Projections and fractional dynamics of COVID-19 with optimal control analysis

When the entire world is eagerly waiting for a safe, effective and widely available COVID-19 vaccine, un-precedented spikes of new cases are evident in numerous countries. To gain a deeper understanding about the future dynamics of COVID-19, a compartmental mathematical model has been proposed in this paper incorporating all possible non-pharmaceutical intervention policies. Model parameters have been calibrated using sophisticated trust-region-reflective algorithm and short-term projection results have been illustrated for Argentina, Bangladesh, Brazil, Colombia and India. Control reproduction numbers ( ℛ c ) have been calculated in order to get insights about the current epidemic scenario in the above-mentioned countries. Forecasting results depict that the aforesaid countries are having downward trends in daily COVID-19 cases. However, it is highly recommended to use efficacious face coverings and maintain strict physical distancing, as the pandemic is not over in any country. Global sensitivity analysis enlightens the fact that efficacy of face coverings is the most significant parameter, which could significantly control the transmission dynamics of the novel coronavirus compared to other non-pharmaceutical measures. In addition, reduction in effective contact rate with isolated patients is also essential in bringing down the epidemic threshold ( ℛ c ) below unity. All necessary graphical simulations have been performed with the help of Caputo-Fabrizio fractional derivatives. In addition, optimal control problem for fractional system has been designed and the existence of unique solution has also been showed by using Picard-Lindelof technique. Finally, the unconditionally stability of the given fractional numerical technique has been proved.