Computational Modeling of SEIPR Model for the Transmission Dynamics of Hand, Foot and Mouth Disease in Sarawak

Chan, Sze Jan (2019) Computational Modeling of SEIPR Model for the Transmission Dynamics of Hand, Foot and Mouth Disease in Sarawak. Masters thesis, Universiti Malaysia Sarawak (UNIMAS).

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Abstract

This thesis aims to develop a suitable model to describe the transmission dynamics of hand, foot and mouth disease (HFMD) specifically in addressing the insight on the ability of the virus to survive in the respiratory secretion and stool of a patient for a period of time in order to predict the periodic cycle of HFMD infectious cases more accurately. This was found necessary since a basic SIR (Susceptible-Infectious-Fully recovered) model only provide a basic framework to discuss the characteristic of HFMD. Biological characteristics, which are incubation period, infectious period and post-infectious virus shedding period are known to be the factors for the virus spreading. Thus, to provide a complete study framework based on the biological factors of HFMD, basic SIR model was extended to become SEIPR (Susceptible-Incubation period-Infectious-Post infectious virus shedding-Fully recovered) model whereby the incubation period and post-infectious period together with the existing infectious period to act as infected compartments were incorporated. The numerical results of the model were compared with the actual 2006 HFMD infectious data. There is no significance difference between the numerical simulation and the actual data by using the SEIPR during the first wave of the outbreak for ten weeks. Then, SEIPR model is being verified by analyzing the HFMD outbreaks from year 2010 to 2014 and the results during the first wave of the outbreaks are well matched with the actual cases. Hence, with the inclusion of the transmission coefficient gained from incubation period patients, which is β1 and post-infectious patients, which is β6 together with the transmission coefficient from infectious individual, which is β5 to susceptible in the improvement SEIPR model, the numerical simulation results reached a consensus that iv the incorporated infected compartments are able to predict the HFMD cases during the first wave of the outbreaks for ten weeks. Furthermore, SEIPR model provides two main parameters that have been evaluated include basic reproductive number, R0 and the threshold value. The values of R0 calculated are between 1.13 to 1.54, indicating the outbreaks of the disease occurred from year 2010 to 2014. Meanwhile, the threshold value as minimum proportion of the population to create the liability of the disease spreading for each case was found to be in the range 6500 to 9000 people. It is observed that with higher R0 , the transmission coefficient is higher and the threshold value is smaller, which means more people can be infected. Hence, to reduce the number of infected cases, the transmission coefficients need to be reduced, thus, the number of any contact person within the infected region needs to be controlled, so that the impacts of the outbreaks can be reduced. Keywords: Hand, foot and mouth disease, SIR model, SEIPR model, incubation period, post-infectious virus shedding period.

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