Stability and Bifurcation Analysis in a Discrete-Time SIR Epidemic Model with Fractional-Order
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Moustafa El-Shahed
Abstract
In this paper, the dynamical behavior of a discrete SIR epidemic model with fractional-order with non-monotonic incidence rate is discussed. The sufficient conditions of the locally asymptotic stability and bifurcation analysis of the equilibrium points are also discussed. The numerical simulations come to illustrate the dynamical behaviors of the model such as flip bifurcation, Hopf bifurcation and chaos phenomenon. The results of numerical simulation verify our theoretical results.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Modeling the Effects of Health Education and Early Therapy on Tuberculosis Transmission Dynamics
- Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays
- Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy
- Kinetic Flux Vector Splitting Method for Numerical Study of Two-dimensional Ripa Model
- Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems
- A Riccati–Bernoulli sub-ODE Method for Some Nonlinear Evolution Equations
- New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems
- Numerical Solution of Space and Time Fractional Telegraph Equation: A Meshless Approach
- Stability and Bifurcation Analysis in a Discrete-Time SIR Epidemic Model with Fractional-Order
- A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems
- The Multiplicity of Solutions for a Class of Nonlinear Fractional Dirichlet Boundary Value Problems with p-Laplacian Type via Variational Approach
- Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses
- The Optimal Design of a Functionally Graded Corrugated Cylindrical Shell under Axisymmetric Loading
- Application of the Optimal Auxiliary Functions Method to a Permanent Magnet Synchronous Generator
- Investigation of Geometry Effect on Heat and Mass Transfer in Buoyancy Assisting with the Vertical Backward and Forward Facing Steps
- Existence of at Least One Homoclinic Solution for a Nonlinear Second-Order Difference Equation
- Some Novel Solitary Wave Characteristics for a Generalized Nonlocal Nonlinear Hirota (GNNH) Equation
- Fractional Navier–Stokes Equation from Fractional Velocity Arguments and Its Implications in Fluid Flows and Microfilaments
- Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas
- Results on Controllability of Nonlinear Hilfer Fractional Stochastic System
- Effects of Different Turbulence Models on Three-Dimensional Unsteady Cavitating Flows in the Centrifugal Pump and Performance Prediction
Articles in the same Issue
- Frontmatter
- Original Research Articles
- Modeling the Effects of Health Education and Early Therapy on Tuberculosis Transmission Dynamics
- Pulse Inputs Affect Timings of Spikes in Neurons with or Without Time Delays
- Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy
- Kinetic Flux Vector Splitting Method for Numerical Study of Two-dimensional Ripa Model
- Remarks on the Covering of the Possible Motion Area by Solutions in Rigid Body Systems
- A Riccati–Bernoulli sub-ODE Method for Some Nonlinear Evolution Equations
- New Conditions and Numerical Checking Method for the Practical Stability of Fractional Order Positive Discrete-Time Linear Systems
- Numerical Solution of Space and Time Fractional Telegraph Equation: A Meshless Approach
- Stability and Bifurcation Analysis in a Discrete-Time SIR Epidemic Model with Fractional-Order
- A General Method to Study the Co-Existence of Different Hybrid Synchronizations in Fractional-Order Chaotic Systems
- The Multiplicity of Solutions for a Class of Nonlinear Fractional Dirichlet Boundary Value Problems with p-Laplacian Type via Variational Approach
- Chaotic Contact Dynamics of Two Microbeams under Various Kinematic Hypotheses
- The Optimal Design of a Functionally Graded Corrugated Cylindrical Shell under Axisymmetric Loading
- Application of the Optimal Auxiliary Functions Method to a Permanent Magnet Synchronous Generator
- Investigation of Geometry Effect on Heat and Mass Transfer in Buoyancy Assisting with the Vertical Backward and Forward Facing Steps
- Existence of at Least One Homoclinic Solution for a Nonlinear Second-Order Difference Equation
- Some Novel Solitary Wave Characteristics for a Generalized Nonlocal Nonlinear Hirota (GNNH) Equation
- Fractional Navier–Stokes Equation from Fractional Velocity Arguments and Its Implications in Fluid Flows and Microfilaments
- Limits of Solutions to the Isentropic Euler Equations for van der Waals Gas
- Results on Controllability of Nonlinear Hilfer Fractional Stochastic System
- Effects of Different Turbulence Models on Three-Dimensional Unsteady Cavitating Flows in the Centrifugal Pump and Performance Prediction
