Modeling and analysis of HIV/AIDS spread in Pakistan: role of optimal control and behavioral changes

This study presents a mathematical model to analyze the spread of HIV/AIDS in Pakistan using real data from 1992 to 2020. Initially developed without control measures, the model's dynamics were explored through stability analysis. We show that the disease-free equilibrium (DFE) is locally asymptotically stable when the basic reproduction number (BRN) R0<1, and globally asymptotically stable when R0≤1. The model also exhibits a unique endemic equilibrium with a forward bifurcation. Parameter estimation was performed using the nonlinear least squares method, yielding R0≈1.0119. Sensitivity analysis identified key parameters influencing disease spread. An optimal control model incorporating prevention, treatment acceleration, and awareness interventions was developed and solved using Pontryagin's Maximum Principle. Numerical simulations indicate that combined control strategies significantly reduce HIV transmission.

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