The Threshold Dynamics Of A Time-periodic Two-strain SIRS Model With Distributed Delay

Since the influence of ecological environment,various antiviral drugs,biological evo-lution and other factors,the pathogen mutation is more frequent.The mutation of the pathogen increases the duration of the host's infection,therefore the variation of pathogens is of great significance for the spread and prevention of epidemic.In addition,considering the influence of different individual immunity on the latent period of epidemic,so it is necessary to study epidemic with distributed delay.In this paper,a two strain SIRS epidemic model with distributed delay and spatiotemporal heterogeneity is proposed and investigated.We firstly introduce the basic reproduction number R0i and the invasion number R0i(i=1,2)for each strain i.Then the threshold dynamics of the model is established in terms of R0i and R0i by using the theory of chain transitive sets and persistence.It is shown that,if Ro>1(i=1,2),then the two strains will always persist uniformly;If R0i>1? R0j(i ? j,i,j=1,2),the i-th strain will persist uniformly,but the j-th strain will disappear.If R0i<1 or R0i=1(i=1,2)and ?i(x,t)>0,the two strains will disappear.