Numerical Analysis of a Caputo Fractional-Order SEIR Model for COVID-19 Using Hermite Polynomial Collocation and Laplace-Adomian Decomposition Methods - Bosede Abubakre; Morufu Olayiwola; Ajimot Adebisi (Department of Mathematics, Universitas Negeri Gorontalo, 2026)
The rapid transmission of COVID-19 is a vital threat to the health systems of various countries, and the need to receive the correct mathematical models to implement control measures. This paper provides a numerical analysis of an exposed compartment Caputo fractional-order SEIR model with an incubation period of SARS-CoV-2 variants. The model is nonlinear and difficult to solve analytically, so there are no precise solutions. Two methods Hermite Collocation Method (HCM) and Laplace-Adomian Decomposition Method (LADM) are used. The system is turned into nonlinear algebraic equations by HCM through Hermite polynomial expansions whereas LADM uses Laplace transforms and Adomian polys to deal with nonlinearities. Simulations of the Maple indicate that the two methods can effectively estimate the dynamics of the fractional SEIR, although HCM is more accurate and converges more quickly. Fractional-order formulation also includes the effects of memory in the transmission of the disease. This evidence proves that the application of fractional-order modeling with Hermite based numerical methods provides a strong platform through which the dynamics, especially the epidemiological ones, may be analyzed and the adaptive public health responses may be directed.