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<p>This study investigates the influence of non-local memory effects on the nonlinear dynamics of malaria transmission using a fractional-order human mosquito model formulated in the Atangana–Baleanu–Caputo (ABC) sense. The model incorporates a non-singular kernel to capture hereditary characteristics inherent in epidemiological processes, with the fractional order acting as a control parameter governing system dynamics. Analytical results establish positivity, boundedness, and the existence of unique solutions, while stability conditions for disease-free and endemic equilibria are derived. Although the classical threshold structure governed by the basic reproduction number is preserved, the inclusion of memory effects produces significant qualitative changes in transient behavior. Specifically, decreasing the fractional order delays epidemic peaks, reduces infection intensity, and yields smoother convergence toward equilibrium, indicating a memory-induced modulation of nonlinear dynamics. Model parameters are calibrated using malaria incidence data from <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2000--2023\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2000</mn> <mo>-</mo> <mo>-</mo> <mn>2023</mn> </mrow> </math></EquationSource> </InlineEquation>, and numerical simulations confirm the robustness of these effects. The findings demonstrate that fractional dynamics fundamentally reshape transient epidemic evolution, providing new insight into memory-driven processes in complex biological systems and nonlinear epidemiological modeling.</p>

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Memory-induced nonlinear dynamics in a fractional human–mosquito malaria model with data-driven insights

  • 期刊论文

  • 发表日期：

    2026年7月25日

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  • Aastha Ramoliya,
  • Avani Solanki,
  • Kunjan Shah

摘要

This study investigates the influence of non-local memory effects on the nonlinear dynamics of malaria transmission using a fractional-order human mosquito model formulated in the Atangana–Baleanu–Caputo (ABC) sense. The model incorporates a non-singular kernel to capture hereditary characteristics inherent in epidemiological processes, with the fractional order acting as a control parameter governing system dynamics. Analytical results establish positivity, boundedness, and the existence of unique solutions, while stability conditions for disease-free and endemic equilibria are derived. Although the classical threshold structure governed by the basic reproduction number is preserved, the inclusion of memory effects produces significant qualitative changes in transient behavior. Specifically, decreasing the fractional order delays epidemic peaks, reduces infection intensity, and yields smoother convergence toward equilibrium, indicating a memory-induced modulation of nonlinear dynamics. Model parameters are calibrated using malaria incidence data from \(2000--2023\) 2000 - - 2023 , and numerical simulations confirm the robustness of these effects. The findings demonstrate that fractional dynamics fundamentally reshape transient epidemic evolution, providing new insight into memory-driven processes in complex biological systems and nonlinear epidemiological modeling.