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Author: search.filters.author.Tang, I. M.Subject: search.filters.subject.Basic reproductive number

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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.
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