Qualitative Study Of A HIV Infection Model With Discontinuous Treatment Measures

HIV is an human immune deficiency virus,it has been seriously threat to human health,but there is no complete cure at present.In this thesis,in order to study HIV infection systematically,an HIV infection mathematical model with discontinuous treatment measures is established,and the dynamic properties of the model are analyzed,such as the non-negativeness and boundedness of the solutions for the discontinuous treatment model,the existence of sliding mode,the existence and stability of true(false)equilibrium and pseudo-equilibrium points.This study provides theoretical basis for exploring the infection mechanism of HIV and preventing and controlling the occurrence and development of AIDS.In this thesis,we take the health CD4+T cells concentrations as cure critical value,a dynamic model of intercellular HIV infection with a single discontimuous treatment measures is established.The non-negativeness and boundedness of the solutions for the model are studied,and the globally asymptotic stability of each equilibrium is discussed by constructing suitable Lyapunov function and Dulac function.Finally,the software MATLAB is used to carry out the numerical simulations to verify the theoretical results.In addition,numerical simulations with different treatment threshold Te indicate that the inhibition effect of HIV infection is better when the treatment threshold Te is higher.In order to further describe the mechanism of HIV infection,the virus infection with CD4+T cells is introduced.At the same time,the concentrations Tc and Vc of healthy CD4+T cells and HIV are taken as the treatment critical values,a HIV infection model with two discontinuous treatments measures is established.The dynamic behavior of the sliding region of the model is studied by using the Filippov system theory,and the globally dynamical behavior of the different region of the model is discussed in different situation.The results show that the infection ADIS,the concentration of healthy CD4+T cells,infection cells and HIV tend to a stable state by adjusting the relevant parameter and critical value reasonably.At the same time,the theoretical results are verified by using the MATLAB to carry out the numerical simulations.Moreover,numerical simulations with different treatment threshold Vc indicate that the inhibition effect of HIV infection is better when the treatment threshold Vc is lower.A HIV infection model with discontinuous treatment measure is established and developed,and its dynamic behavior is analyzed and simulated.The results show that after certain treatment,the concentration of healthy cells,infected cells and HIV finally reached a stable state after the treatment of HIV infection,at the same time,increasing the treatment threshold T or decreasing the treatment threshold Vc have better inhibitory to HIV infection.