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Comparative Analysis of Stochastic and Predictable Models in the HIV Epidemic Across Genders

This study conducts a comparative analysis of stochastic and deterministic models to better understand the dynamics of the HIV epidemic across genders. By incorporating gender-specific transmission probabilities and treatment uptake rates, the research addresses gaps in existing models that often overlook these critical factors. The introduction of gender-specific treatment, where only one gender receives treatment, allows for a detailed examination of its effects on both male and female populations. Two compartmental models, divided by gender, are analyzed in parallel to identify the parameters that most significantly impact the control of infected populations and the number of treated females. Stochastic methods, including the Euler, Runge-Kutta, and Non-Standard Finite Difference (SNSFD) approaches, demonstrate that stochastic models provide a more accurate and realistic portrayal of HIV transmission and progression compared to deterministic models. Key findings reveal that the stochastic Runge-Kutta method is particularly effective in capturing the epidemic's complex dynamics, such as subtle fluctuations in transmission and population changes. The study also emphasizes the crucial role of transmission probabilities and treatment rates in shaping the epidemic's trajectory, highlighting their importance for optimizing public health interventions. The research concludes that advanced stochastic modeling is essential for improving public health policies and responses, especially in resource-constrained settings.

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