Integrated Mathematical Modeling of HIV Transmission Dynamics in Conflict-Affected Populations: A Static Risk Equation and Optimal Control Framework

Human immunodeficiency virus (HIV) remains a major global public health challenge, with conflict-affected populations experiencing heightened vulnerability due to healthcare disruption, forced displacement, and conflict-related sexual violence. Despite extensive advances in HIV mathematical modeling, limited attention has been given to the combined effects of armed conflict, mass rape, and disrupted healthcare systems on HIV transmission dynamics. This dissertation develops an integrated modeling framework to investigate the impact of conflict-driven mass rape on HIV transmission and evaluate intervention strategies in conflict-affected settings, with emphasis on the Tigrai conflict in Ethiopia. The framework integrates three complementary approaches: a static risk equation model (SREM), a deterministic compartmental transmission model incorporating a rape-exposed infectious compartment (Ir), and an optimal control framework. The SREM, calibrated using Monte Carlo simulation (10,000 iterations), quantifies excess HIV infections attributable to conflict-related mass rape. Findings indicate that, under intermediate conflict intensity, mass rape contributes a median of 112 additional annual HIV infections among women aged 5–49 years (interquartile range:55–235), a 12.6% increase in annual HIV incidence. Sensitivity analysis identifies conflict intensity as the strongest determinant of HIV risk, followed by rapeprevalence, while health system functionality emerges as the most influential protective factor. The deterministic compartmental model is analyzed to examine epidemiological dynamics and qualitative properties of disease transmission. The basic reproduction number R0 is derived, with R0 < 1 indicating disease elimina tion and R0 > 1 indicating sustained transmission without effective interventions. Equilibrium and stability analyses establish global stability of both disease-free and endemic equilibria using Lyapunov methods, while bifurcation analysis reveals for ward bifurcation only, implying that R0 < 1 is sufficient for disease elimination. The model is extended to an optimal control problem incorporating post-exposure prophylaxis (PEP), antiretroviral therapy (ART), and structural protection to reduce rape exposure. Necessary optimality conditions are derived using Pon tryagin’s Maximum Principle and solved numerically. Numerical simulations and cost-effectiveness analysis demonstrate that combined PEP and ART produces the greatest reduction in HIV burden and is the most cost-effective intervention. The findings provide quantitative insights to support HIV prevention and recovery planning in post-conflict Tigrai. Recognizing substantial uncertainty in conflict settings, the framework is intended as an analytical tool for exploring plausible interactions among conflict intensity, healthcare disruption, sexual violence, and treatment interventions. Beyond the Tigrai context, the study contributes a uni fied, scenario-based mathematical framework for assessing HIV transmission and informing intervention prioritization in other conflict-affected populations.