An Efficient Numerical Approach to Solve SEIR Epidemic of Measles of Fractional Order by Using Hermite Wavelets

Mathematical biology is a captivating field of applied mathematics that provides a precise understanding of biological occurrences and their connection to health related matters. Implementing novel mathematical methods and definitions in this field of study will significantly enhance public health by effectively managing certain diseases and utilizing the modern tools at our disposal is the most compelling justification for conducting novel research. In this study, Hermite wavelet and Adams-Bashforth-Moulton predictor-corrector (ABM) methods are employed to solve a nonlinear fractional SEIR measles epidemic model with unspecified parameters. The SEIR model is a set of differential equations used in medical science to investigate medical and epidemiology treatment for those affected. Operational matrices, when used in conjunction with the collocation method, convert fractional-order models into a system of algebraic equations. The Hermite wavelet method (HWM) is employed to graphically represent the chaotic attractors of the fractional SEIR model. The effectiveness of the Hermite wavelet method has been validated through an analysis of its convergence, error, and stability. Furthermore, we have conducted a comparison between solutions obtained using Hermite wavelets and the ABM method to evaluate the accuracy and suitability of the Hermite wavelet scheme.