Controlling infection in predator-prey systems with transmission dynamics

We propose in this paper a prophylactic treatment strategy for a predator-prey system. The objective is to fight against the propagation of an infectious disease within two populations, one of which preys on the other. This propagation is modeled by means of an SIS (susceptible-infectious-susceptible) epidemic model with vital dynamics and infection propagation in both species through contact and predation, including mortality rates in both populations due directly to the disease. Treatment strategies are represented by new parameters modeling the uptake rates in the populations. We analyze the effect of various treatment strategy scenarios (prey only, predator only, or both) via their uptake rates and possible cost structures, on the size of the infected populations. We illustrate if and when applying such preventive treatments lead to a disease prevalence drop in both populations. We conduct our study using an optimal control model seeking to minimize the treatment cost(s), subject to the transmission dynamics and predator-prey dynamics.