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Stochastic epidemic model estimation using Monte Carlo expection maximization algorithm
Journal of the Korean Data & Information Science Society 2018;29:97-109
Published online January 31, 2018
© 2018 Korean Data and Information Science Society.

Boseung Choi1 · Yong Hwa Yoon2

1Department of National Statistics, Korea University Sejong campus
2Department of Statistics and Computer Science, Daegu University
Correspondence to: Professor, Department of Statistics and Computer Science, Daegu University, Gyeongbuk 38453, Korea. E-mail:
Received December 26, 2017; Revised January 11, 2018; Accepted January 16, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this paper, we introduce a statistical method for modeling the spread of disease. Historically, the ordinary differential equation is proposed to construct the epidemic model. However, the deterministic approach for the epidemic model is too simplified to capture the stochastic behavior of spread of disease. We consider the stochastic kinetic networks model for the epidemic modeling and we proposed MCEM (Monte Carlo expectation maximization) method to perform the statistical inference for reaction constants of the stochastic epidemic model. We applied our MCEM method to a synthetic data from the representative stochastic epidemic model, named SIRS (susceptible - infected - recovered - susceptible) model and we compared proposed MCEM method with two Bayesian MCMC methods. The MCEM result gives stable and faster convergence results. We also MCEM method to the data from the onset of early pandemic of H1N1 in the US. The proposed MCEM method can be an alternative to the estimation method for the stochastic epidemic model.
Keywords : Epidemic model, MCEM algorithm, SIRS model, stochastic chemical reaction model.