591
ORIGINAL SCIENTIFIC ARTICLE
Estimation of the reproductive number and the outbreak size of SARS-CoV-2 in Slovenia
Institute of Biostatistics 
and Medical Informatics, 
Faculty of medicine, 
University of Ljubljana, 
Ljubljana, Slovenia
Correspondence/
Korespondenca:
Rok Blagus, e: rok.blagus@
mf.uni-lj.si
Key words:
SARS-CoV-2 pandemics; 
reproductive number; 
non-pharmaceutical 
interventions; modelling 
epidemics; Bayes model
Ključne besede:
pandemija SARS-CoV-2; 
reproduktivno število; 
nefarmakološki ukrepi; 
modeliranje epidemij; 
Bayesov model
Received: 15. 4. 2020
Accepted: 20. 4. 2020
eng slo element
en article-lang
10.6016/ZdravVestn.3068 doi
15.4.2020 date-received
20.4.2020 date-accepted
Public Health (Occupational medicine) Public Health (Occupational medicine) discipline
Original scientific article Izvirni znanstveni članek article-type
Estimation of the reproductive number and 
the outbreak size of SARS-CoV-2 in Slovenia
Ocena stopnje reprodukcije okužbe in deleža 
okuženih z virusom SARS-CoV-2 v Sloveniji
article-title
Estimation of the reproductive number and 
the outbreak size of SARS-CoV-2 in Slovenia
Ocena stopnje reprodukcije okužbe in deleža 
okuženih z virusom SARS-CoV-2 v Sloveniji
alt-title
SARS-CoV-2 pandemics, reproductive number, 
non-pharmaceutical interventions, modelling 
epidemics, Bayes model
pandemija SARS-CoV-2, reproduktivno število, 
nefarmakološki ukrepi, modeliranje epidemij, 
Bayesov model
kwd-group
The authors declare that there are no conflicts 
of interest present.
Avtorji so izjavili, da ne obstajajo nobeni 
konkurenčni interesi.
conflict
year volume first month last month first page last page
2020 89 11 12 591 602
name surname aff email
Rok Blagus 1 rok.blagus@mf.uni-lj.si
name surname aff
Damjan Manevski 1
Maja Pohar Perme 1
eng slo aff-id
Institute of Biostatistics and 
Medical Informatics, Faculty 
of medicine, University of 
Ljubljana, Ljubljana, Slovenia
Inštitut za biostatistiko in 
medicinsko informatiko, 
Medicinska fakulteta, Univerza v 
Ljubljani, Ljubljana, Slovenija
1
Estimating the reproductive number and the 
outbreak size of SARS-CoV-2 in Slovenia
Ocena stopnje reprodukcije okužbe in deleža okuženih z virusom 
SARS-CoV-2 v Sloveniji
Damjan Manevski, Maja Pohar Perme, Rok Blagus
Abstract
Background: We estimate the impact of non-pharmaceutical interventions implemented to 
slow-down the SARS-CoV-2 epidemic in Slovenia. The main measures of interest are the repro-
ductive number in time and the total number of infected individuals.
Methods: We apply a recently proposed Bayesian model, which is built using most recent data 
for 12 (model A) or 10 European countries (model B, Spain and Italy excluded).
Results: The reproductive number estimate after the lock-down equals 0.6, with the whole 95% 
credible interval remaining below 1 [0.3–0.9]. By excluding Italy and Spain from the model (mod-
el B), the estimated reproductive number increases to 0.8 (95% credible interval [0.5–1.2]). The 
estimated proportion of infected individuals in Slovenia is below 1% (0.53 [0.23–1.01]% in model 
A and 0.66 [0.26–1.45]% in model B). Thus, it is our opinion that the official number of confirmed 
cases underestimates the true one approximately by a factor of 10.
Conclusion: The results indicate that the interventions were successful, with the reproductive 
number being below 1. We believe it is sensible to keep the current set of interventions for at 
least 2 more weeks, as we expect that this will ensure at least 5 additional weeks before the need 
to reinitiate lock-down.
