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Fractional ABC Dynamics and Nonlinear Transmission Analysis of Dengue–Malaria Co-infection with Reinfection
(2026-01-01)
Lamwong, Jiraporn
;
Pongsumpun, Puntani
The persistent co-circulation of dengue and malaria in tropical regions poses a significant epidemiological challenge, particularly because classical integer-order models fail to capture the memory-driven reinfection, relapse, and recrudescence mechanisms that sustain long-term disease transmission. To overcome these limitations, this study develops a high-dimensional nonlinear co-infection model formulated using the Atangana–Baleanu–Caputo (ABC) fractional derivative, which incorporates nonsingular and nonlocal kernels to realistically represent hereditary effects in host–vector dynamics. The model integrates primary and secondary dengue infections, recurrent malaria pathways, and interactions across two mosquito species within a unified fractional-order framework. Analytical results establish positivity, boundedness, and existence–uniqueness of solutions, and the basic reproduction number R<inf>0</inf> is rigorously derived via the next-generation matrix method. Numerical simulations reveal that decreasing the fractional order substantially prolongs transient dynamics, increases infection peaks, and strengthens disease persistence relative to the classical system; in particular, when, both pathogens exhibit sustained endemicity amplified under fractional dynamics. These findings demonstrate that memory effects encoded by the ABC operator play a critical role in shaping reinfection outcomes, cross-immunity decay, and recurrent malaria episodes. The proposed framework provides a mathematically rigorous and epidemiologically insightful foundation for understanding nonlinear co-infection dynamics and underscores the importance of fractional calculus in improving predictive modeling and informing long-term vector-borne disease control strategies.
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Correction: Fractional ABC Dynamics and Nonlinear Transmission Analysis of Dengue–Malaria Co-infection with Reinfection (Earth Systems and Environment, (2026), 10.1007/s41748-026-01258-5)
(2026-01-01)
Lamwong, Jiraporn
;
Pongsumpun, Puntani
The authors wish to correct an error in Figs. 2, 3, 4, 5 and 6 of the above-referenced article (https://doi.org/10.1007/s41748-026-01258-5), with regard to the omission of several subfigures in the online published version. Specifically, subfigures 2g–2q in Fig. 2, subfigures 3g–3q in Fig. 3, subfigures 4g–4h in Fig. 4, subfigures 5g–5h in Fig. 5, and subfigures 6g–6h in Fig. 6 were omitted. The corrected figures are provided below. Time–series dynamics of the dengue–malaria co-infection model under varying fractional orders (ABC derivative) Three-dimensional surface representations of the dengue–malaria co-infection dynamics under varying fractional orders (ABC derivative) Three-dimensional surface plots comparing the effects of different mosquito biting rates on the dengue–malaria co-infection dynamics at the fractional order Three-dimensional surface plots illustrating the impact of varying transmission probabilities from aedes mosquitoes to humans during primary dengue infection at the fractional order Three-dimensional surface plots comparing the effects of different transmission probabilities from dengue-infected humans to aedes mosquitoes during primary infection at the fractional order
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The role of a vaccine booster for a fractional order model of the dynamic of COVID-19: a case study in Thailand
(2025-12-01)
Pongsumpun, Puntipa
;
Pongsumpun, Puntani
;
Tang, I. Ming
;
Lamwong, Jiraporn
This article addresses the critical need for understanding the dynamics of COVID-19 transmission and the role of booster vaccinations in managing the pandemic. Despite widespread vaccination efforts, the emergence of new variants and the waning of immunity over time necessitate more effective strategies. A fractional-order mathematical model using Caputo-Fabrizio derivatives was developed to analyze the impact of booster doses, symptomatic and asymptomatic infections, and quarantine measures. The model incorporates real epidemic data from Thailand and includes a sensitivity analysis of parameters influencing disease spread. Numerical results indicate that booster vaccinations significantly reduce transmission rates, and the model’s predictions align well with the observed data. The basic reproduction number was determined to evaluate disease control, showing that a sustained vaccination campaign, including booster doses, is essential to maintaining immunity and controlling future outbreaks. The findings underscore the importance of ongoing vaccination efforts and provide a robust framework for policymakers to design effective strategies for pandemic control.
