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<p>In this study, we propose and study the effect of environmental stochasticity which is introduced by perturbing the horizontal transmission rate of infection in an HIV/AIDS epidemic model with vertical transmission. We demonstrate that the proposed stochastic model admits a unique global positive solution. We explore the asymptotic behavior of stochastic model around equilibria. The sufficient conditions under which the stochastic model can maintain exponential stability at the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1627_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(p^{th}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>p</mi> <mrow> <mi mathvariant="italic">th</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> moment are given. We also develop a criteria for the extinction and persistence in mean of the disease. Additionally, we devise an HIV/AIDS model that encompassing time-dependent prevention strategies. We derive the characteristics of control measures for deterministic as well as stochastic control model by adapting Pontryagin’s maximum principle and stochastic maximum principle, respectively. Ultimately our analytical findings are verified with numerical simulations.</p>

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Threshold dynamics of an HIV/AIDS infection model with optimal control strategies in presence of deterministic and fluctuating environments

  • 期刊论文

  • 发表日期：

    2025年3月17日

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  • M. Senthilkumaran,
  • M. Pitchaimani,
  • K. Ponmari

摘要

In this study, we propose and study the effect of environmental stochasticity which is introduced by perturbing the horizontal transmission rate of infection in an HIV/AIDS epidemic model with vertical transmission. We demonstrate that the proposed stochastic model admits a unique global positive solution. We explore the asymptotic behavior of stochastic model around equilibria. The sufficient conditions under which the stochastic model can maintain exponential stability at the \(p^{th}\) p th moment are given. We also develop a criteria for the extinction and persistence in mean of the disease. Additionally, we devise an HIV/AIDS model that encompassing time-dependent prevention strategies. We derive the characteristics of control measures for deterministic as well as stochastic control model by adapting Pontryagin’s maximum principle and stochastic maximum principle, respectively. Ultimately our analytical findings are verified with numerical simulations.