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Generalized Euler method to study the vaccination effects on dynamics of measles infection model under non-singular
L K Yadav1, M M Gour1, S D Purohit2
1Department of Mathematics, Vivekananda Global University, Jaipur, India.
Scientific Reports
|February 25, 2026
Summary
This study introduces a fractional measles model to analyze disease spread. Mathematical modeling and simulations show that interventions like vaccination significantly reduce measles transmission.
Area of Science:
- Epidemiology
- Mathematical Biology
- Fractional Calculus
Background:
- Measles is a highly contagious viral disease with significant public health implications.
- Mathematical models are crucial for understanding disease dynamics and evaluating control strategies.
Purpose of the Study:
- To develop and analyze a fractional measles infection model using the Atangana-Baleanu fractional derivative.
- To investigate the impact of various control interventions on measles transmission dynamics.
Main Methods:
- Development of a fractional measles model with a nonlocal and non-singular kernel.
- Application of the generalized Euler method (GEM) for numerical analysis.
- Utilizing fixed-point theory for solution uniqueness and convergence analysis.
- Employing the Jacobian determinant method to determine the basic reproduction number.
- Construction of Lyapunov functions for stability analysis of equilibrium points.
Main Results:
- The fractional model provides a more nuanced understanding of measles transmission.
- Numerical simulations demonstrate the effectiveness of interventions such as quarantine, vaccination, and treatment.
- Sensitivity analysis highlights key parameters influencing disease spread.
Conclusions:
- Interventions significantly reduce exposed and infectious populations, aiding disease control.
- Governments should prioritize financial support for enhanced vaccine distribution programs to combat measles effectively.
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