A Mathematical Study of a Coronavirus Model with the Caputo Fractional-Order Derivative

In this work, we introduce a minimal model for the current pandemic. It incorporates the basic compartments: exposed, and both symptomatic and asymptomatic infected. The dynamical system is formulated by means of fractional operators. The model equilibria are analyzed. The theoretical results indicate that their stability behavior is the same as for the corresponding system formulated via standard derivatives. This suggests that, at least in this case for the model presented here, the memory effects contained in the fractional operators apparently do not seem to play a relevant role. The numerical simulations instead reveal that the order of the fractional derivative has a definite influence on both the equilibrium population levels and the speed at which they are attained.

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