Modelling In Vivo HIV Dynamics under Combined Antiretroviral Treatment

B Mobisa,J K Nthiiri,G O Lawi

doi:10.1155/2018/8276317

Abstract

In this paper a within host mathematical model for Human Immunodeficiency Virus (HIV) transmission incorporating treatment is formulated. The model takes into account the efficacy of combined antiretroviral treatment on viral growth and T cell population in the human blood. The existence of an infection free and positive endemic equilibrium is established. The basic reproduction number R0 is derived using the method of next generation matrix. We perform local and global stability analysis of the equilibria points and show that if R0<1, then the infection free equilibrium is globally asymptotically stable and theoretically the virus is cleared and the disease dies out and if R0>1, then the endemic equilibrium is globally asymptotically stable implying that the virus persists within the host. Numerical simulations are carried out to investigate the effect of treatment on the within host infection dynamics.

Highlights

Human Immunodeficiency Virus (HIV) remains a major threat to human life for the last three and half decades
Mathematical modelling of viral infections has led to greater understanding of virus dynamics and helped in predicting and controlling the spread of viral diseases such as HIV, Hepatitis B Virus (HBV), Hepatitis C Virus (HCV), and Dengue Fever
We propose a within host HIV infection model with a logistic incidence rate that explicitly incorporates the two levels of antiretroviral treatment, namely, the reverse transcriptase inhibitors (RTIs) which prevent the reverse transcription of viral RNA into DNA

Summary

Introduction

Human Immunodeficiency Virus (HIV) remains a major threat to human life for the last three and half decades. A four-dimensional system of delayed differential equations, where the production and removal rates of the virus and cells are given by general nonlinear functions, was proposed by [4] Their model investigated the dynamical behaviour of virus target and cell target incidences incorporating humoral immune response. We propose a within host HIV infection model with a logistic incidence rate that explicitly incorporates the two levels of antiretroviral treatment, namely, the reverse transcriptase inhibitors (RTIs) which prevent the reverse transcription of viral RNA into DNA. In this way the RTIs serve to reduce the rate of infection of activated CD4+T cells. A mathematical analysis of the effects of treatment on the within host infection dynamics is carried out

Model Description and Formulation

Analysis of the Model

Numerical Simulation of the Model

Conclusion