Existence, uniqueness, and stability of fractional hepatitis B epidemic model
Amir Khan, Ghulam Hussain, Mustafa İnç, Gul Zaman
Abstract
This paper describes the existence and stability of the hepatitis B epidemic model with a fractional-order derivative in Atangana-Baleanu sense. Some new results are handled by using the Sumudu transform. The existence and uniqueness of the equilibrium solution are presented using the Banach fixed-point theorem. Moreover, sensitivity analysis complemented by simulations is performed to determine how changes in parameters affect the dynamical behavior of the system. The numerical simulations are carried out using a predictor-corrector scheme to demonstrate the obtained results.
Topics & Concepts
UniquenessMathematicsFixed-point theoremStability (learning theory)Applied mathematicsEquilibrium pointPredictor–corrector methodFractional calculusBanach fixed-point theoremOrder (exchange)Fixed pointDerivative (finance)Sensitivity (control systems)Picard–Lindelöf theoremBanach spaceMathematical analysisPure mathematicsComputer scienceDifferential equationElectronic engineeringFinancial economicsFinanceEngineeringEconomicsMachine learningFractional Differential Equations SolutionsMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Differential Equations Analysis