Abstract
The basic reproduction number of an infectious agent is the average number of infections one case can generate over the course of the infectious period, in a naive, uninfected population. This primer article focuses on the basic reproduction number, \(R_0\), for infectious diseases, and other reproduction numbers related to \(R_0\) that are useful in guiding control strategies. Beginning with a simple population model, the concept is developed for a threshold value of \(R_0\) determining whether or not the disease dies out. The next-generation matrix method of calculating \(R_0\) in a compartmental model is described and illustrated. To address control strategies reproduction numbers are defined and these theoretical ideas are then applied to models that are formulated for different SI, SI with incubation delay, SIR, SEIR and SEQIR the novel coronavirus (2019-nCoV) infection model, the reproduction number has been found to vary, reflecting the dynamics of transmission of the coronavirus outbreak as well as the case reporting rate. If \(R_0 > 1\), then the number of latently infected individuals exponentially grows. However, if \(R_0 < 1\) (e.g. due to quarantine measures and contact restrictions imposed by public authorities), then the number of infected decays exponentially. We then consider the avail- able data on the disease development in different countries to show that there are three possible patterns: growth dynamics, growth- de- cays dynamics, and patchy dynamics. During this period of time, the growth rate of the total number of infected was gradually decreasing.
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References
Carlos, W.G., Dela Cruz, C.S., Cao, B., Pasnick, S., Jamil, S.: Novel Wuhan (2019-nCoV) coronavirus. Am. J. Respir. Crit. Care Med. (2020). https://doi.org/10.1164/rccm.2014P7
Gralinski, L.E., Menachery, V.D.: Return of the coronavirus: 2019-nCoV. Viruses 12(2) (2020)
Lu, H.: Drug treatment options for the 2019- new coronavirus (2019-nCoV). Biosci. Trends (2020). https://doi.org/10.5582/bst.2020.01020
Majumder, M., Mandl, K.D.: Early transmissibility assessment of a novel coronavirus in Wuhan, China. Social Sci. Res. Netw. (2020). https://doi.org/10.2139/ssrn.3524675
Zhou, P., Yang, X.L., Wang, X.G., et al.: A pneumonia outbreak associated with a new coronavirus of probable bat origin. Nature (2020). https://doi.org/10.1038/s41586-020-2012-7
World Health Organization. Statement on the Second Meeting of the International Health Regulations. https://www.who.int/news- room/detail/30-01-2020-statement-on-the-second-meeting-of-the- internationalhealth-regulations-(2005)-emergency-committee-regarding-the-outbreakof-novel-coronavirus-(2019-ncov). Accessed 14 Feb 2020
National Health Commission of the People’s Republic of China. The updates of COVID-19 as of 29 February 2020. http://www.nhc.gov.cn/xcs/yqtb/202003/9d462194284840ad96ce75eb8e4c8039.shtml. Accessed Mar 2020
World Health Organization. Coronavirus disease 2019 (COVID- 19) situation report (40). https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200229-sitrep-40-covid-19.sfvrsn = 849d06652. Accessed 11 Mar 2020
Li, Q., Guan, X., Wu, P., et al.: Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia. N. Engl. J. Med. (2020). https://doi.org/10.1056/NEJMoa2001316
Heffernan, J.M., Smith, R.J., Wahl, L.M.: Perspectives on the basic reproductive ratio. J. Royal Soc. Interface 2(4), 281–293 (2005)
Diekmann, O., Heesterbeek, H.: Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. Wiley, New York (2000). PMID: 18405926. https://doi.org/10.1016/j.mbs.2008.02.005
Van den Driessche, P., Watmough, J.: Further notes on the basic reproduction number. In: Mathematical Epidemiology, pp. 159–178. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78911-6_6
Van den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1–2), 2948 (2002)
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Saha, S., Das, K.P. (2024). A Mathematical Study of Basic Reproduction \(R_0\) and its Significance in Controlling of Corona-Virus (COVID-19) Disease Transmission. In: Singh, J., Anastassiou, G.A., Baleanu, D., Kumar, D. (eds) Advances in Mathematical Modelling, Applied Analysis and Computation . ICMMAAC 2023. Lecture Notes in Networks and Systems, vol 953. Springer, Cham. https://doi.org/10.1007/978-3-031-56304-1_14
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