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<p>Typhoid fever remains a persistent public health burden in low- and middle-income countries due to inadequate sanitation, antimicrobial resistance, and asymptomatic carriage. This study develops a Caputo fractional-order compartmental model to capture the memory-dependent dynamics of typhoid transmission, incorporating three core interventions: screening, sanitation, and treatment. The model stratifies the human population into susceptible, exposed, infectious, screened-infectious, and recovered compartments, coupled with an environmental reservoir of <i>Salmonella Typhi</i>. Using fractional calculus, we derive the effective reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {R}_e\)</EquationSource> </InlineEquation> and demonstrate that the disease-free equilibrium is locally asymptotically stable when <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {R}_e &lt; 1\)</EquationSource> </InlineEquation>. Positivity, boundedness, existence, uniqueness, and Hyers–Ulam stability of solutions are rigorously established. Numerical simulations reveal that higher fractional orders accelerate convergence to equilibrium, while increasing screening, sanitation effectiveness, and treatment rates substantially reduce <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {R}_e\)</EquationSource> </InlineEquation>. Contour plots further quantify synergistic intervention effects. The proposed fractional-order framework offers a more realistic representation of disease progression and control than integer-order models, providing actionable insights for typhoid elimination strategies.</p>

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Fractional-order modeling of typhoid fever dynamics with screening, sanitation, and treatment interventions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月4日

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  • Pitos Seleka Biganda,
  • Watson Levens

摘要

Typhoid fever remains a persistent public health burden in low- and middle-income countries due to inadequate sanitation, antimicrobial resistance, and asymptomatic carriage. This study develops a Caputo fractional-order compartmental model to capture the memory-dependent dynamics of typhoid transmission, incorporating three core interventions: screening, sanitation, and treatment. The model stratifies the human population into susceptible, exposed, infectious, screened-infectious, and recovered compartments, coupled with an environmental reservoir of Salmonella Typhi. Using fractional calculus, we derive the effective reproduction number \(\mathcal {R}_e\) and demonstrate that the disease-free equilibrium is locally asymptotically stable when \(\mathcal {R}_e < 1\) . Positivity, boundedness, existence, uniqueness, and Hyers–Ulam stability of solutions are rigorously established. Numerical simulations reveal that higher fractional orders accelerate convergence to equilibrium, while increasing screening, sanitation effectiveness, and treatment rates substantially reduce \(\mathcal {R}_e\) . Contour plots further quantify synergistic intervention effects. The proposed fractional-order framework offers a more realistic representation of disease progression and control than integer-order models, providing actionable insights for typhoid elimination strategies.