ABSTRACT
Everyone is talking about coronavirus from last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed and as many as 180 countries are so far affected with 928,287 (14 September, 2020) deaths within couple of months. Ironically, 29,185,779 are still active cases. Having seen such drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. Major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 01 April to 15 March, 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. Best parameters have been obtained via nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than classical version of the SIR model [4]. Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case (ν = 1). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.