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Author: search.filters.author.Pongsumpun, PuntipaSubject: search.filters.subject.mathematical model

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    A modified optimal control for the mathematical model of dengue virus with vaccination
    (2023-01-01)
    Pongsumpun, Puntipa
    ;
    Lamwong, Jiraporn
    ;
    Tang, I. Ming
    ;
    Pongsumpun, Puntani
    The dengue viruses (of which there are four strains) are the causes of three illnesses of increasing severity; dengue fever (DF), dengue hemorrhagic fever (DHF) and dengue shock syndrome (DSS). Recently, dengue fever has reached epidemic proportion in several countries. Strategies or preventative methods have to be developed to combat these epidemics. This can be done by development of vaccines or by preventing the transmission of the virus. The latter approach could involve the use of mosquito nets or insecticide spraying. To determine which strategy would work, we test the strategy using mathematical modeling to simulate the effects of the strategy on the dynamics of the transmission. We have chosen the Susceptible-Exposed-Infected-Recovered (SEIR) model and the Susceptible, Exposed-Infected (SEI) model to describe the human and mosquito populations, repectively. We use the Pontryagin’s maximum principle to find the optimal control conditions. A sensitivity analysis revealed that the transmission rate (ɣ<inf>ℎ</inf>, ɣ<inf>v</inf>), the birth rate of human population (µ<inf>ℎ</inf>), the constant recruitment rate of the vector population (A) and the total human population (N<inf>ℎ</inf>) are the most influential factors affecting the disease transmission. Numerical simulations show that the optimal controlled infective responses, when implemented, cause the convergence to zero to be faster than that in uncontrolled cases.
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    Mathematical model for Chikungunya disease with two types of Aedes mosquitoes
    (2022-04-28)
    Pongsumpun, Puntipa
    ;
    Pongsumpun, Puntani
    Chikungunya disease is occurred when the infected Aedes mosquitoes bite. Chikungunya virus is a member of the genus Alphavirus family Togaviridae. There are 2 species of Aedes mosquitoes such as Aedes aegypti and Aedes albopictus. We describe the transmission of the disease by using mathematical model. We separated the populations to human and vector populations. We separate the human population to susceptible, infectious and recovered populations. The mosquitoes are separated into susceptible and infectious populations. Then we analyze the model by using standard dynamical analysis. The numerical solutions are shown to see the stability of each equilibrium state. The variances of each parameter are shown to see the behavior of each population. The basic reproduction number of this disease is shown to reduce the transmission of this disease.