Search results for: P. Pongsumpun

Authors: P. Pongsumpun

Abstract:

One of the important tropical diseases is Chikunkunya. This disease is transmitted between the human by the insect-borne virus, of the genus Alphavirus. It occurs in Africa, Asia and the Indian subcontinent. In Thailand, the incidences due to this disease are increasing every year. In this study, the transmission of this disease is studied through dynamical model analysis.

Keywords: Chikunkunya, dynamical model, Endemic region, Routh-Hurwitz criteria.

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Authors: R. Kongnuy, P. Pongsumpun

Abstract:

We used mathematical model to study the transmission of dengue disease. The model is developed in which the human population is separated into two populations, pregnant and non-pregnant humans. The dynamical analysis method is used for analyzing this modified model. Two equilibrium states are found and the conditions for stability of theses two equilibrium states are established. Numerical results are shown for each equilibrium state. The basic reproduction numbers are found and they are compared by using numerical simulations.

Keywords: Basic reproductive number, dengue disease, equilibrium states, pregnancy.

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Authors: P. Pongsumpun

Abstract:

Herpes zoster is a disease that manifests as a dermatological condition. The characteristic of this disease is an irritating skin rash with blisters. This is often limited to one side of body. From the data of Herpes zoster cases in Thailand, we found that age structure effects to the transmission of this disease. In this study, we construct the age structural model of Herpes zoster in Thailand. The local stability analysis of this model is given. The numerical solutions are shown to confirm the analytical results.

Keywords: Age structural model, Herpes zoster, local stability, Numerical solution.

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Authors: R. Kongnuy, P. Pongsumpun

Abstract:

Dengue, a disease found in most tropical and subtropical areas of the world. It has become the most common arboviral disease of humans. This disease is caused by any of four serotypes of dengue virus (DEN1-DEN4). In many endemic countries, the average age of getting dengue infection is shifting upwards, dengue in pregnancy and infancy are likely to be encountered more frequently. The dynamics of the disease is studied by a compartmental model involving ordinary differential equations for the pregnant, infant human and the vector populations. The stability of each equilibrium point is given. The epidemic dynamic is discussed. Moreover, the numerical results are shown for difference values of dengue antibody.

Keywords: Dengue antibody, infant, pregnant human, mathematical model.

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Authors: P. Pongsumpun

Abstract:

A new strain of Type A influenza virus can cause the transmission of H1N1 virus. This virus can spread between the people by coughing and sneezing. Because the people are always movement, so this virus can be easily spread. In this study, we construct the dynamical network model of H1N1 virus by separating the human into five groups; susceptible, exposed, infectious, quarantine and recovered groups. The movement of people between houses (local level) is considered. The behaviors of solutions to our dynamical model are shown for the different parameters.

Keywords: Dynamical network, H1N1virus, local level, simulation.

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Authors: P. Pongsumpun

Abstract:

The Swine flu outbreak in humans is due to a new strain of influenza A virus subtype H1N1 that derives in part from human influenza, avian influenza, and two separated strains of swine influenza. It can be transmitted from human to human. A mathematical model for the transmission of Swine flu is developed in which the human populations are divided into two classes, the risk and non-risk human classes. Each class is separated into susceptible, exposed, infectious, quarantine and recovered sub-classes. In this paper, we formulate the dynamical model of Swine flu transmission and the repetitive contacts between the people are also considered. We analyze the behavior for the transmission of this disease. The Threshold condition of this disease is found and numerical results are shown to confirm our theoretical predictions.

Keywords: Mathematical model, Steady state, Swine flu, threshold condition.

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Authors: R. Kongnuy., P. Pongsumpun

Abstract:

Mathematical models can be used to describe the transmission of disease. Dengue disease is the most significant mosquito-borne viral disease of human. It now a leading cause of childhood deaths and hospitalizations in many countries. Variations in environmental conditions, especially seasonal climatic parameters, effect to the transmission of dengue viruses the dengue viruses and their principal mosquito vector, Aedes aegypti. A transmission model for dengue disease is discussed in this paper. We assume that the human and vector populations are constant. We showed that the local stability is completely determined by the threshold parameter, 0 B . If 0 B is less than one, the disease free equilibrium state is stable. If 0 B is more than one, a unique endemic equilibrium state exists and is stable. The numerical results are shown for the different values of the transmission probability from vector to human populations.

