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In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

In the paper, suitability of control quality assessment based on delay approximation for delay-free plants is investigated. To this end, the LQG control benchmark, which can be seen as a MV benchmark with bounded control variance, is compared for both linear delay-free continuoustime plants with outputs corrupted by a stochastic disturbance and their lag-delay models. Using approximated plant models, the area of achievable accuracy is then defined for control performance assessment. Control systems with discrete-time PID controllers tuned both classically and optimally in such way that disturbance characteristics are taken into account are considered and compared with the benchmark

In the paper the problem of disturbance attenuation performance in single-loop control system is investigated. Modified MV control strategy with bounded control variance is used as benchmark for both LQG and classically and optimally tuned PID-type controllers. Certain time and frequency domain functions are then examined to further assess the control performance in terms of robustness. It has been shown that as long as the system to be controlled is delay-free, and there is no extreme demand on performance, simple lag-delay system model along with optimally tuned PID control algorithm provides control quality similar to that of LQG controlled original system assuming the same bound on control signal variance. Although the classical performance measure based on substitute delay indicates then almost optimal performance, there is still room for additional improvement that can be attained using both PID and LQG controllers and more sophisticated original delay-free model. The price paid is much larger control variance. It is interesting to note that while LQG systems remain robust this is not longer valid for PID controllers.