Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

Abstract

A fractional-order compartmental model was recently used to describe real data of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons Fractals 144 (2021), Art. 110652]. Here, we modify that model in order to correct time dimensions and use it to investigate the third wave of COVID-19 that occurred in Portugal from December 2020 to February 2021, and that has surpassed all previous waves, both in number and consequences. A new fractional optimal control problem is then formulated and solved, with vaccination and preventive measures as controls. A cost-effectiveness analysis is carried out, and the obtained results are discussed.

The Regional Enlarged Observability for Hilfer Fractional Differential Equations

“…where E η,κ (•) stands for the two-parameter Mittag-Leffler function [4], and one can easily see that the operator ∂ 2 ∂y 2 has a complete set of eigenfunctions φ n = sin(nπy) in the Hilbert space L 2 (Ω 1 ) associated with the eigenvalues λ n = −n 2 π. Let us assume the initial state that needs to be observed in System (44) is given by ν 0 (y) = sin(2πy), η = 0.2, and κ = 0.4.…”

“…In recent decades, fractional calculus theory has proven to be a significant tool for the formulation of several problems in science and engineering, where fractional derivatives and integrals can be utilized to describe the characteristics of various real materials in various scientific disciplines; see, e.g., [1][2][3][4][5]. This theory has recently received a large amount of consideration by many academics; we mention Euler, Laplace, Riemann, Liouville, Marchaud, Riesz, and Hilfer; see, e.g., [6][7][8].…”

Regional Gradient Observability for Fractional Differential Equations with Caputo Time-Fractional Derivatives

“…Fractional calculus is one of the most rapidly spreading domains in mathematics nowadays, especially the use of fractional-order systems to model real-world phenomena [3,4,29,31,32]. It is well known that fractional operators, non-integer order differentiation and non-integer order integration operators, have many outstanding properties that make them fruitful and suitable for describing and studying the characteristics of certain real-world problems.…”

Regional gradient observability for fractional differential equations with Caputo time-fractional derivatives

“…Fractional calculus is one of the most rapidly spreading domains in mathematics nowadays, especially the use of fractional-order systems to model real-world phenomena [25][26][27][28][29][30]. It is well known that fractional operators, noninteger order differentiation and non-integer order integration operators have many outstanding properties that make them fruitful and suitable for describing and studying the characteristics of certain real-world problems.…”