### Modeling the evolution of the COVID-19 virus in Belgium

We model here **the evolution of three key health care system indicators directly affected by the spread of the COVID-19 pandemic in Belgium.**The main goal is to understand the day-to-day evolution of these indicators with the purpose of predicting their s**hort term evolution `one-day-ahead’. **A secondary analysis compares the daily-observed infections with an epidemiological model **to assess directly the effect of the lockdown measures on the rate with which the virus spreads. This study was conducted between February 4 ^{th }- April 2^{nd.}**

By now the COVID-19 virus has extended according to WHO to 206 countries, areas or territories and has touched more than 800.000 people worldwide. With lockdown restrictions affecting the lives of countless people throughout the world, it is important to understand and model the spread and consequences of this pandemic. The approach each country takes to tackle the virus has sensible differences and is directly influenced by the capacity of their own health care system.

**We focus here on the case of Belgium and describe the situation it faces, with the goal of predicting the short-term evolution of three key indicators that put pressure on the Health care system: Number of people hospitalized, Number of patients on intensive care units (ICU) and Number of cases that have died as a result of the infection. **We present in the graph below the evolution of the three indicators up to the latest official released figures, as well as the predictions from a statistical model used to identify the underlying trend in the data and provide based on it a prediction `one-day-ahead’. As there is an unavoidable degree of imprecision and uncertainty related to a forecast for the future, the point-wise prediction is accompanied by a prediction interval. This interval is constructed such that in most cases it covers the true future value if the data maintain the trend.

**Our analysis shows that the time effect seems to dampen for the number of people hospitalized, resulting in a more stable number of new people being hospitalized in the coming period. **The number of ICU patients seems to have exited an exponential growth regime and entered a linear increment phase. As the ICU capacity is limited, one still needs a close monitoring of this indicator in the coming days. **The number of deaths still follows an exponential increment at this point in time, which implies that for the following days the number of deaths will most probably still raise. **

Based on these findings and if the data maintain the current trend, the above models predict that for April 2^{nd }**the total number of people hospitalized will lie with high probability between 4946 and 5411, the total ICU cases will lie between 1125 and 1202 and the total number of deaths will, with high probability be within the limits 950 and 1033. **The actual officially reported numbers for April 2^{nd }are 5376 persons hospitalized, 1144 ICU patients and 1011 persons that lost their lives due to the infection, and **all lie within the proposed bounds from the model.**

It is instructive to asses as well how effective the lockdown measures are in terms of preventing the spread of the virus. For this we compare the number of observed infections in Belgium with an epidemiological framework (known by the acronym SIR) that models the spread of a virus by dividing the population in three groups __S__usceptible (healthy people that can get infected by the virus), __I__nfectious (people that have contracted the virus and are still infected at a fixed moment in time) and __R__ecovered (people that have contracted the virus in the past and have recovered). The framework assumes there is no interventional effect and as such comparisons serve to evaluate how effective the governmental measures are in hindering the spread of COVID-19. **The dynamics of these three groups across time as predicted by the SIR model are presented below, and suggest that if measures were not taken to prevent the spread, Belgium would have attained a peak of infection of more than 540.000 cases between end of April and beginning of May.**

**Conclusion:**

The proposed models recover well the trajectory of the three indicators. If the data maintain the trend, on the short term **the number of Hospitalized persons will most probably stabilize, the number of people in need of ICU increases linearly, while the number of deaths will still follow an exponential increment**.

The analysis presented here has been obtained with limited resources: the open source software **R**and freely available packages such as**shiny**, **coronavirus**, **deSolve**, **mgcv, ****SemiPar**as well as freely available data. More details about the computational implementation to obtain and reproduce these results for other countries can be found at: https://www.statsandr.com/blog/covid-19-in-belgium/ while a Shiny app for predicting `one-day-ahead’ the three key performance indicators is available at: https://eugenpircalabelu.shinyapps.io/covid19-forecasting/

**UPDATE: New ****data** in the period February 4^{th }- April 7^{th}

**Summary:**

We model here the evolution of three key health care system indicators directly affected by the spread of the COVID-19 pandemic in Belgium. The main goal is to understand the day to day evolution of these indicators with the purpose of predicting their short term evolution `one-day-ahead’. A secondary analysis, compares the daily observed infections with an epidemiological model to assess directly the effect of the lockdown measures on the rate with which the virus spreads.

