Communicable disease model in view of fractional calculus

The COVID-19 pandemic still gains the attention of many researchers worldwide. Over the past few months, China faced a new wave of this pandemic which increases the risk of its spread to the rest of the world. Therefore, there has become an urgent demand to know the expected behavior of this pandemic in the coming period. In this regard, there are many mathematical models from which we may obtain accurate predictions about the behavior of this pandemic. Such a target may be achieved via updating the mathematical models taking into account the memory effect in the fractional calculus. This paper generalizes the power-law growth model of the COVID-19. The generalized model is investigated using two different definitions in the fractional calculus, mainly, the Caputo fractional derivative and the conformable derivative. The solution of the first-model is determined in a closed series form and the convergence is addressed. At a specific condition, the series transforms to an exact form. In addition, the solution of the second-model is evaluated exactly. The results are applied on eight European countries to predict the behavior/variation of the infected cases. Moreover, some remarks are given about the validity of the results reported in the literature.