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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.
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    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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    The dynamical model of dengue vertical transmission
    (2017-01-01)
    Dengue disease is usually found in many parts of the world, including Africa, Asia, South America and Australia. Dengue disease can pass from one individual to another by two distinct mechanisms such as horizontal transmission and vertical transmission. In horizontal transmission, susceptible individuals can be infected by direct or indirect contacts with infectious individuals who are stays at the same time. Vertical transmission means to direct transmission from infected parents to their offspring before or during birth. In this study, the dynamical model of dengue disease was formulated by considering the vertical transmission in Aedes mosquitoes. The analysis of our model was given. The results of this study should introduce the alternative ways to reduce the dengue outbreak.
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    Transmission model of dengue virus by Aedes aegypti and Aedes albopictus
    (2013-12-01)
    Sungchasit, R.
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    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 for 4 serotypes of dengue virus with vaccination
    (2018-12-01)
    Lamwong, Jiraporn
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    In this study, we formulate the SIR model to consider the transmission cycle between two population groups; Human and mosquito populations. We are interested in the cases of unvaccinated and vaccinated where human populations are infected from DEN1, DEN2, DEN3 and DEN4. For mosquito population, we divided it into susceptible and infected populations. The model is analyzed by using dynamical modeling method. The basic reproductive number is obtained from next generation matrix. If the basic reproductive number is less than one, the solutions of our model converge to the disease free steady state. The solutions of our model oscillate to the endemic steady state for the basic reproductive number is greater than one. The numerical solutions are found to support our analytical results.
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    Simplified Modeling Approach to Characterize Sudden Load Disturbances in WirelessHART FOPDT Systems
    This paper presents the simplified modelling approach to characterize sudden load disturbance in WirelessHART™. Two approaches are presented. The model was firstly formulated through Laplace transformation, where the resulting integral equation renders non-linear optimization problems into simple linear optimizations. Experiments were conducted on a coupled tanks system connected through the WirelessHART™ protocol. Based on the initial fit to the experimental results, the second model then places two locally affine relationships, one for the load flow disturbances, and the other for the level measurements to the responses. The extended locally affine model gave on average a 25% reduction in errors, compared to the Laplace-based method, while better captured the non-linear effects resulting from the WirelessHART™.
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    Mathematical model for the transmission of two plasmodium malaria
    (2011-03-01)
    Malaria is transmitted to the human by biting of infected Anopheles mosquitoes. This disease is a serious, acute and chronic relapsing infection to humans. Fever, nausea, vomiting, back pain, increased sweating anemia and splenomegaly (enlargement of the spleen) are the symptoms of the patients who infected with this disease. It is caused by the multiplication of protozoa parasite of the genus Plasmodium. Plasmodium falciparum, Plasmodium vivax, Plasmodium malariae and Plasmodium ovale are the four types of Plasmodium malaria. A mathematical model for the transmission of Plasmodium Malaria is developed in which the human and vector population are divided into two classes, the susceptible and the infectious classes. In this paper, we formulate the dynamical model of Plasmodium falciparum and Plasmodium vivax malaria. The standard dynamical analysis is used for analyzing the behavior for the transmission of this disease. The Threshold condition is found and numerical results are shown to confirm the analytical results.
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    Stability and oscillations of time-delayed model for the testosterone regulation
    (2013-11-04)
    Tanutpanit, T.
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    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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    Dynamics of a new strain of the H1N1 influenza a virus incorporating the effects of repetitive contacts
    (2014-01-01) ;
    Tang, I. Ming
    The respiratory disease caused by the Influenza A Virus is occurring worldwide. The transmission for new strain of the H1N1 Influenza A virus is studied by formulating a SEIQR (susceptible, exposed, infected, quarantine, and recovered) model to describe its spread. In the present model, we have assumed that a fraction of the infected population will die from the disease. This changes the mathematical equations governing the transmission. The effect of repetitive contact is also included in the model. Analysis of the model by using standard dynamical modeling method is given. Conditions for the stability of equilibrium state are given. Numerical solutions are presented for different values of parameters. It is found that increasing the amount of repetitive contacts leads to a decrease in the peak numbers of exposed and infectious humans. A stability analysis shows that the solutions are robust. © 2014 Puntani Pongsumpun and I-Ming Tang.
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    Effect of Rainfall for the Dynamical Transmission Model of the Dengue Disease in Thailand
    (2017-01-01)
    Chanprasopchai, Pratchaya
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    Tang, I. Ming
    The SEIR (Susceptible-Exposed-Infected-Recovered) model is used to describe the transmission of dengue virus. The main contribution is determining the role of the rainfall in Thailand in the model. The transmission of dengue disease is assumed to depend on the nature of the rainfall in Thailand. We analyze the dynamic transmission of dengue disease. The stability of the solution of the model is analyzed. It is investigated by using the Routh-Hurwitz criteria. We find two equilibrium states: a disease-free state and an endemic equilibrium state. The basic reproductive number (R0) is obtained, which indicates the stability of each equilibrium state. Numerical results taking into account the rainfall are obtained and they are seen to correspond to the analytical results.
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    Analysis of model for menstrual cycle with the effect of body mass index
    (2014-01-01)
    Mumtong, W.
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    Tang, I. Ming
    Menstrual cycle is the tissue that peeled off from the lining of the uterus. It is caused by changes in female hormones associated with ovulation. Obesity often affects the balance of estrogen hormone, hormone for ovulation control that may cause menstrual abnormalities. If there is no ovulation, then there would be no menstruation occurs. This article has examined the above factors that affect the balance of hormones on the control of the ovulation cycle.