# American Institute of Mathematical Sciences

doi: 10.3934/cpaa.2021155
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## Transmission dynamics and high infectiousness of Coronavirus Disease 2019

 1 Institute of NBC Defense of PLA, Beijing 102205, China 2 Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China 3 School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China 4 Ministry of Education Key Laboratory of Environment and Health, State Key Laboratory of Environmental Health (Incubating), School of Public Health, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430063, China 5 Institute of Biotechnology, Academy of Military Medical Sciences, Beijing 100071, China 6 XiangYa School of Public Health, Central South University, Changsha, Hunan 410078, China

* Corresponding author

Received  February 2021 Revised  July 2021 Early access September 2021

Coronavirus disease 2019 (COVID-19) has rapidly spread around the world since the early 2020. Recently, a second wave of COVID-19 has resurged in many countries. The transmission dynamics and infectiousness of the COVID-19 pandemic remain unclear, and developing strategies to mitigate the severity of the pandemic is a top priority for global public health. According to the infection mechanism of COVID-19, a novel susceptible-asymptomatic-symptomatic-recovered (SASR) model with control variables in a patchy environment was proposed not only to consider the key characteristics of asymptomatic infection and the effects of seasonal variation but also to incorporate different control measures for multiple transmission routes. The basic reproduction number $R_{0}$ was established to describe the spreading behavior in the natural state over a long time horizon, and the natural reproduction number $R_{n}$, which describes the development trend of the disease during a short time in the future, was defined according to the actual propagation characteristics. In addition, the effective reproduction number $R_{e}$ considering the control strategies was proposed to evaluate the impact of non-pharmaceutical interventions. The results of numerical simulations for COVID-19 cases in Wuhan, China, based on the SASR model indicate that $R_{0}$ was 3.58, $R_{n}$ ranged from 2.37 to 4.91, and $R_{e}$ decreased gradually from 4.83 on December 8, 2019 to 0.31 on March 8, 2020, reaching 1.40 on January 23, 2020, when the lockdown was lifted in Wuhan. We further concluded that the total number of infections, including asymptomatic infections, was approximately 301, 804 as of March 8, 2020, in Wuhan, China. In particular, this article proposes a dynamic method to distinguish the impact of natural factors and human interventions on the development of the pandemic, and provides a theoretical basis for fighting the global COVID-19 pandemic.

Citation: Shunxiang Huang, Lin Wu, Jing Li, Ming-Zhen Xin, Yingying Wang, Xingjie Hao, Zhongyi Wang, Qihong Deng, Bin-Guo Wang. Transmission dynamics and high infectiousness of Coronavirus Disease 2019. Communications on Pure &amp; Applied Analysis, doi: 10.3934/cpaa.2021155
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show all references

##### References:
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Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New York, 1993.  Google Scholar [12] X. Hao, S. Cheng and D. Wu, Reconstruction of the full transmission dynamics of COVID-19 in Wuhan, Nature, 584 (2020), 420-424.  doi: 10.1038/s41586-020-2554-8.  Google Scholar [13] X. He, E. H. Y. Lau and P. Wu, Temporal dynamics in viral shedding and transmissibility of COVID-19, Nat Med, 26 (2020), 672-675.  doi: 10.1038/s41591-020-0869-5.  Google Scholar [14] J. Hellewell, S. Abbott and A. Gimma, Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts, The Lancet Global Health, 8 (2020), 488-496.  doi: 10.1016/S2214-109X(20)30074-7.  Google Scholar [15] C. Huang, Y. Wang and X. Li, Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China, The Lancet, 395 (2020), 497-506.  doi: 10.1016/S0140-6736(20)30183-5.  Google Scholar [16] G. M. Hwang, P. J. Mahoney and J. H. James, A model-based tool to predict the propagation of infectious disease via airports, Travel Medicine Infectious Disease, 10 (2020), 32-42.   Google Scholar [17] S. M. Kissler, C. Tedijanto and E. Goldstein, Projecting the transmission dynamics of SARS-CoV-2 through the post-pandemic period, Science, 368 (2020), 860-868.  doi: 10.1126/science.abb5793.  Google Scholar [18] J. S. Lavine, M. Poss and B. T. Grenfell, Directly transmitted viral diseases: modeling the dynamics of transmission, Trends Microbiol, 16 (2020), 165-172.  doi: 10.1016/j.tim.2008.01.007.  Google Scholar [19] J. Lee, G. Chowell and E. Jung, A dynamic compartmental model for the Middle East respiratory syndrome outbreak in the Republic of Korea: A retrospective analysis on control interventions and superspreading events, J. Theor. Biol., 408 (2016), 118-126.  doi: 10.1016/j.jtbi.2016.08.009.  Google Scholar [20] Y. Liu, Z. Ning and Y. Chen, Aerodynamic analysis of SARS-CoV-2 in two Wuhan hospitals, Nature, 582 (2020), 557-560.  doi: 10.1038/s41586-020-2271-3.  Google Scholar [21] L. Marc, C. Ted and C. Ben, Transmission dynamics and control of severe acute respiratory syndrome, Science, 300 (2003), 1966-1970.   Google Scholar [22] V. J. Munster, M. Koopmans and N. van Doremalen, A Novel coronavirus emerging in China-key questions for impact assessment, N. Engl. J. Med., 382 (2020), 692-694.   Google Scholar [23] R. A. Neher, R. Dyrdak and V. Druelle et al., Potential impact of seasonal forcing on a SARS-CoV-2 pandemic, Schwzerische medizinische Wochenschrift, 150 (2020). Google Scholar [24] S. Novo, R. Obaya and A. M. Sanz, Topological dynamics for monotone skew-product semiflows with applications, J. Dyn. Differ. Equ., 25 (2013), 1201-1231.   Google Scholar [25] A. Pan, L. Liu and C. 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Liu, Research progress of basic regeneration number in COVID-19, Chinese Science Bulletin, 65 (2020), 2334-2341.  doi: 10.1360/TB-2020-0413.  Google Scholar [34] WHO, Middle East respiratory syndrome coronavirus (MERS-CoV). Google Scholar [35] WHO, Statement on the second meeting of the International Health Regulations (2005) Emergency Committee regarding the outbreak of novel coronavirus (2019-nCoV), 30 January 2020 Statement Geneva, Switzerland. Google Scholar [36] W. Wang and X. Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Differ. Equ., 20 (2008), 699-717.  doi: 10.1007/s10884-008-9111-8.  Google Scholar [37] J. T. 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, The Lancet, 395 (2020), 689-697.  doi: 10.1016/S0140-6736(20)30260-9.  Google Scholar [38] Z. Yang, Z. Zeng and K. Wang, Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions, J. Thorac. Dis., 12 (2020), 165-174.  doi: 10.21037/jtd.2020.02.64.  Google Scholar [39] X. Q. Zhao, Dynamical Systems in Population Biology, Springer-Verlag, New York, 2017. Google Scholar [40] N. Zhu, D. Zhang and W. Wang, For the China Novel Coronavairus Investigating and Reaseach Team. A Novel coronavirus from patients with pneumonia in China, 2019., N. Engl. J. Med., 382 (2020), 727-733.   Google Scholar
The variation of basic reproduction number, effective reproduction number and natural reproduction number
The variation of model parameters
Prediction and surveillance of new infected cases and total infected cases
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