Infection on Prey-predator System with Effect of Delay on Predator Population in Marine Ecosystem - A Mathematical Model

The current paper deals with the problem of a three-dimensional prey-predator system with infection on prey population. This three-dimensional prey-predator system is split into three groups, namely susceptible prey, infected prey and predator. Next we have introduced gestation time delay term with the equation of predator population. We observe the dynamical behaviour of this system around each of the equilibria and point out the exchange of stability of the model without time delay and with time delay. We calculate the length of time delay to maintain the stability of the delay system. We see that, there is a Hopf bifurcation with non delay and delay system respectively. In the delay system it is investigated that Hopf bifurcation happen when the time delay crosses a certain critical value. Lastly computer simulations have been carried out to illustrate various analytical results.