Epidemic Dynamics in a Heterogeneous Incompletely Isolated Population with Allowance for Seasonal Variations in the Infection Rate

摘要

Mathematical parasite–host models are generalized to the case when the population mem-bers differ in susceptibility and contagiousness, there is an external source of infection, and the modelparameters depend periodically (seasonally) on time. The model is proved to have a periodic solutionthat is unique and exponentially stable for sufficiently small periodic oscillations of the coefficients.