The Stability Analysis of Eco-Epidemiological System with Disease

Mathematical models in biology are divided into two fields the first one describe the dynamical behavior of an interacting species in ecology which is known as ecological models, while the second field, which studying the spread and control of diseases in human or animal population, is known as epidemiological model, these two majors of field of study are merged and renamed as a new field of study called eco-epidemiology which can help us to understand the natural world well from ecology and epidemic perspectives. Furthermore, we can control the transmission of diseases among different species through varying the key parameters when the dynamical behaviors of the corresponding models have been discussed clearly, in this book a prey-predator model with two infectious diseases in prey population only is proposed and analyzed. This model deals with SI and SIS epidemic diseases transmitted within the same species by contact and external source. The existence, uniqueness and boundedness of the solution are discussed. The stability analysis and local bifurcations of the model are carried out analytically as well as numerically.