Izvleček
Izhodišče: Članek ocenjuje vpliv uveljavljenih ukrepov za obvladovanje epidemije okužbe z vi-
rusom SARS-CoV-2 na stopnjo reproduciranja okužbe z virusom in ocenjuje delež okuženih v Slo-
veniji.
Metode: Uporabljen je Bayesov model, ki predpostavlja enako učinkovitost ukrepov v različnih 
državah in je zgrajen na podlagi podatkov o številu umrlih za 12 (model A) oz. 10 evropskih držav 
(izločeni Španija in Italija, model B).
Rezultati: Ocenjena stopnja reproduciranja virusa v Sloveniji po sprejetih ukrepih je 0,6; pod 1 je 
celoten 95-odstotni interval kredibilnosti [0,3–0,9]. Če pri gradnji modela izločimo Italijo in Špa-
nijo (model B), je ocena stopnje reproduciranja v Sloveniji po sprejetih ukrepih 0,8 (95-odstotni 
interval kredibilnosti [0,5–1,2]). Ocenjeni delež okuženih v Sloveniji je manjši od enega odstotka 
(0,53 [0,23–1,01] % pri modelu A in 0,66 [0,26–1,45] % pri modelu B), uradno število potrjenih 
primerov pa podcenjuje dejansko število za približno faktor 10.
Zaključek: Dosedanji sprejeti ukrepi so bili uspešni, saj menimo, da je trenutna stopnja repro-
duciranja virusa SARS-CoV-2 pod 1. Pri sproščanju ukrepov je smiselno počakati vsaj 2 tedna, saj 
ocenjujemo, da to pomeni vsaj dodatnih 5 tednov zamika do ponovnih zaostritev.
Slovenian
Medical
Journal
592
PUBLIC HEALTH (OCCUPATIONAL MEDICINE)
Zdrav Vestn | November – December 2020 | Volume 89 | https://doi.org/10.6016/ZdravVestn.3068
1 Introduction
The novel coronavirus SARS-CoV-2 
has spread rapidly across the globe. One 
of the key reasons for its rapid spread is 
the high reproductive number (Rt). The Rt 
value is the average number of people that 
an individual infects during the course 
of their infectiveness, with t standing for 
the calendar time, as Rt can change (due 
to interventions, weather, etc.). With Rt < 
1, the number of new cases declines. With 
Rt > 1, the number of new cases increas-
es until the pandemic reaches its peak, 
at which point the number of new cases 
starts to decline because of the obtained 
collective immunity. The estimate of R0, 
the basic reproductive number, differs for 
the SARS-CoV-2, and is around 3 (1-7). 
Such a high reproductive number means 
an exponential rise in the number of cas-
es, leading to a fast increase in the number 
of people who require hospital and ICU 
treatment. Due to limited capacities of the 
healthcare system, this can quickly lead to 
a state when it is no longer possible to pro-
vide care to everyone in need.
Slovenia, similar to numerous other 
countries around the world, has adopted 
certain nonpharmaceutical interventions 
for reducing the reproductive rate of the 
infection. Among others, on 10 March 
2020, the government enacted the prohibi-
tion of organising closed events with over 
100 people in attendance; from 16 March 
2020 on, all preschools and schools closed, 
and on that same date, all public trans-
portation was stopped; from 20 March 
2020, there has been a prohibition of pub-
lic gatherings. It is essential to assess the 
effect of these NPIs on Rt. In their recent 
Cite as/Citirajte kot: Manevski D, Pohar Perme M, Blagus R. Estimating the reproductive number and the 
outbreak size of SARS-CoV-2 in Slovenia. Zdrav Vestn. 2020;89(11–12):591–602.
DOI: https://doi.org/10.6016/ZdravVestn.3068
Copyright (c) 2020 Slovenian Medical Journal. This work is licensed under a
Creative Commons Attribution-NonCommercial 4.0 International License.
study, Flaxman et al. studied the impact of 
non-pharmaceutical interventions on Rt 
for 11 European countries, including Italy, 
Spain, France, Austria and Sweden (Slove-
nia was not included), and showed that af-
ter the introduction of NPIs, Rt decreased 
from the initial value of 3.87 (median for 
all 11 countries) to 1.43 (range from 0.97 
for Norway to 2.64 for Sweden (7), where-
by they took into account the data until 28 
March 2020.
