English abstract
Abstract
Predator-Prey models with disease in Prey
Azza Hamood Mohammed Al-Harthy
Two models for the interaction of susceptible and infected Tilapia population with Pelican population are studied. Here, we consider that pelican interact with both susceptible and infected Tilapia proportional to their abundance. Stability near non-zero equilibri presented. It has been found that if the multiple of the rate of infection and the carrying capacity is less than the death rate of infected prey then infected fish population will disappear from ecosystem and the system will eventually become disease free. Under this condition we can save Pelican population. If the growth rate of susceptible fish is not very high then whole fish population will become infected. Hence Pelican population plays an important role to make environment disease free. In the second model, time delay is incorporated in the disease transmission term and Hopf bifurcation is analyzed by taking time delay as a bifurcation parameter. And it has been observed that the positive equilibrium point switches from stable to unstable. In the sense of ecology, Hopf bifurcation has helped us in finding the existence of a region of instability in the neighborhood of non-zero equilibrium where prey and predator populations both will survive undergoing regular fluctuations. Numerical simulations confirm the analytical results. Keywords: Susceptible Tilapia; Infected Tilapia; Pelican; switching; stability; time delay; Hopfbifurcation.
