A Wavelet based Numerical Study Of Epidemic Models With special Reference to SIR and SEIR Models

Abstract

Mathematical models offer an excellent methodology for conceptualizing knowledge about a process in a very compact form. They are widely used in social and natural sciences and play significant roles in physics, chemistry, earth sciences, computer science, and biology. Mathematical modeling has applications in diverse areas, such as heat transfer, population growth, chemical reactions, and disease dynamics, especially in epidemiology. This work deals with the numerical study of mathematical models, particularly the SIR and SEIR models. These models play a vital role in mathematical biology for understanding and predicting the spread of infectious diseases. newlineFractional calculus is a branch of calculus that generalizes the derivative of a function to arbitrary order. In recent years, fractional calculus has become the focus of interest for many researchers in applied science and engineering because realistic modeling of a physical phenomenon can be efficiently executed by utilizing fractional calculus. The primary feature of the fractional-order models is their non-local nature, due to which they can represent common physical processes and dynamical systems more accurately than the conventional integer-order models. Owing to the advantage of fractional-order models, we aim to obtain the numerical solutions of classical as well as fractional-order SIR and SEIR epidemic models. newlineOn the other hand, wavelet theory is a relatively new and emerging area in mathematical research. It has been applied in a wide range of engineering disciplines; particularly, they have been successfully employed in signal analysis for waveform representations, timefrequency analysis, and fast algorithms for easy implementation. Wavelet-based collocation methods have gained a significant place in numerical analysis, primarily due to their simple procedure, less computational cost, and fast convergence. The present work provides a comprehensive study of different wavelet collocation methods such as the Haar wavelets, Fibonacci wavelets, and V...