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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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    Mathematical model for 4 serotypes of dengue virus with vaccination
    (2018-12-01)
    Lamwong, Jiraporn
    ;
    Pongsumpun, Puntani
    In this study, we formulate the SIR model to consider the transmission cycle between two population groups; Human and mosquito populations. We are interested in the cases of unvaccinated and vaccinated where human populations are infected from DEN1, DEN2, DEN3 and DEN4. For mosquito population, we divided it into susceptible and infected populations. The model is analyzed by using dynamical modeling method. The basic reproductive number is obtained from next generation matrix. If the basic reproductive number is less than one, the solutions of our model converge to the disease free steady state. The solutions of our model oscillate to the endemic steady state for the basic reproductive number is greater than one. The numerical solutions are found to support our analytical results.
      1
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    Mers model of thai and south korean population
    (2018-01-01)
    Lamwong, Jiraporn
    ;
    Tang, I. Ming
    ;
    Pongsumpun, Puntani
    Coronavirus (MERS-Cov) caused the occurrence of Corona. First infected case was reported in 2012 during a poultry outbreak in Saudi Arabia. After that, there were the reports of the sporadic outbreaks in all regions. In this study, we considered the transmission cycle between two population groups: Thai and South Korea. Each population group was divided into susceptible, exposed, infected, quarantine and recovered groups. The behaviors of the solutions were obtained using a standard dynamical modeling method. The stability conditions for the disease free equilibrium state and disease endemic equilibrium states were determined. The basic reproductive number R <inf>0</inf> is obtained. When R <inf>0</inf> <1, the disease-free state was locally asymptotically stable. If R <inf>0</inf> >1, the endemic equilibrium state was locally asymptotically stable. The numerical solutions were shown for supporting the theoretical results. We found that when we decreased α <inf>1</inf> (the rate of susceptible Thai human changes to become an exposed Thai human and μ <inf>1</inf> (the rate at which South Korean population moved out the country), the number of coronavirus case was decreased and outburst of coronavirus epidemic was shorter.
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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.
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    Mathematical model of the symptomatic and asymptomatic infections of swine flu
    (2011-01-06)
    Pongsumpun, P.
    ;
    Tang, I. M.
    Swine flu (swine influenza) is a respiratory disease caused by type A influenza. This disease is transmitted between the persons through coughing or sneezing with the virus. Persons may also become infected by touching something, contaminated with flu virus and then touching their eyes, nose or mouth. The most common clinical findings are fever, cough, sore throat, malaise, headache, vomiting and diarrhea have also been common, both of which are unusual features of seasonal influenza. In this paper, the transmission of Swine flu is studied through standard dynamical modeling method. The symptomatic and asymptomatic patients are considered with the different transmission rates. The analytical solutions of the model are obtained. The numerical simulations are shown to support the theoretical predictions. The basic reproductive number is produced for introducing the alternative way to decrease the disease outbreak.
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    Mathematical model of Plasmodium Vivax and Plasmodium falciparum malaria
    (2009-09-30)
    Pongsumpun, P.
    ;
    Tang, I. M.
    Malaria is transmitted to the person by the biting of infectious Anopheles mosquitoes. This infectious disease caused by the parasite genus Plasmodium. Four species of this parasite cause human malaria, namely, Plasmodium vivax, Plasmodium falciparum, Plasmodium ovale and Plasmodium malariae. The difference between P.vivax and P. falciparum is that a person suffering from P. vivax infection can suffer relapses of the disease. This is due the parasite being able to remain dormant in the liver of the cases where it is able to re-infect the case after a passage of time. During this stage, the case is classified as being in the dormant class. The model to describe the transmission between falciparum and vivax malaria consists of a human population divided into four classes, the susceptible, the infectious, the dormant and the recovered classes. The vector population is separated into two classes, the susceptible and infectious classes. We analyze our model by using standard dynamic modeling method. Two stable equilibrium states, a disease free state E<inf>0</inf> and an endemic state E<inf>1</inf>, are found to be possible. It is found that the E<inf>0</inf> state is stable when a basic reproductive number R<inf>0</inf> is less than one. If R<inf>0</inf> is greater than one, the endemic state E<inf>1</inf> is stable. The conditions for the local stability of each equilibrium state are established. The numerical simulations are shown to confirm the results.
      1