Mathematical modelling of the COVID-19 pandemic with demographic effects
Tóm tắt
In this paper, a latent infection susceptible–exposed–infectious–recovered model with demographic effects is used to understand the dynamics of the COVID-19 pandemics. We calculate the basic reproduction number (
$${R}_{0}$$
) by solving the differential equations of the model and also using next-generation matrix method. We also prove the global stability of the model using the Lyapunov method. We showed that when the
$${R}_{0}<1$$
or
$${R}_{0}\le 1$$
and
$${R}_{0}>1$$
or
$${R}_{0}\ge 1$$
the disease-free and endemic equilibria asymptotic stability exist theoretically. We provide numerical simulations to demonstrate the detrimental impact of the direct and latent infections for the COVID-19 pandemic.
Tài liệu tham khảo
De Wit, E., Van Doremalen, N., Falzarano, D., Munster, V.J.: SARS and MERS: recent insights into emerging coronaviruses. Nat. Rev. Microbiol. (2016). https://doi.org/10.1038/nrmicro.2016.81
Cui, J., Li, F., Shi, Z.L.: Origin and evolution of pathogenic coronaviruses. Nat. Rev. Microbiol. (2019). https://doi.org/10.1038/s41579-018-0118-9
WHO (World Health Organization), Novel Coronavirus (2019-nCoV) Situation Report—142 (2020). https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200610-covid-19-sitrep-142.pdf?sfvrsn=180898cd_6
Perlman, S.: Another decade, another coronavirus. N. Engl. J. Med. (2020). https://doi.org/10.1056/nejme2001126
Wang, C., Horby, P.W., Hayden, F.G., Gao, G.F.: A novel coronavirus outbreak of global health concern. Lancet (2020). https://doi.org/10.1016/S0140-6736(20)30185-9
World Health Organization: Statement on the meeting of the International Health Regulations (2005) Emergency Committee regarding the outbreak of novel coronavirus (2019-nCoV), WHO (2020)
Centers for Disease Control and Prevention (CDC): Symptoms of Coronavirus, 2020. https://www.cdc.gov/coronavirus/2019-ncov/symptoms-testing/symptoms.html
World Health Organisation (WHO): How COVID-19 Spreads, CDC Bull. (2020) Coronavirus disease (COVID-19): How is it transmit. https://www.who.int/news-room/q-a-detail/coronavirus-%0Adisease-covid-19-how-is-it-transmitted
WHO, Coronavirus disease (COVID-19): How is it transmitted?, Q&A Detail. (2020) Coronavirus disease (COVID-19) pandemic. https://www.who.int/news-room/q-a-detail/q-a-how-is-covid-19-transmitted
Kimball, A., Hatfield, K.M., Arons, M. et al.: Asymptomatic and Presymptomatic SARS-CoV-2 Infections in Residents of a Long-Term Care Skilled Nursing Facility—King County, Washington, March 2020, MMWR. Morb. Mortal. Wkly. Rep. (2020). https://doi.org/10.15585/mmwr.mm6913e1
Anastassopoulou, C., Russo, L., Tsakris, A., Siettos, C.: Data-based analysis, modelling and forecasting of the COVID-19 outbreak. PLoS ONE 3, 1–21 (2020). https://doi.org/10.1371/journal.pone.0230405
Zhao, S., Lin, Q., Ran, J., 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, 214–217 (2020). https://doi.org/10.1016/j.ijid.2020.01.050
Read, J.M., Bridgen, J.R., Cummings, D.A., Ho, A., Jewell, C.P.: Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions. MedRxiv. (2020). https://doi.org/10.1101/2020.01.23.20018549
Furukawa, N.W., Furukawa, N.W., Brooks, J.T., Sobel, J.: Evidence supporting transmission of severe acute respiratory syndrome coronavirus 2 while presymptomatic or asymptomatic. Emerg. Infect. Dis. (2020). https://doi.org/10.3201/eid2607.201595
W.H.O. Health, E. Programme, E.A. Panel, I.P.C. Preparedness, I.P.C. Guidance, D. Group, I.P.C. Gdg, S. Preparedness, R. Plan, Transmission of SARS-CoV-2: implications for infection prevention precautions (2020), pp. 1–10. https://www.who.int/news-room/%0Acommentaries/detail/transmission-of-sars-cov-2-implications-for-infection-prevention-%0Aprecautions
Van Den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2002). https://doi.org/10.1016/S0025-5564(02)00108-6
LaSalle, J.P.: The stability of dynamical systems. CBMS-NSF Reg. Conf. Ser. Appl. Math. 25, 1–88 (1976). https://doi.org/10.1007/s13398-014-0173-7.2
Li, Q., Guan, X., Wu, P., Wang, X., et al.: Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia. N. Engl. J. Med. 2020, 1199–1207 (2020). https://doi.org/10.1056/nejmoa2001316
Chen, T., Rui, J., Wang, Q., Zhao, Z., Cui, J.-A., Yin, L.: A mathematical model for simulating the transmission of Wuhan novel Coronavirus. Infect. Dis. Povert. (2020). https://doi.org/10.1101/2020.01.19.911669
Wang, H., Wang, Z., Dong, Y., Chang, R., et al.: Phase-adjusted estimation of the number of coronavirus disease 2019 cases in Wuhan, China. Cell Discov. (2020). https://doi.org/10.1038/s41421-020-0148-0