Forecasting of COVID-19 pandemic: From integer derivatives to fractional derivatives

In this work, a new compartmental mathematical model of COVID-19 pandemic has been proposed incorporating imperfect quarantine and disrespectful behavior of citizens towards lockdown policies, which are evident in most of the developing countries. An integer derivative model has been proposed initially and then the formula for calculating basic reproductive number, $$ of the model has been presented. Cameroon has been considered as a representative for the developing countries and the epidemic threshold, $$ has been estimated to be  ~ 3.41 $$ as of July 9, 2020. Using real data compiled by the Cameroonian government, model calibration has been performed through an optimization algorithm based on renowned trust-region-reflective (TRR) algorithm. Based on our projection results, the probable peak date is estimated to be on August 1, 2020 with approximately 1073 $$ daily confirmed cases. The tally of cumulative infected cases could reach  ~ 20, 100 $$ cases by the end of August 2020. Later, global sensitivity analysis has been applied to quantify the most dominating model mechanisms that significantly affect the progression dynamics of COVID-19. Importantly, Caputo derivative concept has been performed to formulate a fractional model to gain a deeper insight into the probable peak dates and sizes in Cameroon. By showing the existence and uniqueness of solutions, a numerical scheme has been constructed using the Adams-Bashforth-Moulton method. Numerical simulations have enlightened the fact that if the fractional order α is close to unity, then the solutions will converge to the integer model solutions, and the decrease of the fractional-order parameter (0  <  α  <  1) leads to the delaying of the epidemic peaks.