Deterministic modeling for HIV and aids epidemics with viral load detectability

Abstract

We proposed and analyzed a nonlinear ordinary differential equation model for HIV and AIDS epidemics with viral load detectability and derived the interaction mechanisms between model compartments. The model is studied qualitatively and obtain a threshod parameter that represents the largest eigenvalue by using next-generation approach. Furthermore, local and global stability conditions for disease free and endemic equilibria are determined, similarly, we perfomed birfucation analysis and sensitivity analysis of the model. In addition, using the numerical results, we showed the condition on which the disease can die out (R_0^d < 1) and also when the disease invade the population (R_0^d > 1). Lastly, the results showed that people living with HIV to lower the viral loads to Undetectable level by taking the prescribed dozes as shown in Figure (7) resulting to viral suppression.