Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Mathematical analysis for COVID-19 resurgence in the contaminated environment

School of Mathematics and Statistics, Southwest University, Chongqin 400715, China

Special Issues: Modeling the Biological, Epidemiological, Immunological, Molecular, Virological Aspects of COVID-19

A mathematical model is proposed that incorporates the key routes of COVID-19 resurgence: human-to-human transmission and indirect transmission by inhaling infectious aerosols or contacting public facilities with the virus. The threshold condition for the disease invasion is established, and the relationships among the basic reproduction number, peak value and final size are formulated. The model is validated by matching the model with the data on cases of COVID-19 resurgence in April of 2020 from Heilongjiang province in China, which indicates that the predictive values from the mathematical model fit the real data very well. Based upon the computations from the model and analytical formulae, we reveal how the indirect transmission from environmental pathogens contribute to the disease outbreak and how the input of asymptomatic individuals affect the disease spread. These findings highlight the importance of mass detection and environmental disinfection in the control of COVID resurgence.
  Article Metrics


1. Y. Chen, Q. Liu, D. Guo, Emerging coronaviruses: Genome structure, replication, and pathogenesis, J. Med. Virol., 92 (2020), 418-423.

2. C. Huang, Y. Wang, X. Li, L. Ren, J. Zhao, Y. Hu, et al., Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China, Lancet Infect. Dis., 395 (2020), 497-506.

3. S. Li, Y. Shan, Latest research advances on novel corona virus pnuemonia, J. Shandong University (Health Science), 58 (2020), 19-25.

4. Guidance document for COVID-19. Available from: https://www.who.int/zh/emergencies/diseases/novel-coronavirus-2019.

5. Y. Ye, W. Fan, W. Wang, H. Wang, J. Pan, Y. Nie, et al., Difference in epidemic characteristics between asymptomatic infected persons and confirmed cases in COVID-19 clustered epidemics, Chin. J. Infect. Control, 19 (2020), 1-6.

6. Y. Chen, A. Wang, B. Yi, K. Ding, H. Wang, J. Wang, et al., Epidemiological characteristics of infection in COVID-19 close contacts in Ningbo city, China J. Epidemiol., 41 (2020), 667-671.

7. Heilongjiang Provincial Health Committee. Available from: http://wsjkw.hlj.gov.cn/.

8. Jilin Provincial Health Committee. Available from: http://wjw.jlcity.gov.cn/.

9. C. Xiong, A detailed explanation of survival time for COVID-19 virus in the environment, China Food Safty Magazine, 5 (2020), 22-25.

10. S. Huang, Z. Peng, Z. Jin, Studies of the strategies for controlling the COVID-19 epidemic in China: Estimation of control efficacy and suggestions for policy makers, Sci. Sin. Math., 50 (2020), 1-14.

11. B. Tang, X. Wang, Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions, J. Clin. Med., 9 (2020), 1-13.

12. S. Tang, B. Tang, N. L. Bragazzi, F. Xia, T. Li, S. He, et al., Analysis of COVID-19 epidemic traced data and stochastic discrete transmission dynamic model, Sci. Sin. Math., 50 (2020), 1-16.

13. S. Zhao, Q. Lin, J. Ran, S. S. Musa, G. Yang, W. Wang, et al., Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak, Int. J. Infect. Dis., 92 (2020), 214-217.

14. Y. Hu, K. Wang, W. Wang, Regional difference of COVID-19 for transmission capacity and epidemic control efficacy, Acta Math. Appl. Sinica (Chinese Series), 43 (2020), 227-237.

15. S. Wang, X. Liu, J. Qin, S. Li, Nucliec acid screening results of 738 close contacts of coronavirus disease 2019, Chin. J. Infect. Control, 19 (2020), 297-300.

16. National Health Commission of the People's Republic of China. Available from: http://www.nhc.gov.cn/.

17. X. Zhao, X. Liang, L. Zhang, Basic reproduction ratios for periodic abstrac functional differential equations, J. Dyn. Differ. Equ., 31 (2019), 1247-1278.

18. P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2020), 29-48.

19. O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R0 in the models for infectious disease in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382.

20. W. Wang, X. Zhao, Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments, J. Dyn. Diff. Equat., 20 (2008), 699-717.

21. Z. Feng, Final and peak epidemic size for SEIR models with quarantine and isolation, Math. Biosci. Eng., 4 (2007), 675-686.

22. R. M. Anderson, R. M. May, Infectious Diseases of Humans: Dynamics and Control, Cambridge University Press, New York, 1991.

23. J. Arino, F. Brauer, P. van den Driessche, J. Watmough, J. Wu, A final size relation for epidemic models, Math. Biosci. Eng., 4 (2007), 159-175.

24. J. Cui, Z. Feng, Y. Zhang, Influence of non-homogeneous mixing on final epidemic size in a meta-population model, J. Bio. Dyn., 13 (2019), 31-46.

25. J. Li, Q. Xu, Y. Wang, J. Xu, Y. Huang, W. Liu, et al., Analysis in characteristics of asymptomatic infection patients with coronavirus disease 2019 in Yangzhou City of Jiangsu Province, J. Clin. Med. in Practice, 24 (2020), 10-13.

26. The integrated platform of COVID-19 prevention and control. Available from: http://xgpt.clas.ac.cn/service.

27. Y. Xu, L. Wang, W. Zhang, T. Gao, C. Wu, Epidemiological and clinical charateristics 35 cases of COVID-2019 pneumonia, J. Clin. Pul. Med., 25 (2020), 1082-1086.

28. Heilongjiang province people's government. Available from: http://www.hlj.gov.cn/.

© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved