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Stochastic methods for epidemic models: An application to the 2009 H1N1 influenza outbreak in Korea

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  • Lee, Hyojung
  • Lee, Sunmi
  • Lee, Chang Hyeong

Abstract

In this paper, we present stochastic methods for computation of influenza transmission models. First, SEIR type deterministic epidemiological models are revisited and stochastic modeling for those models are introduced. The main motivation of our work is to present computational methods of the stochastic epidemic models. In particular, the moment closure method (MCM) is developed for some influenza models and compared with the results under the standard stochastic simulation algorithm (SSA). All epidemic outcomes including the peak size, the peak timing and the final epidemic size of both methods are in a good agreement, however, the MCM has reduced the computational time and costs significantly. Next, the MCM has been employed to model the 2009 H1N1 influenza transmission dynamics in South Korea. The influenza outcomes are compared under the standard deterministic approach and the stochastic approach (MCM). Our results show that there is a considerable discrepancy between the results of stochastic and deterministic models especially when a small number of infective individuals is present initially. Lastly, we investigate the effectiveness of control policies such as vaccination and antiviral treatment under various scenarios.

Suggested Citation

  • Lee, Hyojung & Lee, Sunmi & Lee, Chang Hyeong, 2016. "Stochastic methods for epidemic models: An application to the 2009 H1N1 influenza outbreak in Korea," Applied Mathematics and Computation, Elsevier, vol. 286(C), pages 232-249.
    • Handle: RePEc:eee:apmaco:v:286:y:2016:i:c:p:232-249
    DOI: 10.1016/j.amc.2016.04.019
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    Cited by:

    1. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Stationary distribution of a stochastic cholera model between communities linked by migration," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    2. Liu, Qun & Jiang, Daqing, 2020. "Stationary distribution of a stochastic cholera model with imperfect vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    3. Yongin Choi & James Slghee Kim & Heejin Choi & Hyojung Lee & Chang Hyeong Lee, 2020. "Assessment of Social Distancing for Controlling COVID-19 in Korea: An Age-Structured Modeling Approach," IJERPH, MDPI, vol. 17(20), pages 1-16, October.
    4. Nian, Fuzhong & Yao, Shuanglong, 2018. "The epidemic spreading on the multi-relationships network," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 866-873.
    5. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed & Ahmad, Bashir, 2020. "Threshold behavior in two types of stochastic three strains influenza virus models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    6. Sun, Shulin & Sun, Yaru & Zhang, Guang & Liu, Xinzhi, 2017. "Dynamical behavior of a stochastic two-species Monod competition chemostat model," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 153-170.
    7. Pilwon Kim & Chang Hyeong Lee, 2018. "Epidemic Spreading in Complex Networks with Resilient Nodes: Applications to FMD," Complexity, Hindawi, vol. 2018, pages 1-9, March.

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