Mathematical modeling and numerical analysis of COVID-19 transmission using a Hermite collocation SEIARW framework

The COVID-19 pandemic continues to motivate reliable numerical tools for epidemic systems involving asymptomatic and environmental transmission. In this study, we formulate a normalized nonlinear SEIARW model and solve it using the Hermite Collocation Method (HCM). Unlike earlier collocation-based COVID-19 studies built on reduced compartmental structures, this work considers a richer framework with susceptible, exposed, symptomatic infectious, asymptomatic infectious, removed, and environmental reservoir classes. The normalization procedure is presented explicitly, and the biological feasibility of the model is established through existence, positivity, and boundedness of solutions. Numerical results show that HCM produces stable approximations and converges rapidly across successive iterations for all compartments. Overall, the study shows that HCM is an efficient computational approach for nonlinear multi-compartment epidemic models with hidden and reservoir-driven transmission.