Coefficient identification in a SIS fractional-order modelling of economic losses in the propagation of COVID-19

A fractional-order SIS (Susceptible-Infectious-Susceptible) model with time-dependent coefficients is used to analyse some effects of the novel coronavirus 2019 (COVID-19). This generalized model is suitable for describing the COVID dynamics since it does not presume permanent immunity after contagion. The fractional derivative activates the memory property of the dynamics of the susceptible and infectious population time series. A coefficient identification inverse problem is posed, which consists of reconstructing the time-varying transmission and recovery rates, which are of paramount importance in practice for both medics and politicians. The inverse problem is reduced to a minimization problem, which is solved in a least squares sense. The iterative predictor-corrector algorithm reconstructs the time-dependent parameters in a piecewise-linear fashion. The economic losses emerging from social distancing using the calibrated model are also discussed. A comparison between the results obtained by the classical model and the fractional-order model is included, which is validated by ample tests with synthetic and real data.