| Citation: |
Jie Bai, Jin Wang. A TWO-PATCH MODEL FOR THE COVID-19 TRANSMISSION DYNAMICS IN CHINA[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1982-2016. doi: 10.11948/20200302
|
A TWO-PATCH MODEL FOR THE COVID-19 TRANSMISSION DYNAMICS IN CHINA
-
Abstract
In this paper, we study the COVID-19 epidemic in China and investigate its transmission dynamics. We propose a two-patch model in a spatially heterogeneous setting that incorporates multiple transmission pathways. We focus our attention on the roles of the environmental reservoir and the spatial heterogeneity in shaping the overall epidemic pattern. We conduct a detailed analysis on the global dynamics of the model, and demonstrate the application of our model through the incorporation of realistic data.
-
-
References
[1] J. F. W. Chan, S. Yuan, K. H. Kok, et al., A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster, Lancet, 2020, 395, 514-523. doi: 10.1016/S0140-6736(20)30154-9 [2] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 2002, 180, 29-48. doi: 10.1016/S0025-5564(02)00108-6 [3] N. van Doremalen, T. Bushmaker, D. H. Morris, et al., Aerosol and surface stability of SARS-CoV-2 as compared with SARS-CoV-1, New Engl. J. Med., 2020, 382, 1564-1567. doi: 10.1056/NEJMc2004973 [4] T. Ellerin, The new coronavirus: What we do-and don't-know, Harvard Health Blog, January 25, 2020. Available at https://www.health.harvard.edu/blog/the-new-coronavirus-what-we-do-and-dont-know-2020012518747 [5] N. Imai, A. Cori, I. Dorigatti, M. Baguelin, C. A. Donnelly, S. Riley, and N. M. Ferguson, Report 3: Transmissibility of 2019-nCoV, published online January 25, 2020. Available at https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/news-wuhan-coronavirus/ [6] K. Leung, J. Wu, D. Liu, and G. M. Leung, First-wave COVID-19 transmissibility and severity in China outside Hubei after control measures, and second-wave scenario planning: a modelling impact assessment, Lancet, 2020, 395, 1382-1393. doi: 10.1016/S0140-6736(20)30746-7 [7] Q. Li, X. Guan, P. Wu, X. Wang, L. Zhou, Y. Tong, et al., Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia, N. Engl. J. Med., 2020, 382(13), 1199-1207. doi: 10.1056/NEJMoa2001316 [8] R. Li, S. Pei, B. Chen, Y. Song, T. Zhang, W. Yang, and J. Shaman, Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2), Science, 2020, 368, 489-493. doi: 10.1126/science.abb3221 [9] J. M. Read, J. R. E. Bridgen, D. A. T. Cummings, A. Ho and C. P. Jewell, Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions, available at medRxiv. DOI: https://doi.org/10.1101/2020.01.23.20018549 [10] B. Tang, X. Wang, Q. Li, N. L. Bragazzi, S. Tang, Y. Xiao, and J. Wu, Estimation of the Transmission Risk of 2019-nCoV and Its Implication for Public Health Interventions, J. Clin. Med., 2020, 9(2), 462. doi: 10.3390/jcm9020462 [11] J. Wang, Mathematical models for COVID-19: applications, limitations, and potentials, J. Public Health Emerg., 2020, 4, 9. doi: 10.21037/jphe-2020-05 [12] J. Wu, K. Leung, and G. M. Leung, Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study, Lancet, 2020, 395, 689-697. doi: 10.1016/S0140-6736(20)30260-9 [13] C. Yang and J. Wang, A mathematical model for the novel coronavirus epidemic in Wuhan, China, Math. Biosci. Eng., 2020, 17(3), 2708-2724. doi: 10.3934/mbe.2020148 [14] C. Yeo, S. Kaushal and D. Yeo, Enteric involvement of coronaviruses: is faecal-oral transmission of SARS-CoV-2 possible? Lancet Gastroenterol., 2020, 5(4), 335-337. doi: 10.1016/S2468-1253(20)30048-0 [15] Centers for Disease Control and