Mathematical model of deforestation effects on wildlife with Holling type-II and type-III functional response

Abstract

Deforestation is the consequence of large growth in human population. The increasing human population has resulted in increasing demand for forest resources. As the forest land decreases, wildlife species that are fully dependent on forest resources will lose their food sources and natural habitat. In this paper, we present a mathematical model to study the impact of deforestation on wildlife species. The model consist of two types, namely using the Holling type II and type III functional response on interaction between wildlife and forest resources. From the result, each type of model has six equilibrium points. The extinction equilibrium point, the extinction of both human population and wildlife species equilibrium point, and the extinction of human population equilibrium point. Those three equilibrium points are unstable, while the extinction of forest resource and wildlife species equilibrium point, the extinction of wildlife species equilibrium point, and the coexistence equilibrium point are locally asymptotically stable with some conditions. Furthermore, a numerical simulation was performed to determine the comparison of population growth in the forest resources and wildlife species from both the models. Based on the analysis of the model, it can be concluded that wildlife has a level of utilization of forest resources following the Holling type III descend slower than wildlife that have utilization rates following the Holling type II. This happens because wildlife with predation level following the Holling type III will look for other forest resources if the forest resources that they normally consume are running out, as a result the forest resources in the model with the Holling type III decreased more significantly than the model with the Holling type II.