Effect of pollution on prey-predator system with infected predator

Abstract

In this paper, we consider effect of pollution on prey-predator model with infected predator. We have modified the prey-predator model by introducing pollutant in susceptible predator and infected predator population. The pollutant effects both susceptible and infected predator at the same rate. It is assumed that prey population grows with logistic growth rate. Local stability analysis is done for boundary and interior equilibrium point $E^*$. Further, we have proved that if the rate of infection and the rate of depletion of predator due to pollutant is less than some threshold i.e., $\beta<\beta^*$ and $g<g^*$ then $E^*$ becomes unstable and periodic solutions bifurcates from $E^*$ and thus, Hopf bifurcation occurs. Finally, persistence of the system is obtained and numerical simulations are done in support of our results using MATLAB software. https://doi.org/10.28919/cmbn/3350