This is what scientists at BCAM are researching in connection with the COVID-19 pandemic
Several members of the Basque Center for Applied Mathematics - BCAM explain the issues related to coronavirus they are currently working on
Since the beginning of the health crisis, BCAM has put its mathematical and statistical modelling experience and knowledge at the disposal of the administration in order to provide helpful information based on advanced research on the evolution of the COVID-19 pandemic.
In fact, several BCAM members in collaboration with Ikerbasque, the University of the Basque Country and health institutions are taking part in a working group on COVID-19 and are focusing their research on real-time prediction of the epidemiological evolution of coronavirus, the estimation of the number of expected hospital admissions and on the improvement, comparison and evaluation of advanced models of prediction of the disease. This multidisciplinary group is made up of scientists with experience in Mathematical Modelling in Biology, Data Science and Artificial Intelligence.
In view of the economic and social impact caused by the COVID-19 epidemic, BCAM proposes to continue contributing, focusing its fundamental research capacities, to strengthen the fight against the disease and to contribute to recovery and to minimize possible future impacts.
Below, several researchers explain the topics related to the coronavirus on which they are currently working:
In fact, several BCAM members in collaboration with Ikerbasque, the University of the Basque Country and health institutions are taking part in a working group on COVID-19 and are focusing their research on real-time prediction of the epidemiological evolution of coronavirus, the estimation of the number of expected hospital admissions and on the improvement, comparison and evaluation of advanced models of prediction of the disease. This multidisciplinary group is made up of scientists with experience in Mathematical Modelling in Biology, Data Science and Artificial Intelligence.
In view of the economic and social impact caused by the COVID-19 epidemic, BCAM proposes to continue contributing, focusing its fundamental research capacities, to strengthen the fight against the disease and to contribute to recovery and to minimize possible future impacts.
Below, several researchers explain the topics related to the coronavirus on which they are currently working:
Epidemiological modelling of the dynamics of COVID-19 to study the impact of the pandemic
• Coordinator: Maíra Aguiar (BCAM-Ikerbasque)
• Collaborators: Nico Stollenwerk (University of Lisbon) and the Department of Health of the Basque Government and Osakidetza
At BCAM, this line of research is being explored by the Ikerbasque Research Fellow Maíra Aguiar, an expert in mathematical modelling in public health epidemiology who leads the Mathematical and Theoretical Biology group at the center. Dr Aguiar has extensive experience in the development and analysis of descriptive and predictive models of infectious diseases, with special attention to the study of dengue fever and other vector bone diseases as well as vaccine preventable diseases such as influenza and measles.
She is currently working on modelling the dynamics of COVID-19 to study the impact of the pandemic in the Basque Country and other European regions. In order to properly describe the expansion process of the disease, Dr Aguiar and her collaborator use stochastic SHARUCD-type models that consider the following groups:
• S: Susceptible persons
• H: Hospital admission cases and sever cases prone to hospitalization
• A: Asymptomatic infected cases, including mild and sub-clinical infections
• R: Recovered patients
• U: Patients admitted to intensive care units (ICU)
• C: Recorded cumulative positive cases (which includes all new positive cases for each class of H, A, U and R)
• D: Deceased patients
Predictions made by the model between 04-03-2020 and 05-05-2020, based on the data reported in the Basque Country
Future developments:
The effect of control measures on the infectivity of the population is now monitored in order to make longer-term predictions of the epidemic and to discuss future decisions on the relaxation of the social distancing measures that are still in place. In this framework, many public health questions can be addressed such as testing capacity, social behavior and self quarantining and eventually vaccination strategies. Models refinement are dove as new data becomes available.
Statistical and operations research techniques for estimating hospital admissions, infections and under reporting
The second group researching on COVID-19 at BCAM is made up of several researchers from the center’s Applied Statistics research line in collaboration with the University of the Basque Country.
1) A Bayesian SEIR Model for predicting COVID19 hospital admissions and infected cases in the Basque Country
Some of the strengths of this model are that it is age-stratified, it allows for uncertainty quantification and allows including prior knowledge.
