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Zbl 1194.92053
Jiang, Daqing; Ji, Chunyan; Shi, Ningzhong; Yu, Jiajia
The long time behavior of DI SIR epidemic model with stochastic perturbation. (English)
[J] J. Math. Anal. Appl. 372, No. 1, 162-180 (2010). ISSN 0022-247X

Summary: We present a differential infectivity (DI) SIR epidemic model with two categories of stochastic perturbations. The long time behavior of the two stochastic systems is studied. Mainly, we show how the solution goes around the infection-free equilibrium and the endemic equilibrium of the deterministic system under different conditions.

MSC 2000:: *92C60 Medical epidemiology
34F05 ODE with randomness
60J70 Appl. of diffusion theory
92D30 Epidemiology

Keywords: stochastic DI SIR epidemic model; Itô's formula; stochastic Lyapunov function; asymptotically stable

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