Normal distribution model
The number of COVID-19 patients admitted per day is modelled as a normal distribution in time.
​Philip Gerlee and Torbjörn Lundh

They predict the need for care for covid-19 patients

​Healthcare has a great interest in being able to plan the need for care for patients with covid-19. Two projects at the Department of Mathematical Sciences use different mathematical models and different input data to help with this.

​How large is the need for care over time?

Philip GerleeThrough various contacts Philip Gerlee, Associate Professor in Biomathematics, was contacted by the Logistics Group at Sahlgrenska University Hospital in the end of March. They asked if he could help with predictions about whether the expected care need for covid-19 patients would increase or decrease over time, when the peak would come and when the number of cases would subside. Philip brought his colleague, Professor Torbjörn Lundh, and together with the logisticians Ingrid Fritzell and Julia Karlsson at Sahlgrenska, they sketched on a model which could answer when the peak would come and how high it would be.

– At first, the model was simple. With data from Wuhan and Lombardy, we assumed that 0.2 percent of the population would be admitted to in-patient care. The question was, when? We assumed a normal distribution, but realised that this model perhaps was too rough. In parallel, we also used an infection model (SIR). The prognoses then became somewhat different, and Sahlgrenska used both these and other sources to form a balanced prognosis.

Measurements of infectivity

Now when the peak of the hospital admissions has passed and the need for care need seems to be on the way down, another model is needed. The Public Health Agency of Sweden has used an extended infection model, SEIR, which also includes the phase when a person is infected but not yet infectious, and fit the model for the Stockholm area. During late spring, Philip and Torbjörn used the same model for Gothenburg. In June, they received funding from Chalmers Areas of Advance to continue the development of the model and to develop new methods for measuring the infectivity in the population, which depends on both how many contacts people have each day and the probability that they infect through contact. The idea is that the disease transmission is high in the beginning of the pandemic but decreases when different restrictions causes people to have fewer contacts.

Several indicators will be used to estimate the number of contacts. One of them is the number of passengers using the local transport company Västtrafik, since the infectivity in the model of the Public Health Agency matches the decline in travel well. The proportion of positive test results is another, and data from the telephone health care counselling 1177 a third. A study in Östergötland led by Armin Spreco showed that the number of calls to 1177 concerning breathing difficulties for adults could be correlated with the number of hospitalised covid-19 patients 15 days later. The goal is to be able to make better predictions of the need for care. There will also be a follow-up of the prognoses issued in spring in order to see what worked best, to continue to develop this before next pandemic.

Individual data – how serious will it be for the patient?

Marina Axelson-FiskMarina Axelson-Fisk, Professor in Mathematical Statistics, had previously collaborated with Robert Feldt, Professor at the Department of Computer Science and Engineering, and Lars-Erik Magnusson, chief physician at the infection clinical department of the Östra Hospital. Then it was a matter of being able to distinguish early between blood poisoning (sepsis) and winter vomiting flu (norovirus). The two diseases may have a similar onset with fever, vomiting and dizziness, but sepsis is a serious condition that is important to detect early and not misdiagnose.

A master’s degree project about this with Marina as supervisor began in January, and patient data was to be provided by the Östra Hospital. But then, the corona pandemic broke out and everything was put on hold. Would it be possible to work with input data from patients with covid-19 instead? The issue then became whether the patient has covid-19 or not, but also how early in the process the disease can be discovered and whether it is possible to tell how serious it will become for the patient, preferably a week before the patient needs to be admitted to hospital.

Lots of raw data

The master’s degree projects had to be about the theoretical models for the computations instead, so the basis is ready. Marina applied for and received funding from Chalmers Areas of Advance together with Robert and Richard Torkar, also a Professor at Computer Science and Engineering, so now the work of producing a software that works in reality begins. Lots of raw data has arrived and will now be handled and processed. Marina’s part of the work is to optimise the theoretical models, which are based on so-called Markov Decision Processes and are computionally complex. As they are heavy to handle, it takes approximations and all sorts of computer science “tricks” for healthcare personnel to be able to use it and get results within a reasonable time limit, and this is the main task for the computer scientists.

– It would of course be good to have this ready quite soon, many people believe that the need for care may increase again. We therefore take some shortcuts now in the beginning, to build a more complete model in the long run. Even if the work does not have time to make such  big difference for the corona pandemic this autumn, healthcare will benefit greatly from the work in the future in other contexts – but of course we hope to come up with something that is possible to use soon.

Texts and photos: Setta Aspström

Published: Fri 09 Oct 2020.