Applied Mathematics Commons^™

The goal of this paper is to motivate the need and lay the foundation for the analysis of stochastic epidemiological models with seasonal forcing.We consider stochastic SIS and SIR epidemic models, where the internal noise is due to the random interactions of individuals in the population. We provide an overview of the general theoretic framework that allows one to understand noise-induced rare events, such as spontaneous disease extinction. Although there are many paths to extinction, there is one path termed the optimal path that is probabilistically most likely to occur. By extending the theory, we have identified the quasi-stationary solutions …

The goal of this paper is to motivate the need and lay the foundation for the analysis of stochastic epidemiological models with seasonal forcing.We consider stochastic SIS and SIR epidemic models, where the internal noise is due to the random interactions of individuals in the population. We provide an overview of the general theoretic framework that allows one to understand noise-induced rare events, such as spontaneous disease extinction. Although there are many paths to extinction, there is one path termed the optimal path that is probabilistically most likely to occur. By extending the theory, we have identified the quasi-stationary solutions …

Viruses and bacteria responsible for infectious diseases often mutate and are carried between geographical regions. We consider a mathematical model which begins to account for these factors. We assume two disjoint populations that only occasionally co-mingle and two strains of a disease present in these populations. Of interest are the equations describing the dynamics of this system, the conditions under which epidemics will occur, and the long term behavior of the system under various initial conditions. We fi#12;nd general conditions

under which a state of disease-free equilibrium is stable. Additionally, we #12;find existence of a biologically relevant equilibrium where two …