Qualitative Analysis Of Prey Model And HIV Model

In this paper, by combining of mathematics and biology, we establish a predator-preymodel and use the theory of diferential equations to study it. By analyzing Jacobian de-terminant,the LaSalle invariant principle, using suitable Lyapunov functionas and thecenter manifold theory and delay diferential theory,we discuss the stability of the equilib-ria and the Hopf bifurcation, get several new conclusions and generalize the correspondingresults in the literature.In Chapter1,we deal with a predator-prey model with Holling type III functionalresponse incorporating a constant prey refuge:Depending on the nt prey refuge m, which provides a condition for protectingm of prey form predation and by analysis the characteristic equations, the instability andglobal stability of the equilibria is established. By use Poincare-Bendixsion Theorem, theexistence of limit cycles of the mole are obtained. We also show the influences of preyrefuge on equilibrium density values.In Chapter2, an HIV infection model with Holling type II functional response isinvestigated:an intracellular delay accounting for the time between viral entry into a target celland the production of new virus particles is investigated. By analyzing the characteristicequations and using suitable Lyapunov functionas and the LaSalle invariant principle, itis shown that threshold quantity R0is derived which determines whether the disease diesout or remains existence. In Chapter3, an HIV infection model with an intracellular delay accounting for thetime between viral entry into a target cell and the Hopf bifurcation are investigated:By analyzing the eristic equations and using the center manifold theory anddelay diferential theory, it is shown that the stability of the equilibria is established andthe direction and stability of the Hopf bifurcation are also discussed.