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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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