KMITL

Permanent URI for this communityhttps://dspace.kmitl.ac.th/handle/123456789/1

Browse

Settings

Author: search.filters.author.Lamwong, JirapornSubject: search.filters.subject.Stability

Search Results

Now showing 1 - 3 of 3
  • Loading...
    Thumbnail Image
    Some of the metrics are blocked by your 
    consent settings
    Item type:Item,
    Global stability of the transmission of hand-foot-mouth disease according to the age structure of the population
    (2021-01-01)
    Lamwong, Jiraporn
    ;
    Wongvanich, Napasool
    ;
    Tang, I. Ming
    ;
    Changpuek, Thurdkwun
    ;
    Pongsumpun, Puntani
    This study investigates a transmission model of Hand-Foot-Mouth disease (HFMD) where the age structure of the population is taken into account. Most infections in Thailand occur among children below the age of 10 years, whose immunity to HFMD is lower than people of age greater than 10 years. Therefore, a mathematical model was developed in which the population was separated into two groups with respect to age: one comprised of children aged less than 10 years, and another comprised of the rest of the population. The reproductive number was obtained by the next-generation matrix approach. Global asymptotical stability of the developed model was assured using Lyapunov’s direct method. The model was validated by showing that the 2D and 3D trajectories of the numerical solutions for the different sub-population groups converged to the endemic equilibrium states when the reproduction number was greater than one, thus supporting the theoretical conclusions. Results show that the time series behaviors of the different normalized populations groups converge to the disease-free state when the values of the parameters are such that the basic reproductive number is 0.591481 (i.e., less than one) and to an endemic state when the values of the parameters are such that R<inf>0</inf> = 54.4523 and R<inf>0</inf> = 192.575 R = (i.e. greater than one). The results of this study can suggest ways for reducing the outbreak of this disease.
  • Loading...
    Thumbnail Image
    Some of the metrics are blocked by your 
    consent settings
    Item type:Item,
    Mathematical model for 4 serotypes of dengue virus with vaccination
    (2018-12-01)
    Lamwong, Jiraporn
    ;
    Pongsumpun, Puntani
    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.
  • Loading...
    Thumbnail Image
    Some of the metrics are blocked by your 
    consent settings
    Item type:Item,
    Mers model of thai and south korean population
    (2018-01-01)
    Lamwong, Jiraporn
    ;
    Tang, I. Ming
    ;
    Pongsumpun, Puntani
    Coronavirus (MERS-Cov) caused the occurrence of Corona. First infected case was reported in 2012 during a poultry outbreak in Saudi Arabia. After that, there were the reports of the sporadic outbreaks in all regions. In this study, we considered the transmission cycle between two population groups: Thai and South Korea. Each population group was divided into susceptible, exposed, infected, quarantine and recovered groups. The behaviors of the solutions were obtained using a standard dynamical modeling method. The stability conditions for the disease free equilibrium state and disease endemic equilibrium states were determined. The basic reproductive number R <inf>0</inf> is obtained. When R <inf>0</inf> <1, the disease-free state was locally asymptotically stable. If R <inf>0</inf> >1, the endemic equilibrium state was locally asymptotically stable. The numerical solutions were shown for supporting the theoretical results. We found that when we decreased α <inf>1</inf> (the rate of susceptible Thai human changes to become an exposed Thai human and μ <inf>1</inf> (the rate at which South Korean population moved out the country), the number of coronavirus case was decreased and outburst of coronavirus epidemic was shorter.