Stability analysis and numerical simulations of the fractional COVID-19 pandemic model
Ahmad Alalyani, Sayed Saber
Abstract
Abstract The purpose of this article is to formulate a simplified nonlinear fractional mathematical model to illustrate the dynamics of the new coronavirus (COVID-19). Based on the infectious characteristics of COVID-19, the population is divided into five compartments: susceptible S ( t ), asymptomatic infection I ( t ), unreported symptomatic infection U ( t ), reported symptomatic infections W ( T ) and recovered R ( t ), collectively referred to as (SIUWR). The existence, uniqueness, boundedness, and non-negativeness of the proposed model solution are established. In addition, the basic reproduction number R 0 is calculated. All possible equilibrium points of the model are examined and their local and global stability under specific conditions is discussed. The disease-free equilibrium point is locally asymptotically stable for R 0 leq 1 and unstable for R 0 > 1. In addition, the endemic equilibrium point is locally asymptotically stable with respect to R 0 > 1. Perform numerical simulations using the Adams–Bashforth–Moulton-type fractional predictor–corrector PECE method to validate the analysis results and understand the effect of parameter variation on the spread of COVID-19. For numerical simulations, the behavior of the approximate solution is displayed in the form of graphs of various fractional orders. Finally, a brief conclusion about simulation on how to model transmission dynamics in social work.