Standard Rt assessment is based on the 
number of infected individuals, which is 
not appropriate for SARS-CoV-2, as this 
data is severely underestimated. The num-
ber of confirmed cases strongly depends 
on the strategy and methodology of test-
ing, which differs between countries and 
the stage of the epidemic. Therefore, these 
differences do not allow for a direct com-
parison of the epidemic between countries 
in a given time period. Flaxman et al. used 
the data on the number of the deceased 
as the basis for their Rt assessment. These 
data are among the most valuable and re-
liable information which can be compared 
between countries (7). Bayesian model 
was used to assess the infection cycle to 
the detected cases of death.
In this article, we will also include Slo-
venia into the proposed model in order to 
estimate the actual number and the share 
of those infected with the SARS-CoV-2 
and evaluate the effect of the adopted NPIs 
on Rt. Below, we will first provide a short 
presentation of the methodology used, 
then present the key results and conclu-
sions.
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ORIGINAL SCIENTIFIC ARTICLE
Estimation of the reproductive number and the outbreak size of SARS-CoV-2 in Slovenia
2 Methods
Data on the number of deaths for 
Slovenia was obtained from Sledilnik 
COVID-19 [https://covid-19.sledilnik.
org/]. Data for other countries was ob-
tained from the ECDC website (8). We an-
alysed the obtained data up to and includ-
ing 13 April 2020. The cumulative number 
of deaths for Slovenia over this period is 
shown in Figure 1.
The used model was thoroughly pre-
sented by Flaxman et al. in detail  (7); here, 
we only sum up some of the key charac-
teristics.
The model is assessed with data on the 
number of deaths for 12 countries (be-
sides Slovenia, the analysis also includes 
Austria, Belgium, Denmark, France, Italy, 
Figure 1: Total number of deaths in time in Slovenia.
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2020
Germany, Norway, Spain, Sweden, Swit-
zerland, and United Kingdom). The data 
on the number of deceased on a particu-
lar day is taken into account, with the first 
day of the analysis being set to 30 days 
before there were 10 deceased in a coun-
try; this excludes the impact of patients 
who were infected outside of their home 
country. The key assumptions are that the 
NPIs have a similar effect on Rt across all 
12 countries, and that the effectiveness of a 
given NPI does not change over time. This 
way, we can estimate the model by using 
the data from several countries, there-
by obtaining more precise estimates. We 
point out that countries with more deaths, 
for example Italy and Spain, have a bigger 
impact on estimates, and they were also 
the first to adopt the NPIs. Because of the 
bigger number of infections in these two 
countries, it is also possible that the data 
on the number of deceased is less reliable 
or has changed in different ways than in 
other countries (9-10). In order to ver-
ify the impact this has on the results for 
Slovenia, we repeated the analysis by not 
taking into account these two countries 
(model B).
To ensure comparability of different 
NPIs between countries, we classified 
the NPIs in 5 groups in the same way as 
the Flaxman et al. study (7) (Table 1). By 
specifying the dates of NPIs, we defined 
the intervals for which we assessed the Rt: 
R0 value before the NPIs were first intro-
duced (before 9 March 2020), R1 being the 
estimate between the first two NPIs (from 
9 March 2020 to 10 March 2020) etc. The 
value from the last introduced NPI (20 
March 2020) to the date of the analysis (13 
April 2020) is denoted as R4. The model 
assumes that the values are constant with-
in the intervals and are interpreted as av-
erage values on this interval.
When setting the dates of the NPIs for 
Slovenia, our basic principle was to find 
the dates that most fit the definition in the 
Flaxman et al. study (7). In appendix (6.1), 
we explained the selection of the dates for 
Slovenia. It is clear that certain NPIs were 
Table 1: The dates that NPIs were introduced in Slovenia, as defined in 
the Flaxman et al. study (7).
