Simulation of a novel approach in measles disease dynamics models to predict the impact of vaccinations on eradication and control

Abstract

Introduction

Measles, a highly contagious disease caused by Morbillivirus, poses significant public health risks due to its rapid spread and severe complications. Symptoms, such as fever, rashes, red eyes, and coughing, typically appear 8–12 days post-infection. Given recent resurgences, especially in areas with low vaccination coverage, it is essential to understand measles transmission and assess the role of vaccination awareness in outbreak control.

Method

A mathematical model was developed to examine measles transmission and the influence of vaccination awareness. Stability analysis evaluated the model's behavior, while the basic reproductive number, R₀, was derived using the next-generation matrix approach. Sensitivity analysis assessed how parameter variations impact outbreaks. Numerical simulations, utilizing the iterative Laplace transform and Atangana-Baleanu fractional derivative operator, explored solution conditions and stability at various fractional orders.

Results

Simulations showed that vaccination awareness significantly reduces measles transmission. Increased awareness lowered R, decreasing outbreak risk. Fractional orders provided insights into disease persistence, highlighting the importance of behavioral factors in control strategies. Sensitivity analysis identified parameters crucial for targeted interventions.

Conclusion

This study underscores the importance of vaccination awareness in controlling measles, showing that education-based strategies can reduce transmission. By integrating behavioral factors in a fractional calculus framework, this research supports efforts against endemic diseases like measles. The findings suggest that awareness campaigns, alongside vaccination, can alter transmission dynamics, offering a novel approach to enhance control measures. This model provides a basis for further research on behavioral interventions in disease modeling.