Impact of noise on a spatial prey-predator model with infectious prey

Abstract

In this manuscript, a temporal model is extended into classical and stochastic spatio-temporal prey-predator model. The prey population is divided into susceptible prey and infected prey population. The underlying model has five equilibrium points. The numerical solution of underlying models is obtained by an Implicit finite difference scheme. The given scheme is von Neumann stable and consistent with the continuous system. The positivity of scheme for deterministic system is established by using the M-matrix theory and induction method. 2D and 3D plots are drawn to show the efficacy of the scheme. The effect of the noise phenomena is analyzed for various noise strength. It is observed that as the noise strength is increased, the stochastic solution oscillate around the classical solution. For the low noise strength, stochastic solutions resembles with the deterministic solutions. Also, simulations endorse the analytical finding.