Dynamics Of Predator-Prey Models - Wuhaib, Sufyan Abaas (2013)
In this thesis, we studied a number of predator prey system involving factors such as infections, harvesting, phase structure, constant and random refuges and frequent encounters of predator and prey. Through analysis and comparison we found the effect of the infection on the existence and the stability of populations systems; this stability may turn into instability and sometimes into simple Hopf bifurcation. It was also found that harvesting does not affect the existence and stability of systems, but affects the disease, and thus can be used to control the disease, tak- ing into account that excessive harvesting may lead to extinction of communities. We employ the basic reproduction number to construct regions, whereby in these regions all populations survive, disease under control and the continuation of the harvest guaranteed. We propose an optimal harvest policy in that the harvest begins in the initial stages of the presence of disease and this ensures the disease is under control and prevent it from spreading. Another factor affecting disease is the stage structure of the predator. In this model, the prey becomes infected while the predator is divided into two groups, mature and immature. When the disease disap- pears, the model consists of susceptible prey, immature and mature predator and this model is stable. The prey sometimes uses places to escape from the predator and these places are called refuges. The refuges affect the stability of the models and the existence of populations. We studied constant and random refuges to show that the constant refuges are better than random refuges; they are more stable and offer a better chance of survival than random refuges. We next study models of the food chain.