Measure Date
Self-isolation 9. 3. 2020
Public events banned 10. 3. 2020
School closure 16. 3. 2020
Social distancing 16. 3. 2020
Complete lock-down 20. 3. 2020
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not completely equal in all countries, and 
they also differ by how they were named. 
We believe that the classification in Table 
1 is as coherent as possible to the NPIs in 
other countries.
Alternatively, 30 March could also be 
considered as the start of the so-called 
complete lockdown, when Slovenia imple-
mented the limitation of movement out-
side of individual’s municipalities. This 
option is discussed as model C, and the 
results are provided in Appendix (6.3). By 
this we assume that Slovenian NPIs on 20 
March were not as strict as in other coun-
tries. What’s more, this model does not 
permit a jump to this date, as there was no 
similar in-between NPI in other countries. 
Due to this inability to compare with other 
countries, Slovenia could have a possible 
significant limitation to the model: the 
model used cannot answer the question 
if the two periods differ, [20 March –30 
March] and [30 March – 13 April] or by 
how much.
The key parameters in the model are 
infection fatality rate (ifr) and the distri-
bution of time from infection to death, 
which connect the number of deaths with 
the number of cases, thereby allowing us 
to estimate Rt. We used the same approach 
for estimating the time from infection to 
death as Flaxman et al., and assumed that 
the distribution of time from infection to 
death is the same in all countries, i.e., with 
a median value of 23.9 days (7), Figure 2.
Flaxman et al. have calculated ifrm, m 
= 1, …, 11 for each of the 11 countries. 
The mean ifr value, i.e., the mean assumed 
probability of death among the infected 
for the 11 countries, is 0.954% (a range 
from 0.792% for Norway to 1.153% for 
France). The ifr value was estimated based 
on past studies and taking into account 
the age structure of the population and the 
contacts between individuals from differ-
ent age groups in individual countries (7). 
Due to the lack of such data for Slovenia, 
the ifr calculation could not be performed 
using the same approach, so we set ifr for 
Slovenia as: [1] mean ifrm, [2] maximum 
ifrm, [3] minimum ifrm.
In addition, we examined the forecast 
curves of repeated growth of the number 
of infected and dead after NPIs would be 
loosened. For this purpose, we assumed 
different estimated values of the number 
of infected and Rt after the loosening of the 
NPIs (marked with R5). Because the time 
to repeated growth completely depends 
on the assumed value of R5, we mainly fo-
cused in this part of the analysis on the ef-
fect of the so-called delay, before the NPIs 
were be loosened. This is from the end of 
our analysis (13 April) to the date when 
the first NPIs were loosened. This value 
made it possible to estimate the number of 
weeks until growth curves surpass some 
critical values (arbitrarily set at 500 new-
ly infected or 5 deaths per day). Just like 
before, we assumed the estimated value of 
R4 to remain the same for the duration of 
the so-called delay until the first loosened 
NPIs and a constant value of R5 across the 
whole interval after the loosening. 
We performed the analysis using the 
software R (R version 3.6.3) (11)) and the 
rstan package (12). In our results, we re-
port the mean of the a posteriori distribu-
tion with accompanying 95% credibility 
intervals (CI) in square brackets, i.e., the 
interval that includes 95% of the estimated 
a posteriori distribution of the parameter.
Figure 2: Assessed distribution of time from infection to death for the 
deceased.
0 10 20 30 40 50 60
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Time from infection to death (days)
De
ns
ity
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ORIGINAL SCIENTIFIC ARTICLE
Estimation of the reproductive number and the outbreak size of SARS-CoV-2 in Slovenia
3 Results
For Slovenia, we estimate that with 
regard to the medium scenario (mean if-
rm), the basic reproductive number before 
the adopted NPIs equalled  3.4 [2.0–5.0] 
(which is the lowest estimated value, and 
is equal to that estimated for Sweden: 3.4 
[2.6–4.6], the highest estimated value ap-
plies to Belgium: 6.9 [5.6–8.7], and was 
reduced after all NPIs were adopted to 0.6 
[0.3–0.9] (the lowest estimated value for 
Slovenia and Norway: 0.6 [0.4–0.9], the 
highest estimated value for Sweden: 2.1 
[1.6–2.5], Figure 3A (right), Table 2. In 
model B, which was built without taking 
into account Italy and Spain, the final es-
timated reproductive number equals 0.8; 
however, there was less data, so the credi-
bility interval is expectedly broader ([0.5–
1.2], Figure 3B, Table 2). The Rt estimates 
are somewhat higher, when we consider 
the minimum ifrm, and somewhat lower, 
when we consider the maximum ifrm (Ta-
ble 2 and Figure 6 in the appendix).
