Reduction of HIV Infection that Includes a Delay with Cure Rate During Long Term Treatment: A Mathematical Study

Abstract

Progress towards antiviral treatment of HIV infected individual has largely been improved in recent years. From amassed literature it has been observed that antiviral treatment during disease progression can develop CTL and these CTL has an immense importance to control the disease progression. During long term treatment, CD4 and CD8 mediated immune response take part in an effective role against HIV and thus virus load is abridged monotonically or else high virus load leads to have weak immunity. Here we extended our work (Roy PK, Chatterjee AN, Chattopadhyay B (2010) Lecture notes in engineering and computer science: proceedings of the World Congress on engineering 2010:533–538) and further introduced a population model representing long term dynamics of HIV infection in response to available drug therapies considering a cure rate and a discrete time delay in the disease transmission term. We studied the model in different avenue. Our studies reveal that delay in the disease transmission term competes with the killing rate of infected T-cells as well as stimulation rate of CTL. Increasing of delay in this case makes the system progressively unstable and when delay reach to its threshold value, a periodical solution arise through Hopf bifurcation. It is also been observed that increasing value of cure rate could be able to improvise towards stability of the system inspite of delay effect.