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In this paper we present a two species prey predat or reaction–diffusion model with Holling II functional response to study the ef fects of drought to the dynamical behaviour of wildebeest ( Connochaetustaurinus) and lion (pantheraleo) in the Serengeti ecosystem. We discretized our model equations by th e implicit Euler method and the numerical simulations were performed in Matlab. The major limiting factor for wildebeest abundance is availability of enough fora ge and predation. We varied the parameter of drought for prey and predator and obse rved that drought reduces the abundance of both species. If drought persists then i is likely to lead to extinction of both species. Further we found spatial driven variabilit ies arising when both wildebeest and lion move through diffusion processes. The results predict that diffusion of the wildebeest is motivated by search for better forage and avoidi ng predators while the diffusion of lion is motivated by hunting the prey. Our model agrees with different theoretical and empirical studies about the environmental effects t o the survival of wildebeests and lions.

Modelling Predator Prey with Diffusion for Migrating Wildebeest and Lion in the Presence of Drought