Keywords: Dengue disease, mathematical model, season, threshold parameters.

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Authors: P. Pongsumpun

Abstract:

Leptospirosis occurs worldwide (except the poles of the earth), urban and rural areas, developed and developing countries, especially in Thailand. It can be transmitted to the human by rats through direct and indirect ways. Human can be infected by either touching the infected rats or contacting with water, soil containing urine from the infected rats through skin, eyes and nose. The data of the people who are infected with this disease indicates that most of the patients are adults. The transmission of this disease is studied through mathematical model. The population is separated into human and rat. The human is divided into two classes, namely juvenile and adult. The model equation is constructed for each class. The standard dynamical modeling method is then used for analyzing the behaviours of solutions. In addition, the conditions of the parameters for the disease free and endemic states are obtained. Numerical solutions are shown to support the theoretical predictions. The results of this study guide the way to decrease the disease outbreak.

Keywords: Adult human, juvenile human, leptospirosis, mathematical model.

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Authors: P. Pongsumpun

Abstract:

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.

Keywords: Dynamical analysis, Malaria, mathematical model, threshold condition.

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Authors: Puntani Pongsumpun, I-Ming Tang

Abstract:

The incidences of dengue hemorrhagic disease (DHF) over the long term exhibit a seasonal behavior. It has been hypothesized that these behaviors are due to the seasonal climate changes which in turn induce a seasonal variation in the incubation period of the virus while it is developing the mosquito. The standard dynamic analysis is applied for analysis the Susceptible-Exposed- Infectious-Recovered (SEIR) model which includes an annual variation in the length of the extrinsic incubation period (EIP). The presence of both asymptomatic and symptomatic infections is allowed in the present model. We found that dynamic behavior of the endemic state changes as the influence of the seasonal variation of the EIP becomes stronger. As the influence is further increased, the trajectory exhibits sustained oscillations when it leaves the chaotic region.

Keywords: Chaotic behavior, dengue hemorrhagic fever, extrinsic incubation period, SEIR model.

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Authors: P. Pongsumpun, I. M. Tang

Abstract:

Malaria is a serious, acute and chronic relapsing infection to humans. It is characterized by periodic attacks of chills, fever, nausea, vomiting, back pain, increased sweating anemia, splenomegaly (enlargement of the spleen) and often-fatal complications.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. A mathematical model for the transmission of P. vivax is developed in which the human population is divided into four classes, the susceptible, the infected, the dormant and the recovered. In this paper, we formulate the dynamical model of P. vivax malaria to see the distribution of this disease at the district level.

Keywords: Dynamical model, household, local level, Plasmodium Vivax Malaria.

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Authors: P. Pongsumpun

Abstract:

Dengue virus is transmitted from person to person through the biting of infected Aedes Aegypti mosquitoes. DEN-1, DEN-2, DEN-3 and DEN-4 are four serotypes of this virus. Infection with one of these four serotypes apparently produces permanent immunity to it, but only temporary cross immunity to the others. The length of time during incubation of dengue virus in human and mosquito are considered in this study. The dengue patients are classified into infected and infectious classes. The infectious human can transmit dengue virus to susceptible mosquitoes but infected human can not. The transmission model of this disease is formulated. The human population is divided into susceptible, infected, infectious and recovered classes. The mosquito population is separated into susceptible, infected and infectious classes. Only infectious mosquitoes can transmit dengue virus to the susceptible human. We analyze this model by using dynamical analysis method. The threshold condition is discussed to reduce the outbreak of this disease.

Keywords: Transmission model, intrinsic incubation period, extrinsic incubation period, basic reproductive number, equilibriumstates, local stability.

