A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19

COVID-19 is a novel coronavirus affecting all the world since December last year. Up to date, the spread of the outbreak continues to complicate our lives, and therefore, several research efforts from many scientific areas are proposed. Among them, mathematical models are an excellent way to understand and predict the epidemic outbreaks evolution to some extent. Due to the COVID-19 may be modeled as a non-Markovian process that follows power-law scaling features, we present a fractional-order SIRD (Susceptible-Infected-Recovered-Dead) model based on the Caputo derivative for incorporating the memory effects (long and short) in the outbreak progress. Additionally, we analyze the experimental time series of 23 countries using fractal formalism. Like previous works, we identify that the COVID-19 evolution shows various power-law exponents (no just a single one) and share some universality among geographical regions. Hence, we incorporate numerous memory indexes in the proposed model, i.e., distinct fractional-orders defined by a time-dependent function that permits us to set specific memory contributions during the evolution. This allows controlling the memory effects of more early states, e.g., before and after a quarantine decree, which could be less relevant than the contribution of more recent ones on the current state of the SIRD system. We also prove our model with Italy's real data from the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University.

Adaptive Neural State-Feedback Tracking Control of Stochastic Nonlinear Switched Systems: An Average Dwell-Time Method

In this paper, the problem of adaptive neural state-feedback tracking control is considered for a class of stochastic nonstrict-feedback nonlinear switched systems with completely unknown nonlinearities. In the design procedure, the universal approximation capability of radial basis function neural networks is used for identifying the unknown compounded nonlinear functions, and a variable separation technique is employed to overcome the design difficulty caused by the nonstrict-feedback structure. The most outstanding novelty of this paper is that individual Lyapunov function of each subsystem is constructed by flexibly adopting the upper and lower bounds of the control gain functions of each subsystem. Furthermore, by combining the average dwell-time scheme and the adaptive backstepping design, a valid adaptive neural state-feedback controller design algorithm is presented such that all the signals of the switched closed-loop system are in probability semiglobally uniformly ultimately bounded, and the tracking error eventually converges to a small neighborhood of the origin in probability. Finally, the availability of the developed control scheme is verified by two simulation examples.