ANALYSIS OF MATHEMATICAL MODEL FOR RTI AND PI COMBINATION TREATMENT ON CD4+ T CELL

Abstract

Human Immunodeficiency Virus (HIV) is a virus that attacks the immune system, the main target of most viruses is CD4+ T cell. Reverse transcriptase inhibitors (RTI) function to inhibit the viral infection process and protease inhibitors (PI) function to block the performance of the protease enzyme which cuts the viral proteins assembled to form new viruses. The mathematical model was built with a combination of RTI and PI antiretroviral drug therapy. The basic reproduction number (ℛ0 ) is a parameter that determines the level of endemic derived from Next Generation Matrix (NGM). The non-infected equilibrium point locally asymptotically stable if ℛ0 < 1 and is unstable if ℛ0 > 1. The infected equilibrium point locally asymptotically stable when ℛ0 > 1. If 𝜂 < 𝜂𝑐𝑟𝑖𝑡, then ℛ0 > 1 and if 𝜂 > 𝜂𝑐𝑟𝑖𝑡, then ℛ0 < 1. Numerical simulation use to explain the effect of the drug where the value of the efficacy of the critical drug was 𝜂𝑐𝑟𝑖𝑡 = 0.85. Combined two drugs PI and RTI with the overall drug efficacy value η = 0.86 is effective in reducing viral infection in CD4+ T cell. Keywords: CD4+T cell, HIV, RTI, PI , Basic Reproduction Numbe