A sustainable method for analyzing and studying the fractional-order panic spreading caused by the COVID-19 pandemic

Abstract

This study gives us an expression of non-integer order in mathematics via fractional Caputo operator just for the broadcast development of different emotions under emergencies due to any situation or some disease. In this work, we fear the effects of COVID-19 in panic situations, considering incidence data by using power law kernels under a fractal fractional operator. The effects of the emotion that causes COVID-19 are also evaluated locally and globally using stability. Based on the fractional order model of COVID-19 viral infection, equilibrium points devoid of illness, well-posedness, uniqueness, and biological viability of solutions are all demonstrated. The effects of the COVID-19 model’s sensitivity analysis with treatment were also investigated. Unique solution and Picards stability of iterative scheme verified by using the fixed point theory concept. To discover the solution of the fractional order system and evaluate the effect of fractional parameters, an advanced numerical approach is applied. In the simulation, all classes are shown to have convergent properties and to hold their positions over time, which accurately depicts how COVID-19 infection behaves in practice. We find a more comparable outcome when comparing non-integer orders to integer orders, which supports the non-integer order’s position. This model’s tools seem to be reasonably strong and capable of creating the predicted theoretical conditions for the problem.