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The long time behavior of DI SIR epidemic model with stochastic perturbation. (English) Zbl 1194.92053
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:
92C60Medical epidemiology
34F05ODE with randomness
60J70Applications of Brownian motions and diffusion theory
92D30Epidemiology
References:
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