1. Modeling and dynamics of measles via fractional differential operator of singular and non-singular kernels.
- Author
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Farman, Muhammad, Xu, Changjin, Shehzad, Aamir, and Akgul, Ali
- Subjects
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DIFFERENTIAL operators , *MEASLES , *FIXED point theory , *FRACTIONAL differential equations , *DECOMPOSITION method - Abstract
Young children frequently die from measles, which is a major global health concern. Despite being more prevalent in infants, pregnant women, and people with compromised immune systems, it can infect anyone. Novel fractional operators, the constant-proportional Caputo operator, and the constant-proportional Atangana–Baleanu operator are used to create a hybrid fractional order model that helps analyze the dynamic transmission of the measles virus. We assess the measles-free and endemic equilibrium, reproductive number, biological viability, boundedness, well-posedness, and positivity of the model. We apply the Banach contraction principle to verify the uniqueness of the system's solutions. The proposed system is confirmed to be Ulam–Hyres stable by using fixed point theory results. The aforementioned operators are further analyzed, and the Laplace-Adomian decomposition method is used to numerically simulate the system of fractional differential equations. To support our findings, the outcomes are graphically displayed. The efficacy and memory impact of fractional operators are illustrated through comparisons. Based on fractional parameter values, the study determines important disease-control strategies and shows that vaccinations greatly reduce the spread of measles. By reducing the number of infected people, increasing vaccination coverage lowers the burden of disease on the general population. • Measles persists as one of the top causes of fatalities among younger kids globally. • For investigation of the dynamical transmission of measles with CP Caputo and ABC. • We checked out the positivity, boundedness, well-posedness, biological viability, and stablity of model. • Numerically simulated a framework of fractional differential equations with the use of the Laplace-Adomian Decomposition method. • A comparison of the proposed scheme is also discussed to show the efficiency and memory effect of the fractional operator. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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