## Prediction studies of the epidemic peak of coronavirus disease in Brazil via new generalised Caputo type fractional derivatives

ALEXANDRIA ENGINEERING JOURNAL, vol.60, no.3, pp.3189-3204, 2021 (SCI-Expanded)

• Publication Type: Article / Article
• Volume: 60 Issue: 3
• Publication Date: 2021
• Doi Number: 10.1016/j.aej.2021.01.032
• Journal Name:
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, Directory of Open Access Journals
• Page Numbers: pp.3189-3204
• Keywords: COVID-19 epidemic in Brazil, Mathematical model, new generalised Caputo, fractional derivative, Predictor-corrector scheme
• Ondokuz Mayıs University Affiliated: Yes

#### Abstract

The first reported case of coronavirus disease (COVID-19) in Brazil was confirmed on 25 February 2020 and then the number of symptomatic cases produced day by day. In this manuscript, we studied the epidemic peaks of the novel coronavirus (COVID-19) in Brazil by the successful application of Predictor-Corrector (P-C) scheme. For the proposed model of COVID- 19, the numerical solutions are performed by a model framework of the recent generalized Caputo type non-classical derivative. Existence of unique solution of the given non-linear problem is presented in terms of theorems. A new analysis of epidemic peaks in Brazil with the help of parameter values cited from a real data is effectuated. Graphical simulations show the obtained results to classify the importance of the classes of projected model. We observed that the proposed fractional technique is smoothly work in the coding and very easy to implement for the model of non-linear equations. By this study we tried to exemplify the roll of newly proposed fractional derivatives in mathematical epidemiology. The main purpose of this paper is to predict the epidemic peak of COVID-19 in Brazil at different transmission rates. We have also attempted to give the stability analysis of the pro-posed numerical technique by the reminder of some important lemmas. At last we concluded that when the infection rate increases then the nature of the diseases changes by becoming more deathly to the population. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).