Conservation plan for Spanish Imperial Eagle via mathematical modeling

Abstract

Our planet is now in the midst of its sixth mass extinction of plants and animals. Despite evidence that diseases can increase extinction risk in wild animals (Woodroffe 1999; Daszak et al. 1999), few researchers have investigated the factors associated with disease-mediated declines or extinctions. Inspite of availability of tools and data no analytical framework is currently available to do this and predictive models are not validated against historical evidence of the interaction between risk predictors and risk change. Therefore, we urgently need to adopt strategies that limits disease mediated destruction if we want to avoid an acceleration of global extinctions. In this work we mainly focus on the dissemination of rabbit hemorrhagic disease in the rabbit population and its subsequences on Imperial Eagle population extinction. We designed a new eco-epidemiological model with simple law of mass action and Holling type-2 functional response. We perform stability analysis for both non-spatial and spatial model around the equilibrium equilibrium points. We will also gives conservation measures depending on our simulation result of the designed model system. Numerical simulation results confirm the analytical finding and generate beautiful patterns.