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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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Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis
(2022-03-01)
Chamnan, Anusit
;
Pongsumpun, Puntani
;
Tang, I. Ming
;
Wongvanich, Napasool
The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this epidemic in several Southeast Asian countries. The dengue vaccination program requires a total of three injections, 6 months apart at 0, 6, and 12 months. The ages of the recipients are nine years and above. In this paper, we analyze the mathematical dynamics SIR transmission model of the epidemic. The stability of the model is established using Routh–Hurwitz criteria to see if a Hopf Bifurcation occurs and see when the equilibrium states are local asymptotically stable or global asymptotically stable. We have determined the efficiency of CYD-TDV by simulating the optimal numerical solution for each age range for this model. The numerical results showed the optimal age for vaccination and significantly reduced the severity and severity of the disease.
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Local and global stability analysis of dengue disease with vaccination and optimal control
(2021-10-01)
Chamnan, Anusit
;
Pongsumpun, Puntani
;
Tang, I. Ming
;
Wongvanich, Napasool
Dengue fever is a disease that has spread all over the world, including Thailand. Dengue is caused by a virus and there are four distinct serotypes of the virus that cause dengue DENV‐1, DENV‐2, DENV‐3, and DENV‐4. The dengue viruses are transmitted by two species of the Aedes mosquitoes, the Aedes aegypti, and the Aedes albopictus. Currently, the dengue vaccine used in Thailand is chimeric yellow tetravalent dengue (CYD‐TDV). This research presents optimal control which studies the vaccination only in individuals with a documented past dengue infection (seropositive), regardless of the serotypes of infection causing the initial infection by the disease. The analysis of dengue transmission model is used to establish the local asymptotically stabilities. The property of symmetry in the Lyapunov function an import role in achieving this global asymptotically stabilities. The optimal control systems are shown in numerical solutions and conclusions. The result shows that the control resulted in a significant reduction in the number of infected humans and infected vectors.
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Optimal control of the dengue dynamical transmission with vertical transmission
(2019-12-01)
Pongsumpun, Puntani
;
Tang, I. Ming
;
Wongvanich, Napasool
Dengue disease is found in tropical and subtropical regions around the world. Dengue virus is the cause of dengue fever, dengue hemorrhagic fever, and dengue shock syndrome. It consists of 4 serotypes: DEN-1, DEN-2, DEN-3, and DEN-4. There are two modes of transmission for dengue virus in mosquito: horizontal transmission and vertical transmission. The mosquito can be infected when it bites an infectious human by horizontal transmission, but there can also be vertical transmission through sexual contact with an infected mosquito. This research presents a control mechanism based on our previously developed dengue model with vertical transmission. The two policies, namely vaccination and insecticide administration (Policy 1) and isolation and insecticide administration (Policy 2) are considered. The use of Pontryargin’s maximum principle allowed necessary and optimality conditions, thus facilitating the optimal control to be developed. Numerical solutions of our control systems and the conclusions of our two policies are presented.

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