method. We then obtain that the infected individuals are persistent under some simple conditions. As a consequence, a simple sufficient condition that guarantees the extinc...

Extinction and Quasi-Stationarity in the Stochastic Logistic SIS Model - ReadingSample

Persistence and Extinction of an Impulsive Stochastic Logistic Model with Infinite Delay

Abstract This paper considers an impulsive stochastic logistic model with infinite delay at the phase space Cg . Firstly, the definition of solution to an impulsive stochastic functional differential equation with infinite delay is established. Based on this definition, we show that our model has a unique global positive solution. Then we establish the sufficient conditions for extinction, nonp...

The time to extinction for an SIS-household-epidemic model

We analyse a stochastic SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e. have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable fo...

A stochastic SIS epidemic with demography: initial stages and time to extinction.

We study an open population stochastic epidemic model from the time of introduction of the disease, through a possible outbreak and to extinction. The model describes an SIS (susceptible-infective-susceptible) epidemic where all individuals, including infectious ones, reproduce at a given rate. An approximate expression for the outbreak probability is derived using a coupling argument. Further,...