A non-autonomous multi-strain SIS epidemic model.

In this paper we consider a non-autonomous multi-strain SIS epidemic model with periodic coefficients. Reproduction numbers and invasion reproduction numbers are derived which agree well with their counterparts usually derived from autonomous epidemic models. With conditions on these reproduction numbers typical results are obtained, such as the local and global stability of the disease-free equilibrium. Existence and uniqueness of a single-strain periodic solution is established. Based on conditions on the invasion reproduction numbers, local stability of the single-strain periodic solution is shown. In a two-strain version of the model, conditions for uniform strong persistence are derived, and coexistence of the two strains is established. Coexistence, however, does not occur if the transmission rates of the different strains are linearly dependent.