Mathematical Analysis Of Two Classes Of Biomedical Models

Cancer and infectious diseases are two kinds of difficult problems which need to be solved urgently in modern medicine.Mathematical methods provide theoretical support for solving these medical problems,especially through the establishment of differential equation models,people can more intuitively describe some complex pathological processes.In this paper,a model of cancer cells invasion and a model of retrovirus therapy for HIV are analyzed.The invasion and spread of cancer cells have brought a great challenge to the cure of cancer,which have attracted a large number of scholars to establish corresponding mathematical models to study the biological mechanism of the invasion and spread of cancer cells in human body.In Chapter 2,we consider a tumor microenvironment model-cancer cells invasion model with homogeneous Neumann boundary conditions,which contains epithelial-like cancer cells,mesenchymal-like cancer cells,extracellular matrix and matrix-degrading enzymes.Mainly through the Banach fixed point theorem,Schauder estimation,extension of local solutions and other methods,we examine the existence and uniqueness of the local and global solutions of the model.Due to the lack of effective drugs and related treatments,HIV is still one of the main causes of death in the global population,posing a huge challenge to public health and human health.This makes the HIV models a popular infectious disease model.In Chapter 3,we consider an HIV model involving CD4+T cells and phagocytes through viral infection and intercellular viral transmission.The existence,non-negativity and boundedness of the solution are obtained by constructing the upper-lower solutions and comparison principle,and the possible equilibrium points of the model are analyze in further.Finally,we analyze the stability of the equilibrium points are analyzed by constructing Lyapunov function.