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Fractional-order Modeling and Optimal Control of Dengue-Malaria Co-infection with Local and Advanced Treatment Strategies
(2026-01-01)
Pongsumpun, Puntipa
;
Ud Din, Rahim
;
Ullah, Atta
;
Pongsumpun, Puntani
Abstract: This study presents a novel fractional-order co-infection model describing the joint transmission dynamics of dengue and malaria using the generalized fractional derivative. The total human population is divided into eight epidemiological compartments that account for single infections, co-infection, treatment stages, and recovery. The proposed framework incorporates memory effects and nonlocal behavior, offering a more realistic representation of disease progression compared to classical integer-order models. Local and advanced treatment strategies are introduced based on infection severity, allowing targeted intervention for both mild and co-infected cases. The fundamental mathematical properties of the model, including positivity, boundedness, existence, and uniqueness of solutions, are rigorously established. The basic reproduction number is derived, and both local and global stability of the disease-free equilibrium are analyzed using suitable Lyapunov functions. A statistical sensitivity analysis is performed to identify key parameters influencing disease transmission. Furthermore, optimal control strategies are formulated to minimize co-infection prevalence while reducing treatment and implementation costs. Numerical simulations validate the theoretical findings and demonstrate that fractional-order dynamics provide deeper insights into long-term disease behavior. The results offer valuable guidance for policymakers in designing effective and cost-efficient strategies to control dengue and malaria co-infection. Graphic Abstract: (Figure presented.) The
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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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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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The Dynamical Model of Zika Transmission from Mother to Baby
(2023-01-01)
Pongsumpun, Puntipa
;
Pongsumpun, Puntani
Zika virus is transmitted to human by biting of infected Aedes mosquito or having sex with an infected person. This disease can be transmitted between mother and baby. This paper described the transmission of Zika virus by using the transmission model. We analyze the transmission model by using standard dynamical analysis. The equilibrium points are found. The local stabilities are determined. Numerical solutions are shown. The way for reducing the transmission of Zika virus is suggested.
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Transmission model for Zika virus between human and mosquitoes
(2022-09-16)
Pongsumpun, Puntipa
;
Pongsumpun, Puntani
Zika virus is mainly transmitted by mosquitoes. This disease can also be passed through sexually transmission. This disease can be found in South and Central America, the Caribbean, the Pacific islands, Africa, and Asia. Zika virus disease is normally a mild disease. About 80% of infected people do not develop symptoms at all. Transmission of this disease is described by mathematical model. We separated the human into susceptible, infectious and recovered populations. The mosquitoes are divided into susceptible and infectious populations. The transmission model is analyzed by using standard dynamical analysis. Local stability analysis of our transmission model is analyzed. We find the basic reproduction number and the factors which influence the transmission of the disease.
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Mathematical model for Chikungunya disease with two types of Aedes mosquitoes
(2022-04-28)
Pongsumpun, Puntipa
;
Pongsumpun, Puntani
Chikungunya disease is occurred when the infected Aedes mosquitoes bite. Chikungunya virus is a member of the genus Alphavirus family Togaviridae. There are 2 species of Aedes mosquitoes such as Aedes aegypti and Aedes albopictus. We describe the transmission of the disease by using mathematical model. We separated the populations to human and vector populations. We separate the human population to susceptible, infectious and recovered populations. The mosquitoes are separated into susceptible and infectious populations. Then we analyze the model by using standard dynamical analysis. The numerical solutions are shown to see the stability of each equilibrium state. The variances of each parameter are shown to see the behavior of each population. The basic reproduction number of this disease is shown to reduce the transmission of this disease.

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