Mathematical model of COVID-19 spread in Turkey and South Africa: theory, methods, and applications
Tóm tắt
A comprehensive study about the spread of COVID-19 cases in Turkey and South Africa has been presented in this paper. An exhaustive statistical analysis was performed using data collected from Turkey and South Africa within the period of 11 March 2020 to 3 May 2020 and 05 March and 3 of May, respectively. It was observed that in the case of Turkey, a negative Spearman correlation for the number of infected class and a positive Spearman correlation for both the number of deaths and recoveries were obtained. This implied that the daily infections could decrease, while the daily deaths and number of recovered people could increase under current conditions. In the case of South Africa, a negative Spearman correlation for both daily deaths and daily infected people were obtained, indicating that these numbers may decrease if the current conditions are maintained. The utilization of a statistical technique predicted the daily number of infected, recovered, and dead people for each country; and three results were obtained for Turkey, namely an upper boundary, a prediction from current situation and lower boundary. The histograms of the daily number of newly infected, recovered and death showed a sign of lognormal and normal distribution, which is presented using the Bell curving method parameters estimation. A new mathematical model COVID-19 comprised of nine classes was suggested; of which a formula of the reproductive number, well-poseness of the solutions and the stability analysis were presented in detail. The suggested model was further extended to the scope of nonlocal operators for each case; whereby a numerical method was used to provide numerical solutions, and simulations were performed for different non-integer numbers. Additionally, sections devoted to control optimal and others dedicated to compare cases between Turkey and South Africa with the aim to comprehend why there are less numbers of deaths and infected people in South Africa than Turkey were presented in detail.
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Danane, J., Allali, K., Hammouch, Z.: Mathematical analysis of a fractional differential model of HBV infection with antibody immune response. Chaos Solitons Fractals 136, 109787 (2020)
Khan, M.A., Atangana, A.: Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative. Alex. Eng. J. (2020)
Owolabi, K.M., Atangana, A.: Mathematical analysis and computational experiments for an epidemic system with nonlocal and nonsingular derivative. Chaos Solitons Fractals 126, 41–49 (2019)
Tuite, A.R., Fisman, D.N., Greer, L.A.: Mathematical Modelling of Covid-19 Transmission and Mitigation Strategies in the Population of Ontario. CMAJ, Canada (2020)
Anastassopoulou, C., Russo, L., Tsakris, A., Siettos, C.: Data-based analysis, modelling and forecasting of the Covid-19 outbreak, medRxiv (2020)
Kucharski, A.J., Russell, T.W., Diamond, C., Liu, Y., Edmunds, J., Funk, S., Eggo, R.M.: Early dynamics of transmission and control of Covid-19: a mathematical modelling study, Lancet Infect. Dis. (2020)
Baleanu, D., Mohammadi, H., Rezapour, S.: A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative. Adv. Differ. Equ. (2020)
Dhandapani, P.B., Baleanu, D., Thippan, J., Sivakumar, V.: On stiff, fuzzy IRD-14 day average transmission model of COVID-19 pandemic disease. AIMS Bioeng. 7(4), 208–223 (2020)
Nabi, K.M., Abboubakarb, H., Kumar, P.: Forecasting of COVID-19 pandemic: from integer derivatives to fractional derivatives. Chaos Solitons Fractals (2020)
Caputo, M., Fabrizio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1(2), 73–85 (2015)
Atangana, A., Baleanu, D.: New fractional derivatives with non-local and non-singular kernel, theory and application to heat transfer model. Therm. Sci. 20(2), 763–769 (2016)
Republic of Turkey, Ministry of Health, Daily Coronavirus Table of Turkey, https://covid19.saglik.gov.tr, 2020
Covid-19 pandemic in South Africa, https://en.wikipedia.org/wiki/Covid-19_pandemic_in_South_Africa, 2020
Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1), 29–48 (2002)
Atangana, A., Araz, Sİ.: New numerical method for ordinary differential equations: Newton polynomial. J. Comput. Appl. Math. 372, 112622 (2020)
Nababan, S.: A Filippov-type lemma for functions involving delays and its application to time delayed optimal control problems. J. Optim. Theory Appl. 27(3), 357–376 (1979)