A novel mathematical approach to COVID-19 planning

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which is the causative virus of the coronavirus disease 2019 (COVID-19), has caused major global health and economic crisis. As a result, significant efforts have been made by worldwide health authorities to try and control the spread of the SARS-CoV-2. In the majority of countries, the spread of SARS-CoV-2 is characterized by significant geographical and temporal heterogeneity, which requires local tailoring and interventions.

The planning and decision-making process surrounding the COVID-19 pandemic has been heavily influenced by mathematical modeling. Most published COVID-19 mathematical models are at a national scale; therefore, when these models are applied to a regional level, they do not account for inter-regional mobility.

Study: Regional probabilistic situational awareness and forecasting of COVID-19. Image Credit: VideoFlow / Shutterstock.com

In a recent study published on the preprint server medRxiv*, a team of researchers discuss a real-time spatio-temporal SARS-CoV-2 metapopulation model that was successful in practice for assessment, monitoring, and short-term prediction to inform regional and national policy decisions. This model utilizes phone mobility data and is calibrated using a new Monte Carlo Approximate Bayesian Computation (SMC-ABC), which the authors have named Split-SMC-ABC.

About the study

For overall preparedness and capacity planning, regional predictions of hospitalization have been pivotal. The predictions set forth by the authors assume no changes in the short-term transmissibility, which shows what would occur if policies and behavior remained unchanged.

However, the predictions from the authors often trigger behavioral changes and new policies, which may influence reproduction numbers. Thus, all predictions provided by this model have only been produced three weeks ahead.

It remains unclear when predicting hospitalizations whether it is more appropriate to use both test and hospitalization data, or only the latter. Due to the shorter delay, test data typically contains more information regarding recent changes; however, using all available data can reduce any uncertainties. Notably, hospital predictions have the potential to be biased if the two data sources are not appropriately coherent.

The authors compared hospital predictions when calibrating to both test and hospital data to when only calibrating the latter. The results showed that when only calibrating to the hospital data, point predictions were more accurate.

When the test data was used alone, there was an underestimation of the predicted hospitalizations. However, when the hospitalization data was used alone, prediction uncertainty was larger.

The same transmissibility for all regions was assumed when calibrating the model to present the national picture. In Norway, following the commencement of their national lockdown in March 2020, there was an estimated national reduction in transmissibility of 85%, with a reproduction number that was significantly below one. As compared to other interventions, the reopening of schools correlated with a 79% reduction in transmissibility.

Many of the restrictions in Norway were lifted during the late spring 2020; however, the estimated mean/median effective reproduction number stayed below one until the eighth of January 2020, when universities, schools, and borders were reopened. The national reproduction number began to increase during the fall of 2020, which resulted in the reinstatement of restrictions on the eleventh of May 2020. To this end, the authors estimated a reduction of 75% compared to R0.

Compliance with the mobility-reducing policies, such as restrictions on travel, can be monitored through the use of mobility data. There was a clear reduction in mobility of approximately 50% during the lockdown in March 2020, which steadily increased in the summer and corresponded to summer vacations.

The authors examined the predictive performance of the proposed model with reproduction numbers from Norway that varied regionally and compared them to the model using a nationally constant reproduction number. The results show that when predicting hospital admissions and confirmed cases, regional reproduction numbers outperform the national model.


The authors of the current study utilized a single nationwide detection probability for positive COVID-19 cases confirmed by the laboratory, reflecting the national testing criteria. It was discovered that testing practice and detection probabilities may differ between the regions. The results showed that it is possible to estimate separate detection probabilities per region, but with a significant computational cost.

The consistency between test and hospital data was affected by varying testing criteria and the number of tests performed. Including the estimated effects of planned interventions during the three-week-ahead period could improve the accuracy of predictions. The authors suggested future research to be conducted to assess the effect of different restrictions on regional transmissibility.

*Important notice

medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.

Journal reference:
Colin Lightfoot

Written by

Colin Lightfoot

Colin graduated from the University of Chester with a B.Sc. in Biomedical Science in 2020. Since completing his undergraduate degree, he worked for NHS England as an Associate Practitioner, responsible for testing inpatients for COVID-19 on admission.


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