Fractional-Order Epidemic Model for Measles Infection

Area of Science:

• Epidemiological modeling
• Fractional calculus applications
• Infectious disease dynamics

Background:

• Measles remains a significant public health concern globally.
• Mathematical models are crucial for understanding and controlling infectious diseases.
• Fractional-order derivatives offer a more nuanced approach to modeling disease dynamics with memory effects.

Purpose of the Study:

• To develop and analyze a nonlinear, fractional-order SEVIQR measles epidemic model.
• To establish the existence, uniqueness, and stability of model equilibria.
• To investigate the impact of preventive measures on measles transmission.

Main Methods:

• Construction of a Caputo fractional-order SEVIQR measles model.
• Analysis of model equilibria using Jacobian determinant and Lyapunov functions.
• Numerical simulations employing an Adams-type predictor-corrector scheme.

Main Results:

• The existence, uniqueness, and global asymptotic stability of disease-free and endemic equilibria were established.
• The basic reproduction number (ℛ₀) was determined using the Jacobian determinant method.
• Numerical simulations demonstrated that vaccination, quarantine, and treatment reduce infectious and exposed populations.

Conclusions:

• Fractional-order modeling provides valuable insights into measles dynamics.
• Preventive strategies like vaccination, quarantine, and treatment are effective in controlling measles.
• Financial support for vaccine distribution is recommended to enhance disease control efforts.