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Author: search.filters.author.Pongsumpun, PuntaniSubject: search.filters.subject.Mathematical model

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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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    Mathematical modeling and stability of SARS-CoV-2 transmission dynamics among domestic tourists in Thailand
    (2025-02-01)
    Sungchasit, Rattiya
    ;
    Pongsumpun, Puntani
    The defined epidemiological model system explaining the spread of infectious diseases characterized with SARS-CoV-2 is analysed. The resulting SEIQR model is analysed in a closed system. It considers the basic reproductive value, the equilibrium point, local subclinical stability of the disease-free equilibrium point and local subclinical stability of the endemic equilibrium point. This is examined and the asymptotic dynamics of the appropriate model system are investigated. Further, a sensitivity analysis supplemented by simulations is prepared in advance to impose how changes in parameters involve the dynamic behaviours of the model.
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    Analysis of the Mathematical Model of Covid-19 in Thailand
    (2021-08-20)
    Pongsumpun, Puntani
    The purpose of this research is to study the characteristics of the COVID-19 virus in Thailand. We formulate the mathematical model of COVID-19 virus. We separate the human populations into 6 groups. The infected human populations are separated into 2 classes such as infectious human population with no show symptom and infectious human population with symptoms. We study the behavior of the equilibrium points of the model. Determine the conditions for the local stability of the equilibrium points. Numerical results of mathematical models are presented. This will lead to a reduction in the mortality rate of patients in Thailand.
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    Global stability of the transmission of hand-foot-mouth disease according to the age structure of the population
    (2021-01-01)
    Lamwong, Jiraporn
    ;
    Wongvanich, Napasool
    ;
    Tang, I. Ming
    ;
    Changpuek, Thurdkwun
    ;
    Pongsumpun, Puntani
    This study investigates a transmission model of Hand-Foot-Mouth disease (HFMD) where the age structure of the population is taken into account. Most infections in Thailand occur among children below the age of 10 years, whose immunity to HFMD is lower than people of age greater than 10 years. Therefore, a mathematical model was developed in which the population was separated into two groups with respect to age: one comprised of children aged less than 10 years, and another comprised of the rest of the population. The reproductive number was obtained by the next-generation matrix approach. Global asymptotical stability of the developed model was assured using Lyapunov’s direct method. The model was validated by showing that the 2D and 3D trajectories of the numerical solutions for the different sub-population groups converged to the endemic equilibrium states when the reproduction number was greater than one, thus supporting the theoretical conclusions. Results show that the time series behaviors of the different normalized populations groups converge to the disease-free state when the values of the parameters are such that the basic reproductive number is 0.591481 (i.e., less than one) and to an endemic state when the values of the parameters are such that R<inf>0</inf> = 54.4523 and R<inf>0</inf> = 192.575 R = (i.e. greater than one). The results of this study can suggest ways for reducing the outbreak of this disease.
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    Dengue infection model with temperature and the biting of aedes aegypti and ades albopictus in thailand
    (2020-08-05)
    Pongsumpun, Puntani
    Dengue is the transmission disease occurred by biting of infected Aedes aegypti and infected Aedes albopictus. The temperature of each area influences to the transmission of this disease. In this paper, we describe the transmission of this disease by using mathematical model. We separate the human population into susceptible, exposed, infectious and recovered classes. The vector population is divided into Aedes aegypti and Aedes albopictus. The mosquito population is separated into susceptible, exposed and infectious classes. We analyzed our mathematical model by finding the equilibrium points and determined the stability of each steady state. The numerical solutions are shown. The difference of temperatures is shown to describe the behaviors of human and vector populations. From the results, we will see that the temperature influences to the transmission of dengue disease.
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    Local Stability of Influenza Virus with Vaccination
    (2020-05-15)
    Pongsumpun, Puntani
    Influenza virus is an infectious disease. This caused by influenza virus. The symptoms consist of high fever, runny nose, sore throat, muscle and joint pain. In this paper, we construct the mathematical model for the transmission of influenza virus.We separate the human into 2 groups such as group of persons who obtain the vaccination and group of persons who do not obtain the vaccination. Each group, we separated the persons intothe susceptible, exposed, infectious, quarantined and recovered groups. We analyzed the equilibrium point and find the local stability of them by using standard dynamical modeling method. The basic reproduction number of this mathematical model is found. We obtain the condition for the disease fee steady state and endemic disease state will be local stability. Numerical results of the model are shown.
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    Age structural model of the hand foot mouth disease in Thailand
    (2018-12-01)
    Pongsumpun, Puntani
    ;
    Wongvanich, Napasool
    The hand foot mouth disease (HFMD) is a virulent disease caused by virus of the enteroviruses serotypes, whose symptoms include soreness inside or around the mouth, and rashes or blisters on the hands, feet or legs. Most cases are seen in infant and children. The severity of HFMD outbreaks has thus constituted serious threat to general public health. In this work, the transmission model of the HFMD is formulated. Specifically, the population is divided into two subclasses, namely, those under the age of ten, and those over the age of ten. Two SEIR models, one for each subclasses, are then formed. This model is then analyzed through the use of standard dynamical systems method, where two equilibriums of the model, namely the disease-free equilibrium, and the endemic equilibrium, are firstly determined. Stability analyses of the respective equilibriums are then conducted. Results show that the disease-free equilibrium will be stable if the basic reproduction number is less than one, while the endemic equilibrium is stable when the basic reproduction number exceeds unity. These results can be used in controlling the epidemics of the HFMD.
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    The basic reproductive number for the transmission of four serotypes of dengue model
    (2011-06-13)
    Pongsumpun, Puntani
    Dengue disease is transmitted to the human by biting of the infected Aedes Aegypti. This disease is classified as Dengue fever (DF), Dengue hemorrhagic fever (DHF) and Dengue shock syndrome(DSS) depend on the symptom of the patient. There are four serotypes (DEN-1, DEN-2, DEN-3 and DEN-4) of dengue virus. Mathematical model is constructed to describe the transmission of the disease. The severity of the disease depends on the age of the patient. We formulate the mathematical model by dividing the population into juvenile and adult classes. There are the difference transmission probabilities of dengue virus to the juvenile and adult humans for each serotype. We use the standard dynamical modeling method for analyzing this model. The analytical solutions are obtained. The comparisons of the numerical solutions when there are the differences of the basic reproductive numbers are discussed.