Impact of predation in the spread of an infectious disease with time fractional derivative and social behavior

Abstract

The main purpose of this paper is to explore the influence of predation on the spread of a disease developed in the prey population where we assume that the prey has a social behavior. The memory of the prey and the predator measured by the time fractional derivative plays a crucial role in modeling the dynamical response in a predator–prey interaction. This memory can be modeled to articulate the involvement of interacting species by the presence of the time fractional derivative in the considered models. For the purpose of studying the complex dynamics generated by the presence of infection and the time-fractional-derivative we split our study into two cases. The first one is devoted to study the effect of a non-selective hunting on the spread of the disease, where the local stability of the equilibria is investigated. Further the backward bifurcation is obtained concerning basic reproduction rate of the infection. The second case is for explaining the impact of selecting the weakest infected prey on the edge of the herd by a predator on the prevalence of the infection, where the local behavior is scrutinized. Moreover, for the graphical representation part, a numerical simulation scheme has been achieved using the Caputo fractional derivative operator.