A Generalized Mechanistic Model for Assessing and Forecasting the Spread of the COVID-19 Pandemic

Abstract

Since early 2020, the world has been afflicted with an unprecedented global pandemic. The SARS-CoV-19 (COVID-19) has levied massive economic and public health costs across many countries. Due to its virulence, the pathogen is rapidly propagating throughout the world in such a way that makes it incredibly challenging for officials to contain its spread. Therefore, there is a pressing need for national and local authorities to have tools that aid in their ability to assess and extrapolate the future trends of the spread of COVID-19, so they may make rational and informed decisions that minimize public harm. Mechanistic models are prominent mathematical tools that are used to characterize epidemics. In this paper, we propose a generalized mechanistic model with eight states characterizing the COVID-19 pandemic evolution from a susceptible state to discharged states while passing by quarantined and hospitalized states. The parameters of the model are determined by solving a fitting optimization problem with three observed inputs: the number of infected, deceased, and reported cases. The model's objective function is weighted over the training days so as to guide the fitting algorithm towards the latest pandemic period and lead to more accurate trend predictions for a stronger forecast. We solve the fitting problem with the Levenberg-Marquardt algorithm; we compare the performance of the model generated from this algorithm to the one of another state-of-the-art fitting algorithm as well as to the one of another compartmental model widely used in literature. We test the model on the COVID-19 data from four highly afflicted countries. The fitting algorithm has been validated graphically and through numerical metrics, and results show significantly accurate results for most of the countries. Once the model's parameters are estimated, forecasting results are derived and uncertainty regions of the expected scenarios are provided.

Keywords

• COVID-19
• fitting optimization
• mathematical modeling
• mechanistic model
• nonlinear differential equations
• pandemic