Epidemic Model for Vaccination and Quarantine
Abstract
This study aims to develop epidemic model for vaccination and quarantine. The model is formulated based on SEIRVQ (Susceptible-Exposed– Infected - Recovered - Vaccinated - Quarantine) in order to predict the number of infection when an outbreak occurs. The model exhibits two equilibriums, disease-free and endemic equilibriums. The stability theory of differential equations and numerical simulation are used. The results found that the disease-free equilibrium is locally asymptotically stable if the basic reproductive number is less than unity. It means that the disease can be eradicated from the population. On the contrary, in case of the basic reproductive number is greater than unity, the endemic equilibrium is locally asymptotically stable. Furthermore, the formulated model is used to predict the chickenpox outbreak in 2016 at Songkhla, Thailand. Then, the predicted data were compared with the actual cases. Keywords : SEIRVQ epidemic model, basic reproductive number, stabilityReferences
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Van den Driessche, P. and Watmough, J. (2002). Reproduction number and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. ,180, 29-48.
Christopher, M., & Jorge, X. (1995). A Simple Vaccination model with Multiple Endemic State. Math. Biosci., 164, 183-201.
Data analysis activity: Herd Immunity. (2015). Retrieved August, 28, 2016, from
https://www.teachunicef.org/sites/default/files/Data_Analysis.pdf
Diekmann, O., Heesterbeek, J.A.P., & Metz, J.A.J. (1990). On the definition and the computation of the basic reproduction ratio in models for infectious diseases in heterogeneous populations. J. Math. Biol. , 28, 365-382.
Kermack, W.O., & Mckendrick, A.G. (1927). Contributions to the mathematical theory of epidemic. Proc. Roy.
Soc. Lond., 115, 700 -721.
Orawan, T., & Puntani, P. (2013). Chickenpox Transmission Model in Thailand . Journal of Science Ladkrabang,
22(1), 39 – 52 (in Thai)
Puangtong, K. (2014). Haamordotcom. Chickenpox. Retrieved January, 10, 2017, from http:// haamor/ th/ Chickenpox (in Thai)
Songkhla Provincial Public Health office. (2016). Data Center. Retrieved January, 5, 2017, from http://www.skho.moph.go.th/dataservice/ (in Thai)
Van den Driessche, P. and Watmough, J. (2002). Reproduction number and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. ,180, 29-48.
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Published
2017-08-07
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บทความวิจัยจากการประชุมวิชาการระดับชาติ"วิทยาศาสตร์วิจัย"ครั้งที่ 9
