Optimally analyzed fractional Coronavirus model with Atangana–Baleanu derivative

Abstract

In this article, we develop a nonlinear SEIQHR fractional model with Atangana–Baleanu (ABC) derivative for the Corona virus disease (Covid-19). It is significant to mention that using a fractional-order derivative can provide more intricate insights into the complex dynamics of underlying models. We provide two unique equilibrium states of the model in order to analyze the problem. To explore the long-term dynamics of a disease, a threshold parameter for the model utilizing next-generation approach is computed. Local and global asymptotic behaviors of the proposed model at both the equilibrium states are established by imposing some necessary conditions on threshold parameter. To validate our obtained analytical results and to examine the importance of arbitrary order derivative, we implement a recently proposed Toufik–Atangana numerical technique. To reach our conclusions, we investigate a thorough quantitative analysis of the model through the adjustment of quarantine and hospitalization rates as a first constant control technique. Through numerical experiments, it is asserted that the Covid-19 pandemic may be eliminated more quickly if a human community selfishly adopted both of the necessary control measures at various coverage levels with appropriate awareness. The developed model is subjected to sensitivity analysis and the most sensitive parameters are identified. In addition, the bifurcation nature of the Covid-19 model is examined. Furthermore, we develop an optimal control problem along with the associated optimality conditions of Pontryagin type to discover the most effective controls for the both strategies, one for exposed and another for infected individuals. The goal is to reduce both the financial burden of executing these strategies as well as the number of exposed and infected people. The extremals are obtained numerically. The effectiveness and efficiency of the optimal control strategy are finally demonstrated by numerical simulations before and after the optimization. The importance of the current research work is the use of developed structure preserving Toufik-Atangana numerical scheme, backward in time, for the first time to analyze optimally the epidemic models, for example the proposed SEQIHR Covid-19 model.