Epidemic SIS model in air-polluted environment

In this paper, the epidemic model SIS under polluted environment is investigated. Study of epidemic models often focuses on determining under what conditions the disease will disappear or it will persist. With new techniques developed for periodic stochastic differential equations, we are able to classify the longtime behavior of the epidemic model by introducing a threshold value λ . To be more specific, we show that if λ <0 then the disease-free is globally asymptotic stable, i.e., the disease will eventually disappear while the epidemic is strongly stochastically permanent provided that λ >0 . We also give some of numerical examples to illustrate our results. Moreover, the approach in this paper can be used to more general models.