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<p>Herpes simplex virus (HSV) is a widespread infection responsible for painful blisters and ulcers. According to the World Health Organization, approximately 519.5&#xa0;million people aged 15–49 years (13.3%) worldwide are infected with herpes simplex virus type II (HSV-II), the primary cause of genital herpes. In this study, we develop a nonlinear stochastic fractional delay differential equation (SFDDE) model to describe the transmission dynamics of HSV-II in a human population. The population is divided into susceptible <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:S\left(t\right)\)</EquationSource> </InlineEquation>, exposed <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:E\left(t\right)\)</EquationSource> </InlineEquation>, asymptomatic <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:A\left(t\right)\)</EquationSource> </InlineEquation>, symptomatic <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\:I\left(t\right)\)</EquationSource> </InlineEquation>, HSV-infected <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\:H\left(t\right)\)</EquationSource> </InlineEquation>, and recovered <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\:R\left(t\right)\)</EquationSource> </InlineEquation>compartments. The model’s fundamental properties, including existence, uniqueness, positivity, and boundedness of solutions, are established. Local and global stability analyses are conducted around the HSV-free and HSV-present equilibrium points, and the basic reproduction number is derived using the next-generation matrix method along with sensitivity analysis. Numerical simulations based on a stochastic nonstandard finite difference (NSFD) scheme confirm the theoretical results and demonstrate the stability of the proposed model. These findings highlight the importance of nonlinear fractional stochastic modeling in understanding and controlling HSV-II transmission dynamics.</p>

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Nonlinear fractional stochastic delay modeling and computational analysis of herpes simplex virus type II dynamics

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月2日

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  • Ali Raza,
  • Mansoor Alsulami,
  • Marek Lampart,
  • Umar Shafique

摘要

Herpes simplex virus (HSV) is a widespread infection responsible for painful blisters and ulcers. According to the World Health Organization, approximately 519.5 million people aged 15–49 years (13.3%) worldwide are infected with herpes simplex virus type II (HSV-II), the primary cause of genital herpes. In this study, we develop a nonlinear stochastic fractional delay differential equation (SFDDE) model to describe the transmission dynamics of HSV-II in a human population. The population is divided into susceptible \(\:S\left(t\right)\) , exposed \(\:E\left(t\right)\) , asymptomatic \(\:A\left(t\right)\) , symptomatic \(\:I\left(t\right)\) , HSV-infected \(\:H\left(t\right)\) , and recovered \(\:R\left(t\right)\) compartments. The model’s fundamental properties, including existence, uniqueness, positivity, and boundedness of solutions, are established. Local and global stability analyses are conducted around the HSV-free and HSV-present equilibrium points, and the basic reproduction number is derived using the next-generation matrix method along with sensitivity analysis. Numerical simulations based on a stochastic nonstandard finite difference (NSFD) scheme confirm the theoretical results and demonstrate the stability of the proposed model. These findings highlight the importance of nonlinear fractional stochastic modeling in understanding and controlling HSV-II transmission dynamics.