Dynamical analysis of a predator-prey epidemiological model with density dependent disease recovery

Abstract

An epidemiological predator-prey model with a predating scavenger species is proposed and analysed. The intermediate predator community is assumed to have a disease and is classified into infected and susceptible. The recovery of infected predators into susceptible predator is considered to be density-dependent. The role of the crowding factor of the predator population is discussed in the case of all the equilibrium points. The stability analysis for the positive equilibrium is done with the help of Routh–Hurwitz criteria. It is observed that increasing the crowding factor of the predator population promotes the stability of the positive equilibrium. A Period doubling cascade is observed for the increasing mortality rate of scavenger species. The variation of stocks of all the species is observed when mortality rates are increased. A positive effect on the biomass of the scavenger species occurs when scavenger species are removed, culled, or harvested. Finally, the proposed model is modified into a harvesting model by ignoring the mortality rate of susceptible predator and scavenger. The associated control problem has been analyzed for optimal harvesting with help of Pontryagin’s maximum principle.