Stability Analysis Of An HIV Model With Drug Resistance

Infectious disease is a disease which can be caused in a population or between animals and plants.A pathogen,such as bacteria,viruses,parasites or fungi,invades the body and causes the disease.The pathogens multiply or develop in normal cells.The virus destroys its function and causes the infected person to have the disease or even die.AIDS is one of the "killers" that threaten human health.So far,there is no any effective vaccines or effective drugs have been developed to eradicate AIDS.Using mathematical models in AIDS study will help people to better understand the mechanism of transmission of HIV,and get the right prevention strategy and control policy.Furthermore,human body's immune system has a memory function,and the fractional order differential equations just have this property,therefore,the introduction of fractional order models in HIV study is of great significance.In this paper,firstly one HIV model with drug resistance and cell to cell trans-mission has been studied.We have got the sensitive basic reproduction number Rs and drug resistant basic reproduction number Rr related to subsystems.The sufficient condition has been set for global asymptotic stability of the disease-free equilibrium,two boundary equilibria and the unique endemic equilibrium.Secondly,one factional order differential equation model of HIV with drug resistance has been studied.The existence and uniqueness of the equilibrium points were proved.By constructing suitable Lyapunov function,the global asymptotic stability condition has been obtained.Finally,the correctness of theoretical results has been verified by numerical simulation using Matlab.