Dynamics Of A Predator-Prey Model With Disease In Predator

To explore the problem of controlling cat population to recover the endangered bird population inisland ecosystem, we construct a predator-prey model with disease in predator. The functional responsein our model is Beddington-DeAngelis functional response. We analysis the local stability of equilibriaand discuss the e?ect of parameters with numerical simulations. Bifurcations raised by parameters are alsoanalysised. As showed in the paper, with the help of this model, we can reduce the density of cat populationsignificantly and restore the bird population.