Classification of Asymptotic Behavior in a Stochastic SIR Model

Exact solution of a stochastic SIR model

Abstract The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible S can become infectious with an infection rate β by an infectious Itype provided that both are in contact. The Itype may recover with a rate γ and from then on stay immune. Due to the coupling between the differ...

Asymptotic Behavior of a Stochastic Discount Rate

The mean discount rate for a simple stochastic model behaves asymptotically roughly like 1/ √ n in contrast to the usual geometric discounting in a deterministic model. AMS (2000) subject classifications. 60F99, 60J05, 60G42.

Behavior of a Discrete SIR Epidemic Model

I. Introduction Infections and infectious diseases are a great burden on many societies, including the countries. An epidemic may be described as a sudden outbreak of a disease that infects a substantial portion of the population in a region before it disappears. In the nineteenth century, recurrent waves of cholera killed millions in India. The influenza epidemic of 1918-1919 killed at least 2...

A Space-Heterogeneous Stochastic SIR Model

Asymptotic behavior of a regime-switching SIR epidemic model with degenerate diffusion

*Correspondence: [email protected] School of Mathematics and Statistics, Beihua University, Jilin, China Abstract In this paper, we consider a stochastic SIR epidemic model with regime switching. The Markov semigroup theory will be employed to obtain the existence of a unique stable stationary distribution. We prove that, ifRs < 0, the disease becomes extinct exponentially; whereas ifRs > 0 and β...