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Optimal control and stability analysis of influenza transmission dynamics with quarantine interventions
(2025-08-01)
Lamwong, Jiraporn
;
Pongsumpun, Puntani
Seasonal flu results from infection by influenza viruses of either type A or B. Common symptoms include a rapid rise in body temperature, coughing, headaches, muscle and joint aches, throat discomfort, and nasal congestion. This research addresses the need for effective modeling and control of seasonal influenza, which remains a significant health concern globally due to its high transmissibility and potential to cause severe illness. Current approaches to understanding and managing influenza focus on various mathematical models exploring transmission dynamics and control strategies. This study contributes to the field by introducing a Susceptible-Exposed-Infectious-Quarantined-Recovered (SEIQR) model, which uniquely incorporates quarantine as a key intervention, reflecting realistic disease management practices. The methodology utilized involves formulating the SEIQR model to simulate the transmission of influenza and analyze its stability. The stability of both the disease-free and endemic equilibrium points is examined using Lyapunov functions and LaSalle’s invariance principle, ensuring the rigorous validation of the model's behavior. To enhance the model's utility, optimal control theory is applied, incorporating control variables such as vaccination, social measures, and treatment for both infected and quarantined populations. The application of Pontryagin’s Maximum Principle enables the derivation of optimal control strategies that balance epidemiological impact with cost-effectiveness. Numerical simulations provide key results that demonstrate the efficacy of control interventions. Specifically, scenarios implementing control measures reveal a significant reduction in the peak and overall spread of infections. The analysis of different control policies indicates that a combined approach—employing both vaccination and social distancing—is the most effective for curbing the spread of influenza. Sensitivity analysis further underscores the critical influence of parameters like quarantine rate and infection rate on the basic reproduction number, R<inf>0</inf>, reinforcing the importance of targeted interventions. The study’s findings emphasize the importance of timely and multifaceted control measures for achieving the global asymptotic stability of the influenza model. The implications suggest that integrated strategies, particularly those involving vaccination and social controls, are crucial for public health policy to manage and prevent influenza outbreaks effectively. Future research could expand the model to include demographic variations, virus mutations, and interactions with other respiratory diseases, enhancing its predictive power and practical relevance for disease control.
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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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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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Optimal Control Strategy of a Mathematical Model for the Fifth Wave of COVID-19 Outbreak (Omicron) in Thailand
(2024-01-01)
Lamwong, Jiraporn
;
Wongvanich, Napasool
;
Tang, I. Ming
;
Pongsumpun, Puntani
The world has been fighting against the COVID-19 Coronavirus which seems to be constantly mutating. The present wave of COVID-19 illness is caused by the Omicron variant of the coronavirus. The vaccines against the five variants (α, β, γ, δ, and ω) have been quickly developed using mRNA technology. The efficacy of the vaccine developed for one of the strains is not the same as the efficacy of the vaccine developed for the other strains. In this study, a mathematical model of the spread of COVID-19 was made by considering asymptomatic population, symptomatic population, two infected populations and quarantined population. An analysis of basic reproduction numbers was made using the next-generation matrix method. Global asymptotic stability analysis was made using the Lyapunov theory to measure stability, showing an equilibrium point’s stability, and examining the model with the fact of COVID-19 spread in Thailand. Moreover, an analysis of the sensitivity values of the basic reproduction numbers was made to verify the parameters affecting the spread. It was found that the most common parameter affecting the spread was the initial number in the population. Optimal control problems and social distancing strategies in conjunction with mask-wearing and vaccination control strategies were determined to find strategies to give better control of the spread of disease. Lagrangian and Hamiltonian functions were employed to determine the objective function. Pontryagin’s maximum principle was employed to verify the existence of the optimal control. According to the study, the use of social distancing in conjunction with mask-wearing and vaccination control strategies was able to achieve optimal control rather than controlling just one or another.
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A modified optimal control for the mathematical model of dengue virus with vaccination
(2023-01-01)
Pongsumpun, Puntipa
;
Lamwong, Jiraporn
;
Tang, I. Ming
;
Pongsumpun, Puntani
The dengue viruses (of which there are four strains) are the causes of three illnesses of increasing severity; dengue fever (DF), dengue hemorrhagic fever (DHF) and dengue shock syndrome (DSS). Recently, dengue fever has reached epidemic proportion in several countries. Strategies or preventative methods have to be developed to combat these epidemics. This can be done by development of vaccines or by preventing the transmission of the virus. The latter approach could involve the use of mosquito nets or insecticide spraying. To determine which strategy would work, we test the strategy using mathematical modeling to simulate the effects of the strategy on the dynamics of the transmission. We have chosen the Susceptible-Exposed-Infected-Recovered (SEIR) model and the Susceptible, Exposed-Infected (SEI) model to describe the human and mosquito populations, repectively. We use the Pontryagin’s maximum principle to find the optimal control conditions. A sensitivity analysis revealed that the transmission rate (ɣ<inf>ℎ</inf>, ɣ<inf>v</inf>), the birth rate of human population (µ<inf>ℎ</inf>), the constant recruitment rate of the vector population (A) and the total human population (N<inf>ℎ</inf>) are the most influential factors affecting the disease transmission. Numerical simulations show that the optimal controlled infective responses, when implemented, cause the convergence to zero to be faster than that in uncontrolled cases.

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