Application of piecewise fractional differential equation to COVID-19 infection dynamics

We proposed a new mathematical model to study the COVID-19 infection in piecewise fractional differential equations. The model was initially designed using the classical differential equations and later we extend it to the fractional case. We consider the infected cases generated at health care and formulate the model first in integer order. We extend the model into Caputo fractional differential equation and study its background mathematical results. We show that the fractional model is locally asymptotically stable when R-0 < 1 at the disease-free case. For R-0 <= 1, we show the global asymptotical stability of the model. We consider the infected cases in Saudi Arabia and determine the parameters of the model. We show that for the real cases, the basic reproduction is R0 asymptotic to 1.7372. We further extend the Caputo model into piecewise stochastic fractional differential equations and discuss the procedure for its numerical simulation. Numerical simulations for the Caputo case and piecewise models are shown in detail.

Automated summary

We proposed a new mathematical model to study the COVID-19 infection using piecewise fractional differential equations. The model was initially designed using classical differential equations and later extended to the fractional case. We considered infected cases generated in the health care sector and formulated the model in both integer and fractional orders. Through numerical simulations and parameter determination, we verified the reliability of the model.