Analysis Of Two Kinds Infectious Disease Models Affected By Stochastic Disturbance

Studying dynamics of infectious diseases mainly makes qualitative and quantitative analysis through mathematical models,which contributes to the understanding of the transmission mechanism of infectious diseases and the effective prevention and control of diseases.In this paper,two kinds of infectious disease models affected by white noise are established and analyzed based on relevant theoretical knowledge.In the third chapter,a stochastic SIRS type epidemic model with nonlinear incidence is discussed.We obtain a threshold of the stochastic model which determines the extinction and persistence of the epidemic.Compared with the corresponding deterministic model,the threshold of the stochastic model affected by white noise is smaller than the basic reproduction number of the deterministic model.When the noise is small,the stochastic model exists a disease-free absorbing set which implies that the disease dies out with probability one.When the noise is large,it will suppress the epidemic from prevailing.These results are illustrated by computer simulations.In the fourth chapter,a stochastic delayed SIR type epidemic model with temporary immunity and double diseases is studied.Establishing sufficient conditions for extinction and persistence in the mean of the two diseases.Obtaining the threshold between extinction and persistence in the mean of the stochastic system.It is shown that:（i）time delay and environmental white noise have important effects on the extinction and persistence of the two diseases;（ii）the two diseases can coexist under certain conditions.