A SARS-CoV-2 Fractional-Order Mathematical Model via the Modified Euler Method
Ihtisham Ul Haq, Mehmet Yavuz, Nigar Ali, Ali Akgül
Abstract
This article develops a within-host viral kinetics model of SARS-CoV-2 under the Caputo fractional-order operator. We prove the results of the solution’s existence and uniqueness by using the Banach mapping contraction principle. Using the next-generation matrix method, we obtain the basic reproduction number. We analyze the model’s endemic and disease-free equilibrium points for local and global stability. Furthermore, we find approximate solutions for the non-linear fractional model using the Modified Euler Method (MEM). To support analytical findings, numerical simulations are carried out.
Topics & Concepts
UniquenessMathematicsApplied mathematicsEuler's formulaEuler methodStability (learning theory)Banach spaceOrder (exchange)Basic reproduction numberFixed-point theoremContraction principleContraction mappingOperator (biology)Mathematical analysisFractional calculusComputer scienceRepressorMachine learningEconomicsChemistryBiochemistryPopulationGeneFinanceDemographySociologyTranscription factorFractional Differential Equations SolutionsCOVID-19 epidemiological studiesMathematical and Theoretical Epidemiology and Ecology Models