Modelling Interacting Epidemics in Overlapping Populations

Epidemic modelling is fundamental to our understanding of biological, social and technological spreading phenomena. As conceptual frameworks for epidemiology advance, it is important they are able to elucidate empirically-observed dynamic feedback phenomena involving interactions amongst pathogenic agents in the form of syndemic and counter-syndemic effects. In this paper we model the dynamics of two types of epidemics with syndemic and counter-syndemic interaction effects in multiple possibly-overlapping populations. We derive a Markov model whose fluid limit reduces to a set of coupled SIR-type ODEs. Its numerical solution reveals some interesting multimodal behaviours, as shown in our case studies.