期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
卷 21, 期 10, 页码 3429-3440出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2016105
关键词
SIR model; extinction; permanence; stationary distribution; ergodicity
资金
- Vietnam Institute for Advance Study in Mathematics (VIASM)
- Vietnam National Foundation for Science and Technology Development (NAFOSTED) [101.03-2014.58]
In this paper, we consider a stochastic SIR model with the perturbed disease transmission coefficient. We determine the threshold lambda that is used to classify the extinction and permanence of the disease. Precisely, lambda < 0 implies that the disease-free (alpha/mu,0,0) is globally asymptotic stable, i.e., the disease will disappear and the entire population will become susceptible individuals. If lambda > 0 the epidemic takes place. In this case, we derive that the Markov process (S(t),I(t)) has a unique invariant probability measure. We also characterize the support of a unique invariant probability measure and prove that the transition probability converges to this invariant measures in total variation norm. Our result is considered as an significant improvement over the results in [6, 7, 11, 18]
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