A Prey-Predator Mathematical Model With Disease Infection And Treatment In Both Prey And Predator Population

Abstract

We know that the infectious disease plays important roles in the dynamics of a predator prey system with infection in prey and predator population. But in our model system infection in predator plays an important role since the inclusion of disease in predator population and the transmission of disease from infected prey to predator in our model is vital modification of most of the earlier models. So, we have focused our study in observing the role of infection and transmission rate upon predator prey dynamics. The combined effect of infection and predator on prey population leads to a larger effect on the dynamics of the population sizes. In this study a prey predator system is considered. Both population is categorized into susceptible and infected due to the presence of disease and population under treatment is included into the model. Predators are assumed to consume both the susceptible and infected prey with some partial preference given to susceptible ones. Thus, a mathematical model is developed to describing the population dynamics of susceptible prey Infected prey Predator system. Positivity and boundedness of the model are verified. The equilibrium points is found and analysed. Simulation study is conducted so as to verify the results of mathematical analysis. Different simulation scenarios are presented by assigning varying values to the parameters of the system using mathlab. Lastly, conclusions of the results are forwarded.