Numerical computations and theoretical investigations of a dynamical system with fractional order derivative

This manuscript is devoted to consider population dynamical model of non-integer order to investigate the recent pandemic Covid-19 named as severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) disease. We investigate the proposed model corresponding to differ-ent values of largely effected system parameter of immigration for both susceptible and infected populations. The results for qualitative analysis are established with the help of fixed-point theory and non-linear functional analysis. Moreover, semi-analytical results, related to series solution for the considered system are investigated on applying the transform due to Laplace with Adomian polynomial and decomposition techniques. We have also applied the non-standard finite difference scheme (NSFD) for numerical solution. Finally, both the analysis are supported by graphical results at various fractional order. Both the results are comparable with each other and converging quickly at low order. The whole spectrum and the dynamical behavior for each compartment of the pro-posed model lying between 0 and 1 are simulated via Matlab. (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/).

Automated summary

This manuscript investigates the population dynamical model of non-integer order to study the recent Covid-19 pandemic. The proposed model is analyzed qualitatively using fixed-point theory and non-linear functional analysis. Semi-analytical results are obtained through the Laplace transform with Adomian polynomial and decomposition techniques. The numerical solution is also obtained using the non-standard finite difference scheme. The Matlab simulation provides the overall spectrum and dynamical behavior of each compartment of the model.