A Mathematical Model of COVID-19 Transmission

TL;DR

This paper presents a mathematical framework for modeling COVID-19 transmission using the SIR model and related models, incorporating the Lambert W Function to analyze solutions and compare predictive capabilities.

Contribution

It introduces a novel application of the Lambert W Function to solve and analyze the SIR model for COVID-19 transmission, and compares different epidemiological models.

Findings

The Lambert W Function aids in solving the SIR model equations.

Different models vary in their accuracy of predicting disease spread.

Physical distancing and PPE use significantly impact transmission dynamics.

Abstract

Disease transmission is studied through disciplines like epidemiology, applied mathematics, and statistics. Mathematical simulation models for transmission have implications in solving public and personal health challenges. The SIR model uses a compartmental approach including dynamic and nonlinear behavior of transmission through three factors: susceptible, infected, and removed (recovered and deceased) individuals. Using the Lambert W Function, we propose a framework to study solutions of the SIR model. This demonstrates the applications of COVID-19 transmission data to model the spread of a real-world disease. Different models of disease including the SIR, SIRmp and SEIRpqr model are compared with respect to their ability to predict disease spread. Physical distancing impacts and personal protection equipment use are discussed with relevance to the COVID-19 spread.