Classification of Asymptotic Behavior in a Stochastic SIR Model
نویسندگان
چکیده
منابع مشابه
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...
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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...
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*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...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Dynamical Systems
سال: 2016
ISSN: 1536-0040
DOI: 10.1137/15m1043315