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Traditional biomedical approaches treat diseases in isolation, but theimportance of synergistic disease interactions is now recognized. As a firststep we present and analyze a simple coinfection model for two diseasesaffecting simultaneously a population. The host population is affected by the\emph{primary disease}, a long-term infection whose dynamics is described by aSIS model with demography, which facilitates individuals acquiring a seconddisease, \emph{secondary (or \emph{opportunistic}) disease}. The secondarydisease is instead a short-term infection affecting only the primary-infectedindividuals. Its dynamics is also represented by a SIS model with nodemography. To distinguish between short and long-term infection the completemodel is written as a two time scales system. The primary disease acts at theslow time scale while the secondary disease does at the fast one, allowing adimension reduction of the system and making its analysis tractable. We showthat an opportunistic disease outbreak might change drastically the outcome ofthe primary epidemic process, although it does among the outcomes allowed bythe primary disease. We have found situations in which either acting on theopportunistic disease transmission or recovery rates or controlling thesusceptible and infected population size allow to eradicate/promote diseaseendemicity.

A time scales approach to coinfection by opportunistic diseases