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  • ISSN 1674-8301
  • CN 32-1810/R
Volume 38 Issue 2
Mar.  2024
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Ziyu Zhao, Yi Zhou, Jinxing Guan, Yan Yan, Jing Zhao, Zhihang Peng, Feng Chen, Yang Zhao, Fang Shao. The relationship between compartment models and their stochastic counterparts: A comparative study with examples of the COVID-19 epidemic modeling[J]. The Journal of Biomedical Research, 2024, 38(2): 175-188. DOI: 10.7555/JBR.37.20230137
Citation: Ziyu Zhao, Yi Zhou, Jinxing Guan, Yan Yan, Jing Zhao, Zhihang Peng, Feng Chen, Yang Zhao, Fang Shao. The relationship between compartment models and their stochastic counterparts: A comparative study with examples of the COVID-19 epidemic modeling[J]. The Journal of Biomedical Research, 2024, 38(2): 175-188. DOI: 10.7555/JBR.37.20230137
shu

The relationship between compartment models and their stochastic counterparts: A comparative study with examples of the COVID-19 epidemic modeling

  • 1.

    Department of Biostatistics, School of Public Health, Nanjing Medical University, Nanjing, Jiangsu 211166, China

  • 2.

    Nanjing Hanwei Public Health Research Institute Co., Ltd, Nanjing, Jiangsu 210005, China

  • 3.

    China International Cooperation Center for Environment and Human Health, Center for Global Health, Nanjing Medical University, Nanjing, Jiangsu 211166, China

  • 4.

    The Center of Biomedical Big Data and the Laboratory of Biomedical Big Data, Nanjing Medical University, Nanjing, Jiangsu 211166, China

  • 5.

    Jiangsu Key Lab of Cancer Biomarkers, Prevention and Treatment, Collaborative Innovation Center for Cancer Personalized Medicine, Nanjing Medical University, Nanjing, Jiangsu 211166, China

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  • Corresponding author:

    Fang Shao and Yang Zhao, Department of Biostatistics, School of Public Health, Nanjing Medical University, 101 Longmian Avenue, Nanjing, Jiangsu 211166, China. E-mails: shaofang@njmu.edu.cn (Shao) and yzhao@njmu.edu.cn (Zhao)

  • △These authors contributed equally to this work.

  • Received Date: June 10, 2023
  • Revised Date: August 31, 2023
  • Accepted Date: September 05, 2023
  • Available Online: September 06, 2023
  • Published Date: March 04, 2024
    Graphical Abstract
    • Abstract

  • Deterministic compartment models (CMs) and stochastic models, including stochastic CMs and agent-based models, are widely utilized in epidemic modeling. However, the relationship between CMs and their corresponding stochastic models is not well understood. The present study aimed to address this gap by conducting a comparative study using the susceptible, exposed, infectious, and recovered (SEIR) model and its extended CMs from the coronavirus disease 2019 modeling literature. We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations. Based on this equivalence, we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment. The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics. However, it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs. Additionally, we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents. This model offered a balance between computational efficiency and accuracy. The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling. Furthermore, the results had implications for the development of hybrid models that integrated the strengths of both frameworks. Overall, the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.

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  • We thank the editors and reviewers for their insightful comments and suggestions, which significantly enhanced the quality of our manuscript.

    This study was supported by the National Natural Science Foundation of China (Grant Nos. 82173620 to Yang Zhao and 82041024 to Feng Chen). This study was also partially supported by the Bill & Melinda Gates Foundation (Grant No. INV-006371 to Feng Chen) and Priority Academic Program Development of Jiangsu Higher Education Institutions.

    CLC number: R181, Document code: A

    The authors reported no conflict of interests.

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