A time scales approach to coinfection by opportunistic diseases

Abstract

Traditional biomedical approaches treat diseases in isolation, but the importance of synergistic disease interactions is now recognized. As a first step we present and analyze a simple coinfection model for two diseases affecting simultaneously a population. The host population is affected by the \emph{primary disease}, a long-term infection whose dynamics is described by a SIS model with demography, which facilitates individuals acquiring a second disease, \emph{secondary (or \emph{opportunistic}) disease}. The secondary disease is instead a short-term infection affecting only the primary-infected individuals. Its dynamics is also represented by a SIS model with no demography. To distinguish between short and long-term infection the complete model is written as a two time scales system. The primary disease acts at the slow time scale while the secondary disease does at the fast one, allowing a dimension reduction of the system and making its analysis tractable. We show that an opportunistic disease outbreak might change drastically the outcome of the primary epidemic process, although it does among the outcomes allowed by the primary disease. We have found situations in which either acting on the opportunistic disease transmission or recovery rates or controlling the susceptible and infected population size allow to eradicate/promote disease endemicity.