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Authors: Rujira Kongnuy, Puntani Pongsumpun, I-Ming Tang

Abstract:

Dengue fever is an important human arboviral disease. Outbreaks are now reported quite often from many parts of the world. The number of cases involving pregnant women and infant cases are increasing every year. The illness is often severe and complications may occur. Deaths often occur because of the difficulties in early diagnosis and in the improper management of the diseases. Dengue antibodies from pregnant women are passed on to infants and this protects the infants from dengue infections. Antibodies from the mother are transferred to the fetus when it is still in the womb. In this study, we formulate a mathematical model to describe the transmission of this disease in pregnant women. The model is formulated by dividing the human population into pregnant women and non-pregnant human (men and non-pregnant women). Each class is subdivided into susceptible (S), infectious (I) and recovered (R) subclasses. We apply standard dynamical analysis to our model. Conditions for the local stability of the equilibrium points are given. The numerical simulations are shown. The bifurcation diagrams of our model are discussed. The control of this disease in pregnant women is discussed in terms of the threshold conditions.

Keywords: Dengue disease, local stability, mathematical model, pregnancy.

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Authors: Rujira Kongnuy, Puntani Pongsumpun, I-Ming Tang

Abstract:

Mathematical models can be used to describe the dynamics of the spread of infectious disease between susceptibles and infectious populations. Dengue fever is a re-emerging disease in the tropical and subtropical regions of the world. Its incidence has increased fourfold since 1970 and outbreaks are now reported quite frequently from many parts of the world. In dengue endemic regions, more cases of dengue infection in pregnancy and infancy are being found due to the increasing incidence. It has been reported that dengue infection was vertically transmitted to the infants. Primary dengue infection is associated with mild to high fever, headache, muscle pain and skin rash. Immune response includes IgM antibodies produced by the 5th day of symptoms and persist for 30-60 days. IgG antibodies appear on the 14th day and persist for life. Secondary infections often result in high fever and in many cases with hemorrhagic events and circulatory failure. In the present paper, a mathematical model is proposed to simulate the succession of dengue disease transmission in pregnancy and infancy. Stability analysis of the equilibrium points is carried out and a simulation is given for the different sets of parameter. Moreover, the bifurcation diagrams of our model are discussed. The controlling of this disease in infant cases is introduced in the term of the threshold condition.

Keywords: Dengue infection, equilibrium states, maternalantibodies, pregnancy and infancy.

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Authors: P. Pongsumpun, I.M. Tang

Abstract:

Plasmodium vivax malaria differs from P. falciparum malaria in 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 patients where it is able to re-infect the patient after a passage of time. During this stage, the patient is classified as being in the dormant class. The model to describe the transmission of P. vivax malaria consists of a human population divided into four classes, the susceptible, the infected, the dormant and the recovered. The effect of a time delay on the transmission of this disease is studied. The time delay is the period in which the P. vivax parasite develops inside the mosquito (vector) before the vector becomes infectious (i.e., pass on the infection). We analyze our model by using standard dynamic modeling method. Two stable equilibrium states, a disease free state E0 and an endemic state E1, are found to be possible. It is found that the E0 state is stable when a newly defined basic reproduction number G is less than one. If G is greater than one the endemic state E1 is stable. The conditions for the endemic equilibrium state E1 to be a stable spiral node are established. For realistic values of the parameters in the model, it is found that solutions in phase space are trajectories spiraling into the endemic state. It is shown that the limit cycle and chaotic behaviors can only be achieved with unrealistic parameter values.

Keywords: Equilibrium states, Hopf bifurcation, limit cyclebehavior, local stability, Plasmodium Vivax, time delay.

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Authors: Puntani Pongsumpun, I-Ming Tang

Abstract:

The most Malaria cases are occur along Thai-Mynmar border. Mathematical model for the transmission of Plasmodium falciparum and Plasmodium vivax malaria in a mixed population of Thais and migrant Burmese living along the Thai-Myanmar Border is studied. The population is separated into two groups, Thai and Burmese. Each population is divided into susceptible, infected, dormant and recovered subclasses. The loss of immunity by individuals in the infected class causes them to move back into the susceptible class. The person who is infected with Plasmodium vivax and is a member of the dormant class can relapse back into the infected class. A standard dynamical method is used to analyze the behaviors 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 the community. When infected Burmese enter the Thai community, an epidemic state can occur. It is found that the disease-free state is stable when the threshold number is less than one. The epidemic state is stable when a second threshold number is greater than one. Numerical simulations are used to confirm the results of our model.

Keywords: Basic reproduction number, Burmese, local stability, Plasmodium Vivax malaria.

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