Covid-19 outbreak modelling and control

Contents

The COVID-19 outbreak has put human society into a historically unseen situation. BIOMATH and KERMIT support the challenges of facing the pandemic by modelling its spread and the management thereof, by combining compartmental models from epidemiology with model-predictive control techniques from the engineering field. The idea of this site is to group all our efforts and provide access to material we produce.

The scheme below provides an overview of the project.

 

Scheme of the project

 

Predicting COVID-19

To predict the evolution of the number of COVID-19 cases, we will start from the basic SEIRD model, an extension of the simple SIR model. In the SEIRD model, Susceptible people can become Exposed: these are infected, but not yet infectious. After the incubation period, Exposed people become Infectious, and finally either Recover or Die.

 

SEIRD-model

 

The basic SEIRD model can be used to predict the number of people in each of the compartments and in this way support decision-making concerning control and mitigation measures.

Yet, this basic SEIRD model neglects the fact that COVID-19 does not spread evenly across the country and age classes, while advanced tools are required to identify the optimal set of control and mitigation measures. For that reason, BIOMATH and KERMIT are working on a spatial extension of the basic SEIRD model and the development of a controller.

 

Spatio-temporal modelling of COVID-19 spread

COVID-19 does not spread evenly across the country (see map below for the situation on May 7, 2020), resulting in uneven pressure on the healthcare systems. Insight in the human interactions between different regions can help to optimise the distribution of healthcare resources and allow to assess the impact of different lock-down measures in different regions. Therefore, as a next milestone, we aim to incorporate spatial dynamics in our current model. To this end, we will set up a COVID-19 SEIR model for each of Belgium's 43 arrondissements and couple these mutually based on commuter, mobility and cellphone data. Such a spatial SEIR will allow us to assess the efficacy and value of local control and mitigation measures on the pandemic progression nationwide and enable an optimised distribution of healthcare resources and COVID-19 reference hospitals.

Dynamic map of cases

Controlling COVID-19

To predict the impact of different lock-down release strategies, one can implement each strategy (by changing parameters in the SEIR model) and compare the resulting simulation outcomes. However, a more efficient way is to turn this around and determine which strategy is needed to obtain a certain outcome, e.g., avoid the collapse of the health system. Therefore, we developed a model-based predictive controller (MBPC), based on the SEIR model. An example of such a controller can be seen below: the controller indicates the required number of tested people (isolated when positive; dashed line) and the degree of distancing needed (shading) to retain the ICU (Intensive Care Unit) capacity from exceeding its limits (red line).

Controller

In this example, the controller does not take into account the societal costs of the measures it proposes (testing and social distancing). Therefore, we aim to extend the controller to account for the economical, psychological and social impact as well, on top of protecting the health-care system. For this holistic approach, we will collaborate with specialists in the fields of economy and socio-psychology. More information about the collaboration can be found here (in dutch).

 

Lifting the current model to a higher level: FWO-call

With the current model, only short-term predictions are possible. To better support the country’s mitigation and control policy, medium-term predictions are needed. These will allow to assess the impact of different exit strategies, identify the best possible set of measures to keep the pandemic under control and obtain reasoned estimates for the level of vaccination necessary to suppress COVID-19 once a vaccine is available.

In cooperation with our partners from Antwerp University (UA), Hasselt University (UHasselt) and Free University of Brussels (VUB), we applied to the special FWO-call on COVID-19 research. The goal of this project is to extend the model with age-stratification (UA), spatial dynamics (UG) and stochasticity intrinsic to the disease spread (UHasselt). In addition, the model will be finetuned to inform hospitals on needed intensive care capacity (VUB). Finally, we will add a control layer to optimize the lockdown release strategy (UG). To account for economic impact and social well-being, we will add holistic features to this controller.

 

Read more

  • This article illustrates the application of model-predictive control to models that calculate the spread of the disease. (This was also shared on LinkedIN.) 
  • A whitepaper on the same topic is available for download at the bottom of this page.
  • An article on our holistic approach can be found on LinkedIn as well.
  • In this video, professor Jan Baetens explains how to develop a basic mathematical model to predict the number of Corona cases.
  • In this video, Elena Torfs explains how model-based predictive control works.

 

Access to the code

To follow the ongoing work, BIOMATH researchers make the code and its development available in its COVID-19 Model GitHub repository.

 

Collaborators

A list of all collaborators and contributors can be found here.

 

Contact

Questions, comments or contributions? Please contact us!

 

 

 

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COVID-19 model-predictive control whitepaper1.38 MB 1.38 MB