Application of the Adam-Bashforth-Moulton Method to a Fractional-Order Mathematical Model of Dengue with Vector and Non-Vector Pathways
Keywords:
Fractional-order modeling, Dengue transmission dynamics, Adam-Bashforth-Moulton method, Memory effects in epidemiology, Infectious disease modelingAbstract
This study presents a novel fractional-order dengue virus transmission model that integrates vector and non-vector pathways. The model employs the Adam-Bashforth-Moulton (ABM) method to account for memory effects and long-term dependencies, offering a more accurate depiction of disease dynamics compared to traditional methods like the 4th-order Runge-Kutta method (RKM4). The fractional-order framework captures nonlinear interactions among human and mosquito populations, reflecting key epidemiological transitions, including susceptibility, exposure, infection, vaccination, and recovery. Simulation results demonstrate the superiority of ABM in predicting population dynamics, particularly in exposed and infectious compartments, while highlighting deviations in classical methods over time. Phase plots and absolute error analysis further underscore the accuracy and reliability of ABM in solving fractional-order systems. By comparing the results with recent literature, this study emphasizes the critical role of fractional-order methods in infectious disease modeling, addressing limitations in classical approaches and providing insights for public health interventions. These findings contribute to the growing body of knowledge advocating the use of fractional-order techniques for understanding complex epidemiological systems and informing effective disease control strategies.
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