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<p>Dengue transmission, nowadays, becomes a growing global health threat specially in tropical and subtropical regions. In our present work, we develop a nine-compartmental ordinary differential equation model of dengue transmission, incorporating a nonlinear saturated incidence rate with the effect of social awareness. Using the next-generation matrix method, we derive the basic reproduction numbers for humans (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(R_{0}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>) and mosquito (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R_{m}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>m</mi> </msub> </math></EquationSource> </InlineEquation>), and analyze the existence and stability of disease-free and endemic equilibria. The model exhibits a bifurcation at <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(R_{0}=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. We then introduce two controls—mosquito insecticide and human treatment—formulating an objective functional to minimize infections and associated costs. Cost-effectiveness is evaluated using the Incremental Cost-Effectiveness Ratio (ICER) and Infection Averted Ratio (IAR), showing insecticide as most effective under IAR and treatment as most effective under ICER. Sensitivity analysis highlights parameter influence on disease dynamics, and results confirm that incorporating social awareness reduces transmission. All analytical findings are validated by numerical simulations.</p>

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Modeling dengue transmission dynamics: a non-linear framework with social awareness and optimal control measures

  • 期刊论文

  • 发表日期：

    2025年10月31日

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  • Swarnali Sharma,
  • Gayatri Roy,
  • Soovoojeet Jana,
  • Debjit Pal,
  • Dipak Kesh

摘要

Dengue transmission, nowadays, becomes a growing global health threat specially in tropical and subtropical regions. In our present work, we develop a nine-compartmental ordinary differential equation model of dengue transmission, incorporating a nonlinear saturated incidence rate with the effect of social awareness. Using the next-generation matrix method, we derive the basic reproduction numbers for humans ( \(R_{0}\) R 0 ) and mosquito ( \(R_{m}\) R m ), and analyze the existence and stability of disease-free and endemic equilibria. The model exhibits a bifurcation at \(R_{0}=1\) R 0 = 1 . We then introduce two controls—mosquito insecticide and human treatment—formulating an objective functional to minimize infections and associated costs. Cost-effectiveness is evaluated using the Incremental Cost-Effectiveness Ratio (ICER) and Infection Averted Ratio (IAR), showing insecticide as most effective under IAR and treatment as most effective under ICER. Sensitivity analysis highlights parameter influence on disease dynamics, and results confirm that incorporating social awareness reduces transmission. All analytical findings are validated by numerical simulations.