Bi-modal COVID-19 transmission with Caputo fractional derivative using statistical epidemic cases

Abstract

The progression of the still ongoing COVID-19 epidemic must be studied in the world of differential operators other than those specified with integer-order temporal derivatives, according to ongoing scientific studies in the fields of fractional calculus, mathematical modeling, and epidemiology. Infectious diseases leave behind a historical footprint because of their long memory. With this in mind, the article below makes an effort to probe an epidemiological model using a Caputo differential operator with a singular kernel of power-law type. The ability of the Caputo operator to capture the evolution of complicated phenomena has been demonstrated in a number of studies, prompting us to conduct the analysis presented here. The analysis contains solid reasons while using the fractional operator for the COVID-19 epidemiological paradigm and presents the fixed point concept for the existence and uniqueness of its solutions. Hyers–Ulam–Rassias stability aids in finding model equilibrium, and the nonlinear least squares method yields the unknown parameters that also include the model’s fractional order. The actual cases of the infection support the superiority of the Caputo concept with evidence of smaller residuals. The numerical simulations are run to see how varying important parameters affect the disease’s spread.

Keywords

• Caputo
• Real data
• Hyers–Ulam–Rassias stability
• Invariant region
• Contagious
• Numerical simulations