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    Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis
    (2022-03-01)
    Chamnan, Anusit
    ;
    Pongsumpun, Puntani
    ;
    Tang, I. Ming
    ;
    Wongvanich, Napasool
    The effect of vaccination on the dengue fever epidemic described by an age structured modified SIR (Susceptible-Infected-Retired) model is studied using standard stability analysis. The chimeric yellow fever dengue tetravalent dengue vaccine (CYD-TDV™) is a vaccine recently developed to control this epidemic in several Southeast Asian countries. The dengue vaccination program requires a total of three injections, 6 months apart at 0, 6, and 12 months. The ages of the recipients are nine years and above. In this paper, we analyze the mathematical dynamics SIR transmission model of the epidemic. The stability of the model is established using Routh–Hurwitz criteria to see if a Hopf Bifurcation occurs and see when the equilibrium states are local asymptotically stable or global asymptotically stable. We have determined the efficiency of CYD-TDV by simulating the optimal numerical solution for each age range for this model. The numerical results showed the optimal age for vaccination and significantly reduced the severity and severity of the 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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    Transmission model of dengue virus by Aedes aegypti and Aedes albopictus
    (2013-12-01)
    Sungchasit, R.
    ;
    Pongsumpun, P.
    ;
    Tang, I. M.
    Mathematical models are used for describing many diseases. Dengue disease is occurred by biting of infected Aedes aegypti and Aedes albopictus mosquitoes. Dengue outbreak is found during the rainy season. Each Aedes mosquito has the different dengue outbreaks and they depend on the temperature and areas. The standard dynamical modeling method is used in this study. The SIR (susceptible-infectedrecovered) model is modified to describe the transmission of dengue virus by two species of vectors. The transmission of dengue virus is varied with time. The dynamical analysis method is used for analyzing this model. We confirm these results by using numerical results. © 2013 Pushpa Publishing House, Allahabad, India.
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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.
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    The transmission model of P.falciparum and P.vivax malaria between Thai and Burmese
    (2009-08-04)
    Pongsumpun, P.
    ;
    Tang, I. M.
    The transmission of Plasmodium falciparum and Plasmodium vivax malaria of Thais and Burmese is studied through a mathematical model. The population is separated into two groups, Thai and Burmese. Each population is divided into susceptible and infectious subclasses. The loss of immunity by individuals in the infectious class causes them to move back into the susceptible class. Standard dynamical method is used to analyze the behavior of the model. Two stable equilibrium states, a disease free state and an epidemic state are found to be possible in each population. A disease free equilibrium state in the Thai population occurs when there are no infected Burmese entering into the community. When there are infected Burmese enters into the Thai community, the epidemic state can occur. It is found that the disease free state is stable when the threshold number R<inf>0</inf> is less than one. The epidemic state is stable when R<inf>ET</inf> and R<inf>EB</inf> (where these threshold numbers are for the individual populations) are greater than one. The numerical simulations of our model illustrate what the results would be for our theoretical model.
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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.