Three Species Epidemiological Model with Holling Type Functional Responses

In the analytical and numerical study, the interaction between three species is modeled, where in the three species are identified as a prey , which is susceptible, the infected prey and the predator with type-II and type-Iv functional responses, which represents a mathematical model of eco-epidemiology. This study is carried out in both analytically and numerically. The boundedness of the model is studied and the stability analysis of the model is carried out at the positive equilibrium point in terms of locally and globally. The conditions for the occurrence of Hopf bifurcation with fixed biological parameter values are investigated and also it is noticed that the bifurcation occurs by sensitive changes in the parameter values of
30,ll, and which represents the growth rate of a predator, transmission rate from infected prey to susceptible prey and half-saturation constant of predator respectively. Further, the stochastic nature of the model is analyzed both analytically and numerically. It is observed that the system exhibits chaotic behavior with the sensitive parameter values which causes large environmental fluctuations.