Evolutionary implications for interactions between multiple strains of host and parasite

The interaction between multiple parasite strains within different host types may influence the evolutionary trajectories of parasites. In this article, we formulate a deterministic model with two strains of parasites and two host types in order to investigate how heterogeneities in parasite virulence and host life-history may affect the persistence and spread of diseases in natural systems. We compute the reproductive number of strain i (R(i)) independently, as well as the (conditional) "invasion" reproductive number for strains i (R(i)(j), j not equal i) when strain j is at a positive equilibrium. We show that the disease-free equilibrium is locally asymptotically stable if R(i)<1 for both strains and is unstable if R(i)>1 for one stain. We establish the criterion R(i)(j)>1 for strain i to invade strain j. Subthreshold coexistence driven by coinfection is possible even when R(i) of one strain is below 1. We identify conditions that determine the evolution of parasite specialism or generalism based on the life-history strategies employed by hosts, and investigate how host strains may influence parasite persistence.