Ikerbasque Research Fellow Maria Xosé (Coté) Rodriguez, an expert in applied statistics and software development with experience in evaluation of diagnostic and prognostic biomarkers, explains that from the beginning of the health crisis this group has provided health managers periodic reports with the predictions, for seven days, of positive cases and hospital admission for both the Basque Country and its main Integrated Health Organizations (OSI).
Future developments:
To improve the model researchers are considering modelling the time-dependent forcing function using splines and including hospital admissions, ICU cases, deaths and recoveries in the ODE System.
2) Predicting the need for hospital beds and ICU by methods of simulation and operations research
Fernando Garcia García, a postdoc fellow working on artificial Intelligence in prediction for clinical practice (with the support of the Basque Government) who regularly collaborates with the Galdakao-Usansolo Hospital, explains that the system is divided into two steps:
“First, work is done with confirmed incidence data; that is, with the new daily cases of positive COVID-19 tests. For these, a general growth model is adjusted according to the Gompertz function. The adjustment of the data is done by means of Bayesian techniques (under a negative binomial model for the counts) and bootstrapping techniques, in order to estimate the variability in the model parameters.
Operations Research techniques are then used to simulate (using Monte Carlo methods) different scenarios regarding hospital and ICU bed occupancy. In addition to the incidence rate, other factors are considered, such as: the proportion observed in previous days of hospitalizations with respect to positive cases, the rate of ICU admissions for reasons other than COVID-19 in the same spring season of the previous years (2018 and 2019), or the duration of an admission (triangular probability distribution).”
As a result, they obtain estimated scenarios about the daily occupation of beds up to a horizon of 7 days, which are providing support and guidance to hospital management in the hospital resource planning.
3) Using a delay-adjusted case fatality ratio to estimate under-reporting
This last approach is based on the work by Russell et al. from the Center for Mathematical Modelling of Infectious Disease (London School of Hygiene and Tropical Medicine) and it’s an attempt to estimate a corrected CFR (Case Fatality Ratio) to estimate under-reporting of COVID-19 cases in Spain, the autonomous regions and particularly to the Basque Country to evaluate the evolution of the CFR and the percentage of confirmed cases of COVID-19 along time. For this purpose, BCAM researchers are using the accumulated deaths and daily accumulated confirmed cases provided by Instituto de Salud Carlos III. Although the model is based on strong assumptions, this estimation serves to monitor the under-reporting and adapt it to new knowledge about COVID-19.
Future developments:
According to Dae-Jin Lee, leader of the Applied Statistics group at BCAM, this approach could be extended to consider age-group distribution or to model and forecast temporal evolution. “It could also be useful to support and contrast the result with the Bayesian SEIR model we are working on”.
• Coordinators: Inmaculada Arostegui (BCAM-UPV/EHU), Dae-Jin Lee, M.Xosé Rodriguez (BCAM-Ikerbasque)
• BCAM team: Moumita Das, Fernando García García, Joaquín Martínez-Minaya, Abelardo Monsalve and Carlos J. Peña
1) A Bayesian SEIR Model for predicting COVID19 hospital admissions and infected cases in the Basque Country
• Collaborators: Department of Health of the Basque Government and Osakidetza
Some of the strengths of this model are that it is age-stratified, it allows for uncertainty quantification and allows including prior knowledge.
Ikerbasque Research Fellow Maria Xosé (Coté) Rodriguez, an expert in applied statistics and software development with experience in evaluation of diagnostic and prognostic biomarkers, explains that from the beginning of the health crisis this group has provided health managers periodic reports with the predictions, for seven days, of positive cases and hospital admission for both the Basque Country and its main Integrated Health Organizations (OSI).
Future developments:
To improve the model researchers are considering modelling the time-dependent forcing function using splines and including hospital admissions, ICU cases, deaths and recoveries in the ODE System.
2) Predicting the need for hospital beds and ICU by methods of simulation and operations research
Collaborators:
• Fermín Mallor, Quantitative Methods for Uplifting the Performance of Health Service group at the Public University of Navarre.
