Boundaries of applicability of fractional-order modeling in epidemiological and sociological phenomena

Compartmental systems permit the analysis of epidemiological and sociological phenomena, due to the possibility of capturing transitions in stages and interactions. Recently, the authors of this paper studied the role of Caputo fractional calculus in compartmental modeling, in the partial and pure versions of the formulation, where the non-Markovian property is related to variable latency or decision periods and the fractional index controls the decreasing risk of transition. Several mechanistic considerations were made that pointed out some issues with the fractional calculus. In the present work, we provide an expository analysis of fractional compartmental modeling and compare it with the traditional use of delay differential equations, using recent studies on delay models in epidemiology. In general terms, the contribution of fractional calculus remains to be fully justified.