A contiunous-time SIS criss-cross model of co-infection in a heterogeneous population

Marcin Choinski #

We introduce and analyze a continuous-time model of co-infection dynamics in a heterogeneous population consisting of two subpopulations that differ in the risk of getting infected by individuals with both diseases. We assume that each parameter reflecting a given process for each subpopulation has different values, what makes the population completely heterogeneous. Moreover, we establish an epidemic spread for each disease not only in a sole subpopulation, but also criss-cross transmission. The proposed system has a disease-free stationary state and two states reflecting the presence of one disease. We indicate conditions for their existence and local stability. Investigation on the existence of a postulated endemic state corresponding to both disease’s presence leads to a complex analysis, that is why we only give an insight on this issue.