Conserving Iberian Lynx in Europe: Issues and challenges

Existence and uniqueness of solutions are established and shown to be uniformly bounded. The basic reproduction number R0 is obtained and the occurrence of a backward bifurcation at R0=1 is shown to be possible using central manifold theory. The global stability of endemic equilibrium is established using a geometric approach. Criteria for diffusion-driven instability caused by local random movements of European rabbits and Iberian Lynx are obtained. Detailed analysis of Turing patterns formation selected by the reaction-diffusion system under zero flux boundary conditions is presented. We found that diffusion coefficients and transmission rate have appreciable influence on spatial spread of the epidemic. Numerical simulation results confirm the analytical finding and generate beautiful patterns that are consistent with the field observations and suggest that Iberian Lynx might have become extinct from Portugal and neighbouring countries. Suggestions for disease eradication and its control which in turn may increase the population of Iberian Lynx are discussed.