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    SIR transmission model of dengue virus taking into account two species of mosquitoes and an age structure in the human population
    (2015-07-28)
    Sungchasit, R.
    ;
    Pongsumpun, P.
    ;
    Tang, I. M.
    Dengue is a vector-borne disease. It is transmitted to humans by the bites of the Aedes aegypti and Aedes albopictus mosquitoes. The human population is separated into two classes, a child class and an adult class, each class being described by a SIR model. The transmission rates of the two mosquito species are different and depend on what class the humans belong to. We develop a single model taking into account the presence of two type of mosquitoes and two age classes and apply it to dengue fever. The model shows how it is possible for the maximum level of infected human to be reached in a short time. The nature of stability of the equilibrium state and the trajectories of the individual classes in the model are determined by the values of the basic reproduction number by setting the values of the parameters in the model to different values which reflect the environment in which the epidemic is occurring in the model.
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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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    Age structured model for symptomatic and asymptomatic infections of dengue disease
    (2009-01-01)
    Pongsumpun, P.
    Age structure and the emergence of symptom for dengue infection are considered in this study. The transmission model is formulated to see the transmission of this disease. The human population is separated into juvenile and adult classes but only juvenile class being susceptible to infection by the disease. Infectious juvenile human is divided into symptomatic and asymptomatic classes. The transmission probabilities of dengue virus from vector to human are difference to become symptomatic and asymptomatic classes. The standard dynamical analysis method is used for analyzing this model. The basic reproduction number is obtained. Numerical simulations are used to show these results. The alternative way for controlling this disease is discussed in the term of threshold condition.
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    Age structured model for symptomatic and asymptomatic dengue infections
    (2007-12-01)
    Pongsumpun, Puntani
    Age structure and the emergence of symptom for dengue infection are considered in this study. The transmission model is formulated to see the transmission of this disease. The human population is separated into juvenile and adult classes but only juvenile class being susceptible to infection by the disease. Infectious juvenile human is divided into symptomatic and asymptomatic classes. The transmission probabilities of dengue virus from vector to human are difference to become symptomatic and asymptomatic classes. The standard dynamical analysis method is used for analyzing this model. The basic reproduction number is obtained. Numerical simulations are used to show these results. The alternative way for controlling this disease is discussed in the term of threshold condition.