**Our analysis shows that the number of people hospitalized and the number of patients on ICU continue to stabilize. The number of deaths has probably exited an exponential growth regime and entered a linear increment phase, which implies that for the following days the number of deaths will most probably still increase.**

Based on these findings and if the data maintain the current trend, the above models predict that for April 7^{th}, **the total number of people hospitalized will lie with high probability between 5660 and 6076, the total ICU cases will lie between 1231 and 1306 and the total number of deaths will, with high probability be within the limits 1699 and 1925. **The officially reporting for April 7^{th}at the moment of writing is not yet available.

**Conclusion:**

With respect to the effectiveness of the lockdown measures on the spread of the virus in Belgium**, we conclude that relative to the SIR model of April 2 ^{nd} the observed incidence is lower, suggesting the effect of the lockdown measures is now visible in hindering the infections.**

## UPDATE: April 17

## Modeling the evolution of the COVID-19 virus in Belgium in the period February 4th - April 17th

** **

** **

** **

Summary:

We model here the evolutionof three key healthcare systemindicators directly affected by the spread of the COVID-19 pandemic in Belgium. The main goal is to understand the day to day evolution of the seindicators with the purpose of predicting their short term evolution`one-day-ahead’. A secondary analysis, compares the daily observed infections with an epidemiological model to determine the rate with which the virus spreads.

Our analysis shows that **the number of people being hospitalized and the number of patients on ICU are stabilizing** **at slightly lower values than at the peak moments**. Due to the recent developments in the homecare centers and the methodology of reporting regarding this indicator, a model suggesting a steep increment in the number of deaths is still plausible.

Based on these findings and if the data maintain the current trend, the above models predict that for April 17th, **the total number of people hospitalized will lie with high probability between 5030 and 5728, the total ICU cases will lie between 1085 and 1255 and the total number of deaths will, with high probability be within the limits 4927 and 5378**. The official reporting for April 17 that the moment of writing is not yet available.

With respect to the effectiveness of the measures hindering the spread of the virus in Belgium, **we conclude that if the data maintain the current trend, a plausible growth model that fits the observed incidence well, suggests that in the coming period the number of cases should still follow an upwards trend.**

# UPDATE: April 22^{nd}

**Modeling the evolution of the COVID-19 virus in Belgium in the period February 4**^{th }- April 22^{nd}

^{th }- April 22

^{nd}

# Summary:

We model here the evolution of three key health care system indicators directly affected by the spread of the COVID-19 pandemic in Belgium. The main goal is to understand the day to day evolution of these indicators with the purpose of predicting their short-term evolution. A secondary analysis compares the daily observed infections with an epidemiological model to determine the rate with which the virus spreads.

**Our analysis shows that the number of people being hospitalized and the number of patients on ICU are beginning to follow a slight downward trend. A model suggesting increments in the number of deaths is still plausible.**

Based on these findings and if the data maintain the current trend, the above models predict that for April 22^{nd},**the total number of people hospitalized will lie with high probability between 4448 and 5077, the total ICU cases will lie between 970 and 1123 and the total number of deaths will, with high probability be within the limits 6073 and 6299. **The official reporting for April 22^{nd}at the moment of writing is not yet available.

With respect to the effectiveness of the measures hindering the spread of the virus in Belgium, **we conclude that if the data maintain the current trend, a plausible growth model that fits the observed incidence well, suggests that in the coming period the number of cases should still follow an upwards trend.**

# UPDATE: May 4th

**Modeling the evolution of the COVID-19 virus in Belgium in the period February 4**^{th }- May 4^{th}

^{th }- May 4

^{th}

**Summary: **

We model here the evolution of three key health care system indicators directly affected by the spread of the COVID-19 pandemic in Belgium. The main goal is to understand the day to day evolution of these indicators with the purpose of predicting their short-term evolution. A secondary analysis compares the daily observed infections with an epidemiological model to determine the rate with which the virus spreads.

Today is the first phase where the lock-down measures are being relaxed, with a second relaxation foreseen for May 11^{th}.

**Our analysis shows that the number of people being hospitalized and the number of patients on ICU are still on a downward trend, while the number of new deaths is now much lower than it used to be one or two weeks ago. **All the indicators point to the virus losing force and if the trend continues we expect on May 11^{th} to still have over 2000 patients in hospitals, around 350 people in ICU and close to a total of 8300 persons losing their lives due to the virus. If the testing procedure continues by the same protocols, we expect to have on May 11^{th} more than 52200 confirmed cases in Belgium.

**Contacts: **

Dr. Eugen Pircalabelu

Email: eugen.pircalabelu@uclouvain.be

Antoine Soetewey (Phd)