Stability Analyses of the Stochastic Delayed Infectious Models with Reinfection

Abstract

At present, the unprecedented cholera outbreak occurs in Yemen and various kinds of infectious diseases are still threat to us in the high-developed medical technology society. Hence, the strategization to control the spread of the infectious diseases becomes imperative. In the vector-borne diseases such as malaria and dengue fever, there exists time delay caused by an incubation period in the virus development in the vectors on the transmission of disease. It should be noted that there is possibility of getting reinfected in the infectious disease such as malaria. Moreover, in the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the infection, the recovery rates and the vaccination effect. Taking these facts into consideration, we propose two types of the stochastic delayed infectious models with reinfection. Since the spread of infection has reference to the stability of the disease-free steady state (DFS) of the stochastic infectious models, we analyze the stability of the DFS by using the stochastic Lyapunov theorem. By calculating the Lyapunov exponent, we study the influence of the random noise in the infectious model on each population behavior by numerical simulations.