Mathematical Analysis of Non-Autonomous HIV/AIDS Transmission Dynamics with Efficient and Cost-Effective Intervention Strategies (Contemporary Mathematics, 2025)
This study focuses on the analysis of a controlled dynamical system for the time evolution of Human Immunodeficiency Virus/Acquired Immunodeficiency Syndrome (HIV/AIDS) incorporating vertical (mother-to-child) transmission route of HIV and saturated treatment as two distinguishing factors. The impact of key epidemiological parameters of the model on the basic reproduction number is assessed via sensitivity analysis based on the normalized forward sensitivity approach. As a consequence of the sensitivity analysis, three time-dependent control intervention strategies including, therapeutic measure responsible for blocking vertical transmission route of HIV, condom usage measure, and treatment efforts with highly active anti-retroviral treatment (HAART) are considered to hinder HIV/AIDS transmission in the population. The non-autonomous system is analysed using optimal control theory, the existence of optimal control is qualitatively analysed and the optimal control triple is characterized by the famous Pontryagin’s maximum principle. The optimal control triple considered are categorized into three different policies combining any two of the interventions namely, Policy A (combination of vertical transmission preventive effort and control intervention for condom measure); Policy B (combination of vertical transmission preventive effort and treatment measure with HAART); and Policy C (combination of condom usage measure and treatment effort), and detailed analyses of the efficiency and economic methodologies are explored. It is shown among other findings that Policy C is the most efficient and most cost-effective intervention. Therefore, the policy that averts highest cases of HIV/AIDS is recommended. The study emphasizes the importance of cost-effective intervention policies in resource-limited settings, which is crucial for policymakers.
Keywords: HIV/AIDS model; vertical transmission; saturated treatment; optimal control; efficiency index; cost-effectiveness ratio