A mathematical model for SARS-CoV-2 in variable-order fractional derivative

Abstract

A new coronavirus mathematical with hospitalization is considered with the consideration of the real cases from March 06, 2021 till the end of April 30, 2021. The essential mathematical results for the model are presented. We show the model stability when in the absence of infection. We show that the system is stable locally asymptotically when at infection free state. We also show that the system is globally asymptotically stable in the disease absence when . Data have been used to fit accurately to the model and found the estimated basic reproduction number to be . Some graphical results for the effective parameters are drawn for the disease elimination. In addition, a variable-order model is introduced, and so as to handle the outbreak effectively and efficiently, a genetic algorithm is used to produce high-quality control. Numerical simulations clearly show that decision-makers may develop helpful and practical strategies to manage future waves by implementing optimum policies.

Application of variable-order fractional calculus in neural networks: where do we stand?

“…Since the fractional calculus is a generalized form of the integer one and can capture many time-dependent phenomena, it is a more practical and precise approach to the use of the fractional models, especially with time-varying fractional order. Considering this point, in the current collection, some studies have investigated modeling and dynamical investigation of neural networks using variable-order fractional calculus [11][12][13][14][15][16].…”

Assessing the potential impact of COVID-19 Omicron variant: Insight through a fractional piecewise model

“…Since the outbreak of coronavirus, several mathematical models are proposed in various ways to control or reduce the risk of disease transmission worldwide. These includes the use integer and fractional modeling frameworks for different countries incorporating non-pharmaceutical interventions/vaccine [8] , environmental factors [9] , [10] , dead compartments [11] , Omicron variants [8] , [12] , [13] , [14] , social distancing [15] , optimal control [16] , [17] , super spreaders [18] . In particular, authors in [15] used an integer order model to quantify the effect of social distancing on the transmission dynamics of the coronavirus spread in South Africa.…”

“…For more details on other models that have used fractional derivatives to model COVID-19, see the following Refs. [11] , [19] , [20] , [21] . Several other modeling frameworks have been carried out since the emergence of the Omicron variant to look at various ways to understand the disease’s transmissibility and controllability in several countries worldwide.…”

Application of piecewise fractional differential equation to COVID-19 infection dynamics

“…In [18] , the authors constructed a mathematical model using Continuous Markov-Chain to analyze the dynamics of coronavirus infection. A SARS-CoV-2 model using the variable fractional order has been investigated in [19] . A COVID-19 infection model using the control intervention is discussed in [20] .…”