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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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A model for the testosterone regulation taking into account the presence of two types of testosterone hormones
(2015-06-01)
Tanutpanit, T.
;
Pongsumpun, P.
;
Tang, I. M.
The purpose of this paper is to study the effect of sex hormone binding globulin (SHBG) on the mathematical model of the hypothalamic-pituitary-gonadal (HPG) endocrine cycle which regulates the production of the male hormone testosterone. Large amounts of total circulating testosterone are bound to SHBG making them. Standard analytical techniques are used to analyze the modified mathematical model which includes a delay to account for the time required for luteinizing hormone emitted by the pituitary gland to reach the testis, to determine the steady state, its stability and the critical delay needed for the bifurcation. Numerical simulation of the solutions of the model is performed to illustrate the possible behaviors.
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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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Stability and oscillations of time-delayed model for the testosterone regulation
(2013-11-04)
Tanutpanit, T.
;
Pongsumpun, P.
;
Tang, I. M.
In this paper, we develop the mathematical model with a time delay to describe the feedback mechanisms concerning of cyclicity of the male hormonal balance on the influence of variations in the sex hormone-binding globulin (SHBG) concentration. We show that a Hopf bifurcation occurs when a time delay τ passes through a critical value. Numerical simulations are performed to illustrate the analytical results. Moreover, this model can explain the pulsatile secretion of hormones in male.
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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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Transmission network dynamics of Plasmodium Vivax Malaria
(2009-09-30)
Pongsumpun, P.
;
Tang, I. M.
One of the top ten killer diseases in the world is Malaria. In each year, there are between 300 to 500 million clinical episodes of malaria and 1.5 to 2.7 million deaths worldwide. The malaria disease is caused by the multiplication of protozoa parasite of the genus Plasmodium. Malaria in humans is due to 4 types of malaria parasites such that Plasmodium falciparum, Plasmodium vivax, Plasmodium malariae and Plasmodium ovale. P.vivax malaria differs from P. falciparum malaria in that a person suffering from P. vivax malaria can experience relapses of the disease. Between the relapses, the malaria parasite will remain dormant in the liver of the patient, leading to the patient being classified as being in the dormant class. In this paper, the dynamical model of P. vivax malaria is formulated to see the network distribution of this disease.
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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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