The Dynamic Behavior Of Mathematical Model Of Pathogenesis Of Plasmodium Falciparum

Malaria has been one of the major diseases that threaten human health.The pathogenesis of plasmodium falciparum is an important subject in the study of theoretic and medical researchers.A new medical research shows that falciparum can escape the host's natural immune system.In this thesis,mathematical models are established to explain the above phenomena,and the stability and threshold of the models are studied.In the second and third chapters,we study the existence,stability of the e-quilibrium point and the threshold R0.For the model without time delay,it is a model of ordinary differential equations.The disease-free equilibrium is globally asymptotically stable provided R0<1.If 1<R0<1+d3?/d1?,the boundary equilib?rium is globally asymptotically stable.If R0>1d3?/d1?,then there exists a unique positive equilibrium,and it is globally asymptotically stable.For the model with time delay,a sufficient condition is given to ensure that the positive equilibrium is locally asymptotically stable.Hopf bifurcation in positive equilibrium with respect to the time delay r is also addressed.In the fourth chapter,the disease-free equilibrium is globally asymptotically stable provided R0<1,If 1<R0<1+d3?/d1(?-d3g)~p,the boundary equilibrium is locally asymptotically stable.If R0>1+ d3?/d1(?-d3g),we explore the steady state of the positive equilibrium,and stable positive equilibrium can be changed to unsta-ble,what Hopf branches appear nearby.