Comparison of hidden and explicit resources in ecoepidemic models of predator–prey type

Abstract

This paper investigates mathematical models of predator-prey systems where a transmissible disease spreads only among the prey species. Two mathematical models are proposed, analysed and compared to assess the influence of hidden or explicit resources for the predator. The predator is assumed to be a generalist in the first model and a specialist on two prey species in the second one. Existence and boundedness of the solutions of the models are established, as well as local and global stability and bifurcations. The equilibria of two systems possessing the same biological meaning are compared. The study shows that the relevant ecosystem behaviour including stability switching, extinction and persistence for any species depends on four important parameters, viz., the reproduction rate and the infection rate of the main prey, the mortality rate of infected prey and the reproduction rate of the alternative prey. This study ultimately indicates that the simpler formulation with the hidden resource already captures the salient features of the ecosystem. Therefore, modeling explicitly the substitute prey is not needed unless a particular emphasis is placed on the alternative resource behaviour. In such case, the extended model is preferable, at the expenses of a more complicated formulation and analysis. Ultimately, the choice of the model to be used should be guided by the reasons of its formulation and the answers that are sought.