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Abstract

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 find general conditions under which a state of disease-free equilibrium is stable. Additionally, we find existence of a biologically relevant equilibrium where two disease strains of unequal strength coexist in a two-population system and we demonstrate that it is likely unstable.

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