A Hermite Collocation Framework for Nonlinear SEIMAR Modeling of COVID-19 Transmission Dynamics

Abstract

Background: The Coronavirus-related infection requires advanced mathematical models to grasp the nature of the transmission and analyze therapeutic interventions. Multi-compartment epidemic models with their nonlinear complexities are difficult to tackle traditionally by numerical means, especially when treatment strategies are considered.

Purpose: The present work designs and validates the Hermite Collocation Method (HCM) to solve the SEIMAR (Susceptible-Exposed-Infected-Masked-Antiviral-Recovered) COVID-19 epidemic model and compares the performance of the method to the already existing Laplace Adomian Decomposition Method (LADM).

Methods: A six-compartment deterministic SEIMAR model had been developed that includes monoclonal antibody therapy and antiviral treatment compartments in addition to the traditional epidemiological states. HCM was used as the solver of the model because it uses orthogonal Hermite polynomials as the basis functions and transforms the system of nonlinear ordinary differential equations to algebraic equations based on collocation points. The estimation of the parameters was done using the data provided by Nigeria Centre of Disease Control and initial conditions are based on the real-world situation of Plateau State in Nigeria.

Findings: The HCM converged better than LADM and had spectral accuracy as it approximates all six compartments. Numerical experiments showed that the susceptible population dynamics were under the exponential assumptions of the baseline conditions and the errors of convergence to the correct values declined systematically with the succeeding values of the Hermite polynomials. This approach was able to effectively model the nonlinear interactions of disease transmission and therapeutic intervention showing a 40 percent improvement in computational efficiency as compared to the traditional methods. The stability and reliability of HCM solutions was verified by error analysis and absolute errors between successive approximations dropped by orders of magnitude.

Conclusions: Hermite Collocation Method is a powerful, computationally inexpensive approach to the modelling of complex COVID 19 dynamics of transmission within multiple treatment compartments. HCM is better in the convergent properties and spectral accuracy and is thus well-suited to policy decision-making situations when there is a need to have an accurate epidemic projection. Such a strategy has great benefits in terms of assessing therapeutic methods and can be easily applied to other multi-compartment epidemiological models