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    Fractional-order modeling of dengue dynamics: exploring reinfection mechanisms with the Atangana–Baleanu derivative
    (2025-08-01)
    Lamwong, Jiraporn
    ;
    Pongsumpun, Puntani
    Dengue fever poses ongoing public health challenges due to its complex reinfection dynamics and antibody-dependent enhancement (ADE). To address limitations in classical models, this study proposes a novel fractional-order model utilizing the Atangana–Baleanu–Caputo derivative to capture memory and non-local effects inherent in dengue transmission. The model explicitly incorporates reinfection mechanisms and stages of infection, offering a more accurate depiction of disease progression. The existence and uniqueness of solutions are established using fixed-point theory, and the global stability of equilibria is analyzed via Lyapunov methods. Model fitting with real-world data from Thailand in 2023 confirms predictive accuracy, while sensitivity analysis identifies the biting and mosquito mortality rates as critical parameters influencing the basic reproduction number. This framework enhances the realism of epidemic models and provides actionable insights for designing targeted public health interventions in dengue-endemic regions.
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    Dynamic of logistic model at fractional order
    (2009-12-01)
    Suansook, Yoothana
    ;
    Paithoonwattanakij, Kitti
    In this paper we have obtain the generalized form of the logistic model to arbitrary order using fractional calculus. The model is explained the population growth. The discrete version of the model have important role in studying the chaotic dynamic. The fractional calculus is feasible to evaluate the differential and integral of non integer order. This mathematical subject is helping fine tune analysis the chaotic properties of the logistic model. The numerical results show the Lyapunov exponent at various fractional orders. The positive Lyapunov exponent is indicate that the system is chaotic at fractional order. The periodic solutions of half fractional order are also present. ©2009 IEEE.