Prevention: Coronavirus (COVID-19). Available at https://www.cdc.gov/coronavirus/2019-ncov [16] Statistical Bulletin of National Economic and Social Development of WUHAN in 2019, 2020-03-29. Available at http://tjj.wuhan.gov.cn/tjfw/tjgb/202004/t20200429_1191417.shtml [17] Hubei Provincial Bureau of Statistics, Statistical Bulletin of National Economic and Social Development of Hubei Province in 2019, 2020-03-23. Available at http://tjj.hubei.gov.cn/tjsj/tjgb/ndtjgb/qstjgb/202003/t20200323_2188487.shtml [18] National Bureau of Statistics, 2019. Available at http://data.stats.gov.cn/easyquery.htm?cn=C01 [19] The Health Commission of Hubei Province, Available at http://wjw.hubei.gov.cn/fbjd/dtyw/index_16.shtml [20] National Health Commission of the People's Republic of China, Data of Confirmed Cases on COVID-19, 2020. Available at http://www.nhc.gov.cn/xcs/xxgzbd/gzbd_index.shtml -
-
Figures(11) / Tables(3)
Export File
Citation
Jie Bai, Jin Wang. A TWO-PATCH MODEL FOR THE COVID-19 TRANSMISSION DYNAMICS IN CHINA[J]. Journal of Applied Analysis & Computation, 2021, 11(4): 1982-2016. doi: 10.11948/20200302
Format
Content
DownLoad:
- Figure 1. Data fitting for the daily new infections from January 23rd to February 3rd in patch 1. The circles represent the reported data and the solid line represents the fitting result.
- Figure 2. Data fitting for the daily new infections from January 23rd to February 3rd in patch 2. The circles represent the reported data and the solid line represents the fitting result.
-
Figure 3. The phase diagram of
$ I_{1} $ vs.$ E_{1} $ in patch 1 based on the parameter setting in stage 1 (from January 23rd to February 3rd). The trajectories starting from different initial values approach the endemic equilibrium where ($ E_{1}^{EE} $ ,$ I_{1}^{EE} $ ) = ($ 10940 $ ,$ 25826 $ ). -
Figure 4. The phase diagram of
$ I_{2} $ vs.$ E_{2} $ in patch 2 based on the parameter setting in stage 1 (from January 23rd to February 3rd). The trajectories starting from different initial values approach the endemic equilibrium where ($ E_{2}^{E} $ ,$ I_{2}^{E} $ ) = ($ 81893 $ ,$ 220326 $ ). - Figure 5. Data fitting for the daily new infections from February 4th to February 23rd in patch 1. The circles represent the reported data and the solid line represents the fitting result.
- Figure 6. Data fitting for the daily new infections from February 4th to February 23rd in patch 2. The circles represent the reported data and the solid line represents the fitting result.
-
Figure 7. The phase diagram of
$ I_{1} $ vs.$ E_{1} $ in patch 1 based on the parameter setting in stage 2 (from February 4th to February 23rd). The trajectories starting from different initial values approach the disease-free equilibrium where ($ E_{10}^{*} $ ,$ I_{10}^{*} $ ) = ($ 0 $ ,$ 0 $ ). -
Figure 8. The phase diagram of
$ I_{2} $ vs.$ E_{2} $ in patch 2 based on the parameter setting in stage 2 (from February 4th to February 23rd). The trajectories starting from different initial values approach the disease-free equilibrium where ($ E_{20}^{*} $ ,$ I_{20}^{*} $ ) = ($ 0 $ ,$ 0 $ ). - Figure 9. Long-term simulation for the numbers of exposed and infected individuals in patch 1.
- Figure 10. Long-term simulation for the numbers of exposed and infected individuals in patch 2.
-
Figure 11. The impact of the population movement rates
$ a_{2} $ and$ b_{2} $ on the reproduction numbers$ \mathcal{R}_{01} $ and$ \mathcal{R}_{02} $ . Left panel: stage 1 (January 23rd – February 3rd); right panel: stage 2 (February 4th – February 23rd).