The effect of immigration of infectives on disease-free equilibria

摘要

Many disease transmission models exhibit a threshold behaviour based on the basic reproduction number R0, where the disease-free equilibrium is locally asymptotically stable if R0<1 and unstable if R0>1. However, if a system includes immigration of infected individuals, then there is no disease-free equilibrium. We consider how the disease-free equilibrium moves as the level of immigration of infected individuals is increased from 0, finding, under mild assumptions, that the disease-free equilibrium becomes an endemic equilibrium if R0<1 and leaves the biologically relevant space (by having at least one coordinate become negative) if R0>1.