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. INDEX TERMS COVID-19, fitting optimization, mathematical modeling, mechanistic model, nonlinear differential equations, pandemic.

Optimization in the Context of COVID-19 Prediction and Control: A Literature Review

“…Regarding the optimization of COVID-19 prediction models, three main approaches have been reported in the literature. The first uses the SEIR (Susceptible -Exposed -Infectious -Recovered) model (or its derivatives) as its basis and applies machine learning and optimization methods to determine the epidemiological parameters of the model [6][7][8][9][10][11][12][13][95][96][97][98][99][100][101][102][103][104][105][106]. The second approach uses a population-based model to simulate the transmission of the virus [14,15].…”

Switched forced SEIRDV compartmental models to monitor COVID-19 spread and immunization in Italy

“…By increasing their number, we decrease the fit error at the expense of the computation cost, determined by the number of parameters, proportional to the number of switches. In order to choose the best value L we try all the values in the interval [5,85] days, we compute the minimum BIC min over all BIC values and we evaluate: ∆ BIC = BIC X − BIC min where X is any of the considered populations (I,R,D or V).…”

“…We calibrate the model parameter using Algorithm 1. For the solution of the constrained optimization problem, we compared the trust-region reflective (TR) method with the Levemberg Marquardt (LM) one, which overperforms the Broyden-Fletcher-Goldfarb-Shanno (BFGS) as noted in [5]. We report in Table 1 the number of function evaluations FCount and the relative residual RRES for the Infected, Recovered, Dead and Vaccinated compartments.…”

“…Further extensions have been proposed to model the COVID-19 outbreak considering the different social distancing policies and control measures applied in the various geographic areas to contain the epidemic spread. More compartments have been added, making the models more and more complex (see [3], [4], [5], [6], to mention only a few of the most recent).…”

“…Concerning the model parameters, it is well known that COVID-19 epidemic data cannot be accurately represented by any compartmental approach with constant parameters all over the epidemic duration. To face this problem, some authors use variable parameters in the time interval (for example [6] ) or change the fitting function (see [5]). In our approach all the model parameters are constant in each switching time interval, except for the infection rate which is a time-dependent forcing function modelled as piecewise continuous.…”