Modelling the early phase of the Belgian COVID-19 epidemic using a stochastic compartmental model and studying its implied future trajectories

Abstract

Following the onset of the ongoing COVID-19 pandemic throughout the world, a large fraction of the global population is or has been under strict measures of physical distancing and quarantine, with many countries being in partial or full lockdown. These measures are imposed in order to reduce the spread of the disease and to lift the pressure on healthcare systems. Estimating the impact of such interventions as well as monitoring the gradual relaxing of these stringent measures is quintessential to understand how resurgence of the COVID-19 epidemic can be controlled for in the future. In this paper we use a stochastic age-structured discrete time compartmental model to describe the transmission of COVID-19 in Belgium. Our model explicitly accounts for age-structure by integrating data on social contacts to (i) assess the impact of the lockdown as implemented on March 13, 2020 on the number of new hospitalizations in Belgium; (ii) conduct a scenario analysis estimating the impact of possible exit strategies on potential future COVID-19 waves. More specifically, the aforementioned model is fitted to hospital admission data, data on the daily number of COVID-19 deaths and serial serological survey data informing the (sero)prevalence of the disease in the population while relying on a Bayesian MCMC approach. Our age-structured stochastic model describes the observed outbreak data well, both in terms of hospitalizations as well as COVID-19 related deaths in the Belgian population. Despite an extensive exploration of various projections for the future course of the epidemic, based on the impact of adherence to measures of physical distancing and a potential increase in contacts as a result of the relaxation of the stringent lockdown measures, a lot of uncertainty remains about the evolution of the epidemic in the next months.

A data-driven model of the COVID-19 spread among interconnected populations: epidemiological and mobility aspects following the lockdown in Italy

“…has all its eigenvalues with negative real part. Some considerations about the position of the eigenvalues in the complex plane can be performed making use of the Gershgorin circle theorem on matrix eigenvalues 1 .…”

“…Lines: model predictions stand the underlying dynamics, in view of possible similar future situations. As noted by important theoretical studies such as [1,22,32,36,50], the evolution of any pandemic (and particularly the current one) strongly depends on the population actions in the early phase; nevertheless, the model provides a quantitative tool for evaluating the impact of the applied containment measures, in particular of the mobility restrictions, in different epidemic scenarios.…”

“…Moreover, among the most recent (and actually huge) literature on the COVID-19 modeling, we also mention some papers proposing interesting variants of the classical SIR model and using different approaches: the age-structured SIR model [36], the stochastic, discrete, age-structured compartmental model [1] in which distributed time delays related to the periods of incubation, infection, and quarantine are considered as in [35]. Another aspect common to these latter works that matters in relation to our study is that they analyze the first epidemic period (until October 2020) in order to highlight how different strategies implemented in that peculiar time interval can affect the future epidemic trajectory.…”

Analysis and Simulation of Epidemic COVID-19 Curves with the Verhulst Model Applied to Statistical Inhomogeneous Age Groups

“…An example of a more complicated model is given in by Abrams et al [9]. The handling of noisy data in models (transfer functions) with noisy parameters is proposed by Ren et al [10].…”

Prediction of hospital bed capacity during the COVID− 19 pandemic

“…Most efforts then focused on susceptible-infected-removed (SIR) models, and variations thereof, aimed at predicting the number of positive COVID-19 cases at a national level (e.g. [13,14]). While these provide valuable insights into the dynamics of future disease spreading in a population, we could not readily make use of those for hospital planning because they demand input on parameters, such as doubling times and social distancing measures, that were not available for our local setting at that time.…”