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Author: search.filters.author.Tang, I. MingSubject: search.filters.subject.Mathematical model

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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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    Studying menstrual cycle by using mathematical model
    (2014-01-01)
    Mumtong, W.
    ;
    Pongsumpun, P.
    ;
    Tang, I. Ming
    Menstrual cycle can occur in fertile women. It is the scientific term for the physiological changes in human. It is under controlling of the endocrine system that is necessary for reproduction. It is commonly divided into three phases: the follicular phase, ovulation, and the luteal phase. Activin enhances Follicular Stimulating Hormone (FSH) biosynthesis and secretion. It participates in the regulation of menstrual cycle. In this study, we analyze a mathematical model of the human menstrual cycle. The equilibrium point of the model and its stability are shown. Numerical solutions are shown to support the theoretical predictions. © 2014 Pushpa Publishing House, Allahabad, India.
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    Analysis of model for menstrual cycle with the effect of body mass index
    (2014-01-01)
    Mumtong, W.
    ;
    Pongsumpun, P.
    ;
    Tang, I. Ming
    Menstrual cycle is the tissue that peeled off from the lining of the uterus. It is caused by changes in female hormones associated with ovulation. Obesity often affects the balance of estrogen hormone, hormone for ovulation control that may cause menstrual abnormalities. If there is no ovulation, then there would be no menstruation occurs. This article has examined the above factors that affect the balance of hormones on the control of the ovulation cycle.