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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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    Global stability of the age structural transmission model for swine flu
    (2013-09-01)
    Changpuek, T.
    ;
    Pongsumpun, P.
    ;
    Tang, I. Ming
    In this paper, we examine the global stability of swine flu transmission model incorporated the age structure of human population based on SEIQR (susceptible-exposed-infected-quarantined-recovered) model. The human population is divided into three groups such as 1-10 years, 11-20 years and more than 20 years, respectively. We obtain four equilibrium states and then construct Lyapunov functions with the conditions for global stability of these four equilibrium states. © 2013 Pushpa Publishing House, Allahabad, India.
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    Analysis of mathematical model for swine flu transmission by age group
    (2013-02-01)
    Changpuek, T.
    ;
    Pongsumpun, P.
    ;
    Tang, I. Ming
    Effect of age group in the human population is considered for the transmission of swine flu. Susceptible-Exposed-Infected-Quarantined-Recovered (SEIQR) model is used for describing the transmission of this disease. From the swine flu data in Thailand, age of patients is influenced to the transmission of this disease. The human population is separated into three groups such as 1-10 years, 11-20 years, and more than 20 years, respectively. The transmission rates of the disease in all age groups are assumed to be different. Local stability analysis of this model is given. Four equilibrium states are found and the conditions for stability of these four equilibrium states are established. Numerical solutions are shown to confirm the analytical results. The bifurcation diagrams are shown. The basic reproductive number is found and the alternative way to control the disease is discussed. © 2013 Pushpa Publishing House.