The Dynamic Behavior Of Two Stochastic SIS Epidemic Models

In real life,environmental noise often affects the outbreak of infectious dis-eases,so it is necessary to add the noise item to infectious disease model.S-ince different noises have different effects on the spread of infectious diseases,hence we study a stochastic multistrain SIS model with superinfective and white noise and a stochastic SIS epidemic model incorporating the mean-reverting Ornstein-Uhlenbeck process and Square-Root diffusion noise respectively.Firstly,we study a stochastic multistrain SIS model where a more infec-tive strain can superinfect an individual infected by another strain and get the stochastic reproductive number R0k,i.e.the threshold of different strains.The results show that if R0k<1 for all k?{1,2,…,n} the strains will extinct,the disease will die out;if R0k>1 for some k?{1,2,…,n},the k-th strain will exist,the disease will persistence in the mean.Finally,the theoretical results are applied to the three-strain model and verified by numerical simulationsAlso,we study the long time behavior of a SDE SIS epidemic model in-corporating the mean-reverting Ornstein-Uhlenbeck process and Square-Root diffusion noise by defining the stochastic reproductive number R0s in the third chapter.The results show that if R0s<17 the disease will be extinct almost surely(a.s.);if R0s>17 the disease will persist a.s.Meanwhile,we find that smaller speed of reversion and the intensity of Square-Root diffusion noise or bigger intensity of volatility can suppress the outbreak of the disease.Furthermore,we also give the existing condition of the stationary distribution of our model and the mean and variance of the stationary distribution.Finally,the numerical simulations verify the theoretical results.