• Clinical Research Unit at the Galdakao-Usansolo Hospital.
• Department of Health of the Basque Government and Osakidetza.
Fernando Garcia García, a postdoc fellow working on artificial Intelligence in prediction for clinical practice (with the support of the Basque Government) who regularly collaborates with the Galdakao-Usansolo Hospital, explains that the system is divided into two steps:
“First, work is done with confirmed incidence data; that is, with the new daily cases of positive COVID-19 tests. For these, a general growth model is adjusted according to the Gompertz function. The adjustment of the data is done by means of Bayesian techniques (under a negative binomial model for the counts) and bootstrapping techniques, in order to estimate the variability in the model parameters.
Operations Research techniques are then used to simulate (using Monte Carlo methods) different scenarios regarding hospital and ICU bed occupancy. In addition to the incidence rate, other factors are considered, such as: the proportion observed in previous days of hospitalizations with respect to positive cases, the rate of ICU admissions for reasons other than COVID-19 in the same spring season of the previous years (2018 and 2019), or the duration of an admission (triangular probability distribution).”
As a result, they obtain estimated scenarios about the daily occupation of beds up to a horizon of 7 days, which are providing support and guidance to hospital management in the hospital resource planning.
3) Using a delay-adjusted case fatality ratio to estimate under-reporting
• Collaborators: Department of Health of the Basque Government and Osakidetza
This last approach is based on the work by Russell et al. from the Center for Mathematical Modelling of Infectious Disease (London School of Hygiene and Tropical Medicine) and it’s an attempt to estimate a corrected CFR (Case Fatality Ratio) to estimate under-reporting of COVID-19 cases in Spain, the autonomous regions and particularly to the Basque Country to evaluate the evolution of the CFR and the percentage of confirmed cases of COVID-19 along time. For this purpose, BCAM researchers are using the accumulated deaths and daily accumulated confirmed cases provided by Instituto de Salud Carlos III. Although the model is based on strong assumptions, this estimation serves to monitor the under-reporting and adapt it to new knowledge about COVID-19.
Evolution of the corrected fatality rate in the Basque Country based on data reported between 11-03-2020 and 16-04-2020 by the ISCIII
Future developments:
According to Dae-Jin Lee, leader of the Applied Statistics group at BCAM, this approach could be extended to consider age-group distribution or to model and forecast temporal evolution. “It could also be useful to support and contrast the result with the Bayesian SEIR model we are working on”.
Machine Learning approach for the prediction of hospitalizations and intensive care unit admissions
• Coordinator: J.A. Lozano (BCAM-UPV/EHU)
• BCAM Team: Onintze Zaballa
• Collaborators: Department of Health of the Basque Government and Osakidetza
The problem is posed as a time series prediction problem and is carried out through Gaussian processes.
The decision not to use more complex models is based on the current uncertainty about parameters such as the probability of infection, time from infection to the appearance of symptoms, etc. In this sense, the model proposed is mainly an agnostic model based on the data available. As a Bayesian model, it is possible, however, to introduce information a priori into it, and this is done by assuming an expected value for each of the values to be predicted.
In order to select and learn the best prediction models, the data is divided into 2 sets: the training set and the validation set. This second set is formed by the last 7 observations of the data, and the training set, by the observations prior to these. The parameters are adjusted with the training set and learn the model for each of the media functions considered as a priori information for the model.
The model is simple and has a few limitations when it comes to long-term predictions, but it’s fast. It is also a flexible model that can be adapted to other datasets, so it has been shared with the Spanish Committee on Mathematics (CEMat) for cooperative prediction.
Predictions made by the model between 04-04-2020 and 10-04-2020, based on the data provided by the ISCIII at Spanish level
Future developments:
New research projects in the field of artificial intelligence for the tracking of affected people, early detection of symptoms compatible with COVID-19, modelling of asymptomatic population or predict infections' criticality based on current data will be launched. Additionally, other topics such as diagnosis by voice recognition or Rx image analysis for early detection are being explored.
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