A Predator-Prey Model with Logistic Growth for Constant Delayed Migration

Abstract

Predator prey models predict a broad range of results depending on characteristics of predators, prey and the environment in which they interact. The environment in which these species live in and interact is usually made up of many patches, and these patches are connected via migration. The instantaneous migration of these species from one patch to another may not be realistic since there may be barriers during migration such as a busy infrastructure through the natural habitat. A predator-prey model, with logistic growth for both species and constant delayed migration, is developed and analyzed in this paper. It is shown that these species will survive if they migrate at higher rates in search of sustaining resources. Thus, for the species to coexist, we recommend that factors that slow down migration rates should be addressed, for example, reducing human activities and settlement in natural habitat.