Analytical and qualitative investigation of COVID-19 mathematical model under fractional differential operator

In the current article, we aim to study in detail a novel coronavirus (2019-nCoV or COVID-19) mathematical model for different aspects under Caputo fractional derivative. First, from analysis point of view, existence is necessary to be investigated for any applied problem. Therefore, we used fixed point theorem's due to Banach's and Schaefer's to establish some sufficient results regarding existence and uniqueness of the solution to the proposed model. On the other hand, stability is important in respect of approximate solution, so we have developed condition sufficient for the stability of Ulam-Hyers and their different types for the considered system. In addition, the model has also been considered for semianalytical solution via Laplace Adomian decomposition method (LADM). On Matlab, by taking some real data about Pakistan, we graph the obtained results. In the last of the manuscript, a detail discussion and brief conclusion are provided.

Automated summary

In this article, we thoroughly study a mathematical model for a novel coronavirus using Caputo fractional derivative. We investigate the existence and uniqueness of the solution to the model using fixed point theorems and establish conditions for stability. Additionally, we analyze the model using the Laplace Adomian decomposition method and validate the results using real data from Pakistan.