A Stochastic Differential Equation Model for HIVAIDS Transmission Dynamics in Heterosexual Populations

https://doi.org/10.51867/scimundi.maths.5.2.25

Authors

  • John Gregory Matekwa Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya https://orcid.org/0009-0006-5826-4027
  • Kennedy Nyongesa Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya
  • Frankline Tireito Department of Mathematics, Masinde Muliro University of Science and Technology, P. O. Box 190-50100, Kakamega, Kenya https://orcid.org/0000-0002-4106-4022

Keywords:

HIV/AIDS Stochastic Framework, Heterosexual Communities, Environmental Variability, Stochastic Differential Equations, Markov Chain Analysis

Abstract

This study presents a stochastic modeling framework to analyze HIV/AIDS transmission dynamics in heterosexual populations, incorporating environmental variability via stochastic perturbations. The population is divided into three compartments: susceptible S(t), infected I(t), and AIDS cases A(t). Mathematical validity is demonstrated through the analysis of positivity and boundedness of the model. Both the deterministic basic reproduction number R₀ and the stochastic reproduction number Rs₀ are derived, highlighting the significant influence of environmental noise on disease transmission. Stability analysis shows local asymptotic stability at the disease-free equilibrium when Rs₀ < 1, while an endemic equilibrium arises when Rs₀ > 1, exhibiting stochastic oscillations around deterministic predictions. The model extension to a Markov chain structure allows investigation of transition probabilities and stationary distributions under environmental variability. Multiple simulation realizations reveal considerable outcome variability despite identical parameters, underscoring the importance of stochastic effects in epidemic forecasting. This integrated modeling approach offers valuable insights for public health planning, especially in optimizing antiretroviral therapy resource allocation strategies.

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Published

2025-11-20

How to Cite

Matekwa, J. G., Nyongesa, K., & Tireito, F. (2025). A Stochastic Differential Equation Model for HIVAIDS Transmission Dynamics in Heterosexual Populations. SCIENCE MUNDI, 5(2), 262–273. https://doi.org/10.51867/scimundi.maths.5.2.25

Issue

Vol. 5 No. 2 (2025): Jul-Dec 2025

Section

Articles
Copyright & Licensing

Copyright (c) 2025 John Gregory Matekwa, Kennedy Nyongesa, Frankline Tireito

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

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