Prediction of Measles Disease Using Caputo Type Fractional Derivative Operator

Rabia Tehseen; Uzma Omer; Maham Mehr Awan; Rubab Javaid; Ayesha Zaheer

Authors

Rabia Tehseen Department of Computer Science, University of Central Punjab, Lahore, Pakistan
Uzma Omer University of Education, Lahore
Maham Mehr Awan University of Central Punjab, Lahore
Rubab Javaid University of Central Punjab, Lahore
Ayesha Zaheer University of Central Punjab, Lahore

Keywords:

Laplace-Adomian Decomposition, Homotopy Perturbation (HPM), Semi-Analytical, Derivative

Abstract

Although an effective vaccine has been available since 1963, measles continues to be an important public health problem worldwide. Measles was eliminated in the United States in 2000, but imported and secondary cases have remained since 2008 due to the rapid transmissibility of the disease and insufficient vaccination coverage. The disease still poses a significant health and economic burden in endemic areas and reported incidence and mortality rates among children are still alarming. This study proposes a fractional-order mathematical model that is based on the Caputo fractional derivative to understand and control the spread of measles. The model proposed divides the population into susceptible, exposed, infected and recovered compartments and includes recovery through natural immunity and treatment. Both the Laplace Adomian Decomposition Method (LADM) and the Homotopy Perturbation Method (HPM) are used to solve the system of fractional differential equations. Numerical simulations are carried out in MATLAB, and their accuracy is evaluated by comparison with actual epidemiological data. The simulation results show that higher vaccination rates can have a major impact on reducing disease spread and lowering the number of exposed and infected individuals. In particular, the infected population was reduced by an average of 53.2% during the simulation period, and the exposed population was reduced by an average of 41.6% during the same period. Moreover, the fractional-order model had better predictive performance than the classical integer-order model with a lower mean absolute error (MAE = 0.018) than the integer-order model (MAE = 0.047). Good convergence behavior was also observed in the proposed model and it was found to fit the real data with an accuracy of around 92.4%. The results show that the fractional-order model is more suitable for representing the memory effect and the transmission characteristics of measles. The study findings indicate that better vaccination approaches can be of significant importance in the reduction of disease prevalence and in long-term measles eradication efforts, with the help of fractional-order epidemic modelling.

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