The estimated (cumulative) share of in-
fected for Slovenia according to different 
scenarios is presented in Table 3. Accord-
ing to the medium scenario (mean ifrm) 
we estimate that the share of infected in 
Slovenia is 0.5% [0.2–1.0] (lowest estimat-
ed value for Slovenia and Norway: 0.5% 
[0.3–0.9], highest estimated value for Swe-
den: 12.9% [6.2–24.9]). The estimated data 
on the number of cases indicates that the 
official number of confirmed cases is un-
derestimated by approximately a factor of 
10. Using different ifrm estimates for Slove-
nia does not have a significant impact on 
the results; in line with the expectations, 
the estimate is higher if ifrm is lower and 
vice-versa. The results are also not signifi-
Figure 3: Estimates for Slovenia.
Left image: forecasted and actual number of new cases per day. Middle image: forecasted and actual number of deaths per 
day. Right image: Rt at adoption of different NPIs. Up: model A includes all countries. Below: model B does not include Italy 
and Spain. All estimates are made while taking into account the mean ifrm.
0
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Measures
Complete lock-down
Public events banned
School closure
Self-isolation
Social distancing
50%
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Measures
Complete lock-down
Public events banned
School closure
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Social distancing
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cantly affected by the exclusion of Spain 
and Italy from the analysis; model B has 
somewhat higher estimates of the share 
of infected; however, the difference at no 
point exceeds 0.2 percentage point.
The actual number and the forecasted 
number of deaths for Slovenia for the re-
viewed period is depicted in Figure 4 by 
the model used, along with the forecast-
ed number of deaths for the 7 days fol-
lowing the final date of the analysis. In 
both models, we can notice an agreement 
between the actual number and the fore-
casted number of deaths, and in model B, 
the forecast for the next 7 days is some-
what more pessimistic. Using different es-
timates of ifrm has very little effect on the 
Table 2: Estimated Rt (mean and [95 % CI]) at the adoption of various NPIs for Slovenia 
according to different scenarios.
Model Scenario ifrm R0 R1 R2 R3 R4
A mean ifrm 3.4 [2.0-5.0] 3.2 [1.9-4.8] 2.9 [1.7-4.5] 2.1 [1.1-3.2] 0.6 [0.3-0.9]
maximum ifrm 3.4 [1.9-5.1] 3.2 [1.8-4.8] 2.9 [1.6-4.5] 2.1 [1.1-3.5] 0.6 [0.3-0.9]
minimum ifrm 3.6 [2.1-5.1] 3.3 [2.1-4.8] 3.1 [1.8-4.5] 2.2 [1.1-3.3] 0.6 [0.4-0.9]
B mean ifrm 2.8 [1.7-4.4] 2.6 [1.6-4.0] 2.4 [1.5-3.8] 2 [1.1-3.0] 0.8 [0.5-1.2]
maximum ifrm 2.7 [1.6-4.1] 2.6 [1.5-3.8] 2.4 [1.3-3.7] 1.9 [1.0-3.0] 0.8 [0.4-1.2]
minimum ifrm 3 [1.9-4.4] 2.8 [1.8-4.2] 2.6 [1.5-4.0] 2.1 [1.3-3.3] 0.9 [0.5-1.3]
Table 3: The estimated (cumulative) share (%) 
of infected for Slovenia according to different 
scenarios.
Model Scenario ifrm Mean [ 95 % CI ]
A mean ifrm 0.53 [0.23-1.01]
maximum ifrm 0.45 [0.20-0.88]
minimum ifrm 0.66 [0.31-1.22]
B mean ifrm 0.66 [0.26-1.45]
maximum ifrm 0.53 [0.