Researches on the COVID-19 epidemic in the world within a nonextensive SIR model

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Yang Liu Chen-Yue Yu Ke-Ming Shen


The coronavirus disease 2019 (COVID-19) epidemic was investigated within a general Susceptible-Infectious-Removed (SIR) model, especially the distributions of its dead cases and infectious ones. This paper applied its nonextensive modification with respect to more realistic situations. A time-dependent SIR model was modified when particularly regarding control and mitigation measures in response to the societal impacts of epidemics and pandemics. We validated all the theoretical results by fitting the derived q -distributions with data from the COVID-19 pandemic in the world. It was found that not all the changeable fit parameters are independent, some of which shared common properties, a result corroborated by our model prediction. Our modified SIR model was proved to be effective in fitting the COVID-19 epidemic distributions. The relative non-extensive parameter was strongly connected with the freedom of systems, which thus threw a light upon the prevention and treatment of disease next in the world.

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LIU, Yang; YU, Chen-Yue; SHEN, Ke-Ming. Researches on the COVID-19 epidemic in the world within a nonextensive SIR model. Medical Research Archives, [S.l.], v. 10, n. 6, june 2022. ISSN 2375-1924. Available at: <>. Date accessed: 20 apr. 2024. doi:
Research Articles


[1] WHO: Coronavirus disease 2019 (COVID-19): situation report, 51 (2020).
[2] M. Radha and S. Balamuralitharan, Adv. in Diff. Equa. (2020) 2020:523.
[3] Z. Ahmad, et. al., Scientific. Reports (2020) 10:22268.
[4] Teles P. Bull World Health Organ. E-pub: 7 April 2020.
[5] Z. Yang, et. al., J. Thorac. Dis 2020; 12(3): 165-174.
[6] G. Christakos and D. Hristopulos, Spatiotemporal Environmental Health Modelling, Springer Science and Business Media, New York, NY 1998.
[7] D. J. Daley and J. Gani, Epidemic Modelling: An Introduction, vol.15 of Cambridge Studies in Mathematical Biology, Cambridge University Press, New York, NY 1999.
[8] G. Kaniadakis, M. M. Baldi and T. S. Deisboeck, Sci. Rep. 10, 19949 (2020).
[9] Jiale Wang, Yang Liu, Xusheng Liu and Keming Shen, J. Phys.: Conf. Ser. 2148 012002 (2022).
[10] C. Tsallis, J. Stat. Phys. 52, 479 (1988).
[11] Lists of many applications of non-extensive statistics are available at
[12] N. Madhav, et al., Chapter 17: Pandemics: Risks, impacts and mitigation. In Jamison, D. T. et. al. (eds.) Disease Control Priorities: Improving Health and Reducing Poverty. 3rd edition (The World Bank, Washington, 2017).
[13] M. Porta, A Dictionary of Epidemiology. 6th Ed. (Oxford University Press, Oxford, 2014).
[14] W. O. Kermack and A. G. McKendrick, Bulletin of Mathematical Biology. 53 (1991) 33–55.
[15] E. Kenah and J. M. Robins, J. Theor. Biol. 249, 706 (2007).
[16] E. Kenah and J. M. Robins, Phys. Rev. E 76, 036113 (2007).
[17] S. Cauchemez and N. M. Ferguson, J. R. Soc., Interface 5, 885 (2008).
[18] Yong Tao, Phys. Rev. E 102, 032136 (2020).
[19] C. Tsallis and U. Tirnakli, Fron. Phys. 8: (2020) 217.
[20] Vision epidemic data-the world’s most complete epidemic data download station, All the corresponding data are collected from various official websites.