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

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

Autores

  • 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

Palavras-chave:

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

Resumo

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.

Downloads

Não há dados estatísticos.
Dimensions

Din, A., & Li, Y. (2024). Optimizing HIV/AIDS dynamics: stochastic control strategies with education and treatment. The European Physical Journal Plus, 139(9), 812. https://doi.org/10.1140/epjp/s13360-024-05605-1 DOI: https://doi.org/10.1140/epjp/s13360-024-05605-1

Daqing J., Chunyan J., Ningzhong S., (2010) The long time behavior of DI SIR epidemic model with stochastic perturbation. J. Math. Anal. Appl. 372: 162-180. https://doi.org/10.1016/j.jmaa.2010.06.003 DOI: https://doi.org/10.1016/j.jmaa.2010.06.003

Gard T. (2002). Introduction to stochastic differential equations. Math. Biosci.

Tornatore, E., Buccellato, S. M., & Vetro, P. (2005). Stability of a stochastic SIR system. Physica A: Statistical Mechanics and its Applications, 354, 111-126. https://doi.org/10.1016/j.physa.2005.02.057

Kimulu, A. M., Mutuku, W. N., Mwallii, S. M., Malonza, D., & Oke, A. S. (2022). Mathematical Modelling of the Effects Funding on HIV Dynamics Among Truckers and Female Sex Workers Along the Kenyan Northern Corridor Highway.

Meng X. (2000). Stability of a novel stochastic epidemic model with double epidemic hypothesis. New York: Dekker.

Mutwiwa, J. M., Nthiiri, J. K., & Kwach, O. (2018). Mathematical modelling of the role of interference on the transmission dynamics and management of Hiv and Aids.

https://doi.org/10.9734/JAMCS/2018/42819 DOI: https://doi.org/10.9734/JAMCS/2018/42819

Perelson A.S, Nelson, P.W. (1999). Mathematical analysis of HIV-I dynamics in vivo. SIAM Rev.

https://doi.org/10.1137/S0036144598335107 DOI: https://doi.org/10.1137/S0036144598335107

Tornatore E, Buccellato S, Vetro P. (2005). Stability of a stochastic SIR system. Phys A 2005;354:111-26. https://doi.org/10.1016/j.physa.2005.02.057 DOI: https://doi.org/10.1016/j.physa.2005.02.057

Zwahlen, M., Egger, M. (2006). Progression and mortality of untreated HIV-positive individuals living in resource-limited settings.

Meyn, S. P., & Tweedie, R. L. (2009). Markov chains and stochastic stability (2nd ed.). Cambridge University Press. https://doi.org/10.1017/CBO9780511626630 DOI: https://doi.org/10.1017/CBO9780511626630

Roberts, G. O., & Rosenthal, J. S. (2004). General state space Markov chains and MCMC algorithms.

https://doi.org/10.1214/154957804100000024 DOI: https://doi.org/10.1214/154957804100000024

Publicado

2025-11-20

Como Citar

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

Edição

Vol. 5 N.º 2 (2025): Jul-Dec 2025

Secção

Articles
Copyright & Licensing

Direitos de Autor (c) 2025 John Gregory Matekwa, Kennedy Nyongesa, Frankline Tireito

Creative Commons License

Este trabalho encontra-se publicado com a Creative Commons Atribuição-NãoComercial 4.0.

Crossref
Scopus
Google Scholar
Europe PMC