Fractional Order Modeling of Predicting COVID-19 with Isolation and Vaccination Strategies in Morocco

Abstract

In this work, we present a model that uses the fractional order Caputo derivative for the novel Coronavirus disease 2019 with different hospitalization strategies for severe and mild cases and incorporate an awareness program. We generalize the SEIR model of the spread of COVID-19 with a private focus on the transmissibility of people who are aware of the disease and follow preventative health measures and people who are ignorant of the disease and do not follow preventive health measures. Moreover, individuals with severe, mild symptoms and asymptomatically infected are also considered. The basic reproduction number (R 0 ) and local stability of the disease-free equilibrium (DFE) in terms of R 0 are investigated. Also, the uniqueness and existence of the solution are studied. Numerical simulations are performed by using some real values of parameters. Furthermore, the immunization of a sample of aware susceptible individuals in the proposed model to forecast the effect of the vaccination is also considered. Also, an investigation of the effect of public awareness on transmission dynamics is one of our aim in this work. Finally, a prediction about the evolution of COVID-19 in 1000 days is given. For the qualitative theory of the existence of a solution, we use some tools of nonlinear analysis, including Lipschitz criteria. Also, for the numerical interpretation, we use the Adams-Moulton-Bashforth procedure. All the numerical results are presented graphically.

The general Bernstein function: Application to χ‐fractional differential equations

“…Similarly, the fractional integral of a function represents the integration of that function over a fractional order. Fractional calculus is a powerful tool for modeling [5] and understanding various physical, biological [6], and engineering processes such as viscoelasticity, diffusion, signal processing, and control systems [7][8][9]. Fractional calculus is used in many fields, including physics, engineering, finance, control theory, signal processing, and image processing.…”

Transition dynamics between a novel coinfection model of fractional-order for COVID-19 and tuberculosis via a treatment mechanism

“…The treatment of coinfection is indigent due to the dynamic behavior of COVID-19 and TB. An enormous amount of literature is available to understand the transmission dynamics of the COVID-19-only model [ 2 – 5 , 7 , 13 , 14 , 17 , 19 , 25 – 28 , 30 , 31 , 33 , 36 , 37 , 40 , 45 ], the TB-only model [ 1 , 11 , 29 , 41 , 46 , 47 , 53 ], and other models [ 12 , 32 , 35 , 44 , 48 ]. But to date, there is seldom evidence available to study the transmission dynamics of COVID-19 and TB coinfection.…”

Mathematical study of the dynamics of lymphatic filariasis infection via fractional-calculus

“…In [23,24], the authors presented fractional epidemic models for Covid-19 infection by including therapeutic interventions such as vaccinating susceptible individuals and treating the infected population. The researchers in [25] represented nonlinear fractional dynamics through a numerical scheme. The framework of non-integer derivative is effectively used for modeling of real-world problems [26,27].…”