Abstract This study presents a novel fractional-order co-infection model describing the joint transmission dynamics of dengue and malaria using the generalized <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Psi -Caputo\)</EquationSource> </InlineEquation> fractional derivative. The total human population is divided into eight epidemiological compartments that account for single infections, co-infection, treatment stages, and recovery. The proposed framework incorporates memory effects and nonlocal behavior, offering a more realistic representation of disease progression compared to classical integer-order models. Local and advanced treatment strategies are introduced based on infection severity, allowing targeted intervention for both mild and co-infected cases. The fundamental mathematical properties of the model, including positivity, boundedness, existence, and uniqueness of solutions, are rigorously established. The basic reproduction number is derived, and both local and global stability of the disease-free equilibrium are analyzed using suitable Lyapunov functions. A statistical sensitivity analysis is performed to identify key parameters influencing disease transmission. Furthermore, optimal control strategies are formulated to minimize co-infection prevalence while reducing treatment and implementation costs. Numerical simulations validate the theoretical findings and demonstrate that fractional-order dynamics provide deeper insights into long-term disease behavior. The results offer valuable guidance for policymakers in designing effective and cost-efficient strategies to control dengue and malaria co-infection. Graphic Abstract The graphical abstract illustrates the overall structure, analytical framework, and key outcomes of the proposed fractional-order co-infection model for dengue and malaria. The human population is partitioned into eight epidemiological compartments representing susceptibility, exposure, asymptomatic infection, clinical infection, co-infection, treatment classes (local and advanced), and recovery. The schematic highlights the interaction between dengue and malaria transmission pathways and emphasizes the role of treatment-dependent progression. Local treatment is applied to mild and early-stage infections, whereas advanced treatment targets severe and co-infected individuals, reflecting realistic public health interventions. The model is formulated using the generalized Caputo fractional derivative, which captures memory effects and nonlocal dynamics inherent in real epidemiological processes. This fractional framework enhances the understanding of disease persistence and long-term dynamics compared to classical integer-order models. The graphical abstract also presents the computation of the basic reproduction number and illustrates disease-free equilibrium stability, supported by sensitivity analysis identifying the most influential parameters driving transmission. Additionally, the diagram integrates optimal control strategies designed to minimize infection prevalence and intervention costs. Numerical simulations demonstrate how fractional dynamics and control measures jointly reduce disease burden. Overall, the graphical abstract provides a concise visual summary of the modeling approach, mathematical analysis, treatment strategies, and policy-relevant outcomes, emphasizing the significance of fractional-order modeling in guiding effective dengue-malaria co-infection control programs.

Fractional-order Modeling and Optimal Control of Dengue-Malaria Co-infection with Local and Advanced Treatment Strategies

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发表日期：

2026年5月18日

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Puntipa Pongsumpun,
Rahim Ud Din,
Atta Ullah,
Puntani Pongsumpun

摘要

Abstract

This study presents a novel fractional-order co-infection model describing the joint transmission dynamics of dengue and malaria using the generalized \(\Psi -Caputo\) fractional derivative. The total human population is divided into eight epidemiological compartments that account for single infections, co-infection, treatment stages, and recovery. The proposed framework incorporates memory effects and nonlocal behavior, offering a more realistic representation of disease progression compared to classical integer-order models. Local and advanced treatment strategies are introduced based on infection severity, allowing targeted intervention for both mild and co-infected cases. The fundamental mathematical properties of the model, including positivity, boundedness, existence, and uniqueness of solutions, are rigorously established. The basic reproduction number is derived, and both local and global stability of the disease-free equilibrium are analyzed using suitable Lyapunov functions. A statistical sensitivity analysis is performed to identify key parameters influencing disease transmission. Furthermore, optimal control strategies are formulated to minimize co-infection prevalence while reducing treatment and implementation costs. Numerical simulations validate the theoretical findings and demonstrate that fractional-order dynamics provide deeper insights into long-term disease behavior. The results offer valuable guidance for policymakers in designing effective and cost-efficient strategies to control dengue and malaria co-infection.

Graphic Abstract

The graphical abstract illustrates the overall structure, analytical framework, and key outcomes of the proposed fractional-order co-infection model for dengue and malaria. The human population is partitioned into eight epidemiological compartments representing susceptibility, exposure, asymptomatic infection, clinical infection, co-infection, treatment classes (local and advanced), and recovery. The schematic highlights the interaction between dengue and malaria transmission pathways and emphasizes the role of treatment-dependent progression. Local treatment is applied to mild and early-stage infections, whereas advanced treatment targets severe and co-infected individuals, reflecting realistic public health interventions. The model is formulated using the generalized Caputo fractional derivative, which captures memory effects and nonlocal dynamics inherent in real epidemiological processes. This fractional framework enhances the understanding of disease persistence and long-term dynamics compared to classical integer-order models. The graphical abstract also presents the computation of the basic reproduction number and illustrates disease-free equilibrium stability, supported by sensitivity analysis identifying the most influential parameters driving transmission. Additionally, the diagram integrates optimal control strategies designed to minimize infection prevalence and intervention costs. Numerical simulations demonstrate how fractional dynamics and control measures jointly reduce disease burden. Overall, the graphical abstract provides a concise visual summary of the modeling approach, mathematical analysis, treatment strategies, and policy-relevant outcomes, emphasizing the significance of fractional-order modeling in guiding effective dengue-malaria co-infection control programs.