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SIS epidemic models with multiple pathogen strains. (English) Zbl 1047.92041

Summary: The dynamics of discrete-time SIS epidemic models with multiple pathogen strains are studied. The population infected with these strains may be confined to one geographic region or patch or may disperse between two patches. The models are systems of difference equations. It is the purpose of this investigation to study the persistence and extinction dynamics of multiple pathogen strains in a single patch and in two patches.
It is shown for the single patch model that the basic reproduction number determines which strain dominates and persists. The strain with the largest basic reproduction number is the one that persists and outcompetes all other strains, provided its magnitude is greater than one. However, in the two-patch epidemic model, both the dispersal probabilities and the basic reproduction numbers for each strain determine whether a strain persists. With two patches, there is a greater chance that more than one strain will coexist. Analytical results are complemented with numerical simulations to help illustrate both competitive exclusion and coexistence of pathogens strains within the host population.

MSC:

92D30 Epidemiology
39A11 Stability of difference equations (MSC2000)
37N25 Dynamical systems in biology
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