On dynamics of fractional incommensurate model of Covid-19 with nonlinear saturated incidence rate

Abstract

In December 2019, a new virus belonging to the coronavirus strain has been discovered in Wuhan, China, this virus has attracted world-wide attention and it spread rapidly in the world, reaching nearly 216 countries in the world in November 2020. In this chapter, we study the fractional incommensurate SIQR (susceptible, infections, quarantined and removed) COVID-19 model with nonlinear saturated incidence rate using Atangana-Baleanu fractional derivatives. The existence and uniqueness of the solutions for the fractional model is proved using fixed point theorem, the model are shown to have two equilibrium point (disease free and an endemic equilibrium). Some numerical simulations using Euler method are also carried out to support our theoretical results. We estimated the value of the fractional orders and the parameters of the proposed model using the least squares method. Further, the sensitivity analysis of the parameter is performed as a result, our incommensurate model gives a good approximation to real data of COVID-19.

Modeling third waves of Covid-19 spread with piecewise differential and integral operators: Turkey, Spain and Czechia

“…Some examples including the Spanish flu that started in 1918 and ended after three waves in 1920. Another-recent one is the spread of Covid-19 [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] . The disagreement between experimental data and the solutions of mathematical equation are perhaps since complexities of collected data are not sometimes considered.…”

“…This non-singular kernel also has crossover from normal to sub-diffusion, also, the kernel can express crossover from random walk to power-law. However, crossover from deterministic setting to stochastic or from stochastic to deterministic cannot be captured by this kernel, thus a great limitation of such operators to be used in these scenarios [13] , [14] , [15] , [16] .…”