Modelling a predator–prey system with infected prey in polluted environment

Abstract

a b s t r a c tA predator-prey model with logistic growth in prey is modified by introducing an SIS parasite infection in the prey. We have studied the combined effect of environmental toxicant and disease on prey-predator system. It is assumed in this paper that the environmental toxicant affects both prey and predator population and the infected prey is assumed to be more vulnerable to the toxicant and predation compared to the sound prey individuals. Thresholds are identified which determine when system persists and disease remains endemic.

A Model for the Effect of Toxicant on a Three Species Food-Chain System with "Food-Limited" Growth of Prey Population

“…where, 13 /dt to be negative definite are that the following inequalities hold: We note that the first, fourth, fifth, eleventh, twelfth and thirteenth inequalities, i.e., f 11 f 22 > f …”

“…Even at very low atmospheric deposition rates in locations remote from point sources, mercury biomagnification can result in toxic effects in consumers at the top of these aquatic food chains. Poisoning from pesticides can travel up the food chain [13,14]; for example, birds can be harmed when they eat insects and worms that have consumed pesticides. A number of studies [15,16] have shown that pesticides have had harmful effects on growth and reproduction of earthworms, which are in turn consumed by terrestrial vertebrates such as birds and small mammals.…”

Oscillatory Behavior of a Network Epidemic SIS Model with Nonlinear Infectivity

“…Hethcote et al discussed a predator-prey model with infected prey [7]. Sinha et al studied a predator-prey system with infected prey in polluted environment [8]. Those epidemic models are based on uniform mixing population.…”

Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

“…There are many researchers which have investigated the pollution models in recent years [1][2][3]. In addition, a lot of animal populations suffer from infectious disease, so some scholars investigated the predator-prey systems with diseases [4][5][6][7][8]. For example, a deterministic predator-prey model with infected predator in an impulsive polluted environment is described by the following equation: are dose-response parameter to the toxicant.…”