On mathematical modelling of measles disease via collocation approach
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Date
2024-05
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Abstract
Measles, a highly contagious viral disease, spreads primarily through respiratory droplets
and can result in severe complications, often proving fatal, especially in children. In this article, we
propose an algorithm to solve a system of fractional nonlinear equations that model the measles dis ease. We employ a fractional approach by using the Caputo operator and validate the model’s by
applying the Schauder and Banach fixed-point theory. The fractional derivatives, which constitute an
essential part of the model can be treated precisely by using the Broyden and Haar wavelet collocation
methods (HWCM). Furthermore, we evaluate the system’s stability by implementing the Ulam-Hyers
approach. The model takes into account multiple factors that influence virus transmission, and the
HWCM offers an effective and precise solution for understanding insights into transmission dynamics
through the use of fractional derivatives. We present the graphical results, which offer a comprehensive
and invaluable perspective on how various parameters and fractional orders influence the behaviours of
these compartments within the model. The study emphasizes the importance of modern techniques in
understanding measles outbreaks, suggesting the methodology’s applicability to various mathematical
models. Simulations conducted by using MATLAB R2022a software demonstrate practical implemen tation, with the potential for extension to higher degrees with minor modifications. The simulation’s
findings clearly show the efficiency of the proposed approach and its application to further extend the
field of mathematical modelling for infectious illnesses.