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Atangana-Baleanu fractional optimal control for dengue dynamics with stability analysis
(2025-08-01)
Lamwong, Jiraporn
;
Pongsumpun, Puntani
Dengue fever remains a critical public health concern, particularly in regions like Thailand, where the disease exhibits complex transmission dynamics involving human and mosquito populations. Traditional models often fail to address the intricacies of non-local interactions, memory effects, and control dynamics. This research introduces an innovative approach using fractional optimal control problems (FOCPs) integrated with the Atangana-Baleanu fractional derivative in the Caputo sense. The model stratifies human and mosquito populations into detailed compartments, enabling a granular representation of transmission dynamics. The FOCP framework leverages fractional-order equations to incorporate memory-dependent and non-local interactions, ensuring biological feasibility and predictive accuracy. Computational results reveal that the model aligns closely with observed data for dengue fever, dengue hemorrhagic fever, and dengue shock syndrome across fractional orders ranging from 0.83 to 1.00. Sensitivity analyses identify critical parameters, such as biting rates and initial population sizes, as pivotal to disease control. The findings underscore the effectiveness of FOCPs in optimizing public health interventions, offer a robust tool for minimizing infection rates and associated costs. The theoretical global stability analysis confirms the model's reliability in predicting long-term outcomes under varying epidemiological scenarios. Future research could extend this framework to incorporate environmental variables, co-infections, and vaccination strategies, enhancing its applicability across diverse public health challenges. This study represents a significant step forward in the mathematical modeling of epidemic diseases, particularly in optimizing control measures for dengue fever.
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Modeling the spread of hand, foot, and mouth disease using ABC fractional derivatives: a focus on environmental and vaccination impacts in children
(2025-04-01)
Lamwong, Jiraporn
;
Pongsumpun, Puntani
This research focuses on modeling the spread of Hand, Foot, and Mouth Disease (HFMD) among children below the age of 15 using the Atangana-Baleanu Caputo (ABC) fractional derivative. The model incorporates both environmental contamination and vaccination effects to better capture the transmission dynamics of HFMD. The fractional derivative accounts for memory effects, which are crucial in understanding the prolonged impact of past infection rates on the current epidemic dynamics. Real outbreak data from Thailand (May 2023 to October 2023) was used to fit the model parameters through optimization using the fminunc algorithm in MATLAB. The results showed that the model successfully captured key phases of the epidemic, including the initial rise, peak, and decline in cases, as well as a secondary wave of infections. Notably, incorporating memory effects through the ABC fractional derivative enhanced the accuracy of predictions regarding the epidemic’s duration and severity. Furthermore, our analysis of the basic reproduction number (R<inf>0</inf>) and global stability confirmed vaccination's effectiveness in controlling the disease's spread. These findings suggest that the model can serve as a valuable tool for informing public health interventions, particularly in environments with high child population densities such as schools and daycare centers. Future research may explore the application of this model to other infectious diseases and investigate additional factors such as varying immunity levels and seasonal variations.
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A fractional derivative model of the dynamic of dengue transmission based on seasonal factors in Thailand
(2025-03-15)
Lamwong, Jiraporn
;
Pongsumpun, Puntani
Climate variability affects the changes in controlling diseases transferred by insects. An increase in the population, the growth of communities, and a lack of public health infrastructure bring about the return of diseases of which insects are carriers, one of the illness issues. Therefore, the disease control is significant to help reduce the burden on the government and strengthen the country's public health structure. This research proposes a novel approach to modeling dengue fever dynamics, we employ a fractional derivative model with the Atangana–Baleanu–Caputo derivative, which offers a more accurate representation of real-world disease dynamics compared to traditional integer-order models. Basic qualifications are proposed. Equilibrium points and basic reproduction numbers are analyzed. The next-generation matrix method is used to identify the transmission. Besides, parameter sensitivity analysis is performed to learn about factors affecting input parameter values' effects on the basic reproduction number. It was found that the most common parameter affecting the transmission was the biting rate of mosquitoes was 1. In addition, the existence and uniqueness of the solution are examined using the Banach fixed point theorem. The Toufik–Atangana method is used for the numerical examination of a fractional version of the proposed model. We compared different values of fractional-order α=0.965, 0.975, 0.985, 0.995 and 1 it was found that when the order of derivatives decreases, the transmission shall decrease accordingly. This research provides valuable insights for developing effective control strategies to reduce the burden of dengue fever and strengthen public health systems.

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