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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
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Pongsumpun, Puntani
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Tang, I. Ming
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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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Sensitivity analysis and global stability of epidemic between Thais and tourists for Covid -19
(2024-12-01)
Sungchasit, Rattiya
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Tang, I. Ming
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Pongsumpun, Puntani
This study employs a mathematical model to analyze and forecast the severe outbreak of SARS-CoV-2 (Severe Acute Respiratory Syndrome Coronavirus 2), focusing on the socio-economic ramifications within the Thai population and among foreign tourists. Specifically, the model examines the impact of the disease on various population groups, including susceptible (S), exposed (E), infected (I), quarantined (Q), and recovered (R) individuals among tourists visiting the country. The stability theory of differential equations is utilized to validate the mathematical model. This involves assessing the stability of both the disease-free equilibrium and the endemic equilibrium using the basic reproduction number. Emphasis is placed on local stability, the positivity of solutions, and the invariant regions of solutions. Additionally, a sensitivity analysis of the model is conducted. The computation of the basic reproduction number (R0) reveals that the disease-free equilibrium is locally asymptotically stable when R0 is less than 1, whereas the endemic equilibrium is locally asymptotically stable when R0 exceeds 1. Notably, both equilibriums are globally asymptotically stable under the same conditions. Through numerical simulations, the study concludes that the outcome of COVID-19 is most sensitive to reductions in transmission rates. Furthermore, the sensitivity of the model to all parameters is thoroughly considered, informing strategies for disease control through various intervention measures.
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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
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Wongvanich, Napasool
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Tang, I. Ming
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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
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Lamwong, Jiraporn
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Tang, I. Ming
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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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Vaccination’s Role in Combating the Omicron Variant Outbreak in Thailand: An Optimal Control Approach
(2022-10-01)
Lamwong, Jiraporn
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Pongsumpun, Puntani
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Tang, I. Ming
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Wongvanich, Napasool
COVID-19 is the name of the new infectious disease which has reached the pandemic stage and is named after the coronavirus (COVs) which causes it. COV is a single-stranded RNA virus which in humans leads to respiratory tract symptoms which can lead to death in those with low immunities, particularly older people. In this study, a standard dynamic model for COVID-19 was proposed by comparing a simple model and the optimal control model to reduce the number of infected people and become a guideline to control the outbreak. Control strategies are the vaccination rate and vaccine-induced immunity. An analysis was performed to find an equilibrium point, the basic reproduction number (Formula presented.), and conditions that generate stability by using Lyapunov functions to prove the stability of the solution at the equilibrium point. Pontryagin’s maximum principle was used to find the optimal control condition. Moreover, sensitivity analysis of the parameters was performed to learn about the parameters that might affect the outbreak in order to be able to control the outbreak. According to the analysis, it is seen that the efficacy of vaccines (Formula presented.) and the infection rate (Formula presented.) will affect the increased (decreased) incidence of the outbreak. Numerical analyses were performed on the Omicron variant outbreak data collected from the Thailand Ministry of Health, whose analyses then indicated that the optimal control strategy could lead to planning management and policy setting to control the COVID-19 outbreak.
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Mathematical Modeling: Global Stability Analysis of Super Spreading Transmission of Respiratory Syncytial Virus (RSV) Disease
(2022-07-01)
Sungchasit, Rattiya
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Tang, I. Ming
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Pongsumpun, Puntani
In this paper, a model for the transmission of respiratory syncytial virus (RSV) in a constant human population in which there exist super spreading infected individuals (who infect many people during a single encounter) is considered. It has been observed in the epidemiological data for the diseases caused by this virus that there are cases where some individuals are super-spreaders of the virus. We formulate a simply SEI<inf>r</inf> I<inf>s</inf> R (susceptible–exposed–regular infected–super-spreading infected–recovered) mathematical model to describe the dynamics of the transmission of this disease. The proposed model is analyzed using the standard stability method by using Routh-Hurwitz criteria. We obtain the basic reproductive number (R<inf>0</inf>) using the next generation method. We establish that when R<inf>0</inf> < 1, the disease-free state is locally asymptotically stable and the disease endemic state is unstable. The reverse is true when R<inf>0</inf> > 1, the disease endemic state becomes the locally asymptotically stable state and the disease-free state becomes unstable. It is also established that the two equilibrium states are globally asymptotically stable. The numerical simulations show how the dynamics of the disease change as values of the parameters in the SEI<inf>r</inf> I<inf>s</inf> R are varied.
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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
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Pongsumpun, Puntani
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Tang, I. Ming
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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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Unveiling the Influence of the Spectral Irradiance of Indoor Light-Emitting Diodes on the Photovoltaics of a Methylammonium Lead Iodide-Based Device
(2022-01-01)
Supasai, Thidarat
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Soe, Kay Thi
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Smerchit, Thapanut
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Azad, Farhad
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Thongprong, Non
An understanding of the spectrum–property relationship of perovskite solar cells when illuminated by light-emitting diodes that are used for indoor applications is necessary. Herein, it is aimed to explore the influences of correlated-color temperatures on a MAPbI<inf>3</inf>-based device under low-light conditions. Given an irradiance of approximately 3 W m−2 (or ≈1000 lx), a maximum free carrier generation rate of 1.0 × 1021 m−3 s−1 was found. Additionally, power conversion efficiencies (PCEs) up to 31.97%, 30.36%, and 28.98% with maximum power outputs of 13.66, 13.02, and 16.09 μW could be reached at 3000, 4000, and 6500 K, respectively. Additional increases in the PCEs were observed when high-energy blue light (in a range of 400–550 nm) was excluded during the current–voltage sweeps. In combination with the surface photovoltage measurements, intense blue light (under 6500 K) had a minimal influence on the photoinduced charge separation signals when compared to those caused by 3000 and 4000 K light. As a solar cell, the PCE reached as high as 34.52%, which corresponded to 73.08% of the thermodynamic limit of its bandgap at 3000 K.
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Mathematical modeling and optimal control of the hand foot mouth disease affected by regional residency in Thailand
(2021-11-01)
Wongvanich, Napasool
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Tang, I. Ming
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Dubois, Marc Antoine
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Pongsumpun, Puntani
Hand, foot and mouth disease (HFMD) is a virulent disease most commonly found in East and Southeast Asia. Symptoms include ulcers or sores, inside or around the mouth. In this research, we formulate the dynamic model of HFMD by using the SEIQR model. We separated the infection episodes where there is a higher outbreak and a lower outbreak of the disease associated with regional residency, with the higher level of outbreak occurring in the urban region, and a lower outbreak level occurring in the rural region. We developed two different optimal control programs for the types of outbreaks. Optimal Control Policy 1 (OPC1) is limited to the use of treatment only, whereas Optimal Control Policy 2 (OPC2) includes vaccination along with the treatment. The Pontryagin’s maximum principle is used to establish the necessary and optimal conditions for the two policies. Numerical solutions are presented along with numerical sensitivity analyses of the required control efforts needed as the control parameters are changed. Results show that the time t<inf>max</inf> required for the optimal control effort to stay at the maximum amount u<inf>max</inf> exhibits an intrinsic logarithmic relationship with respect to the control parameters.
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Local and global stability analysis of dengue disease with vaccination and optimal control
(2021-10-01)
Chamnan, Anusit
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Pongsumpun, Puntani
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Tang, I. Ming
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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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