Analyzing a SEIR-Type Mathematical Model of SARS-COVID-19 Using Piecewise Fractional Order Operators

Abstract

The continuing public health issue known as COVID-19 (the 2019 Novel Corona virus infection)
 has a global emphasis. Despite (or perhaps because of) the fact that there are significant gaps
 in our understanding of COVID-19 epidemiology, transmission dynamics, research methods, and
 management breakout poses a new kind of global hazard. The good news is that there is currently
 enough knowledge about the epidemic process to allow for the creation of mathematical forecasting
 models. We modify a conventional SEIR epidemic model to the unique dynamic compartments and
 epidemic features of COVID 19 as it spreads in a population with a diverse age structure. Although
 many US states and other nations around the world followed lockdown and reopening processes,
 we perform some analysis on using some techniques of the epidemic course. A new perspective of
 fractional calculus known as piecewise derivatives of fractional order is used to study the proposed
 model. Sufficient conditions are established to show the existence theory. In addition, a numerical
 scheme based on Newton’s polynomials is established to simulate the approximate solutions of the
 proposed model by using various fractional orders. Some real data results are also shown with
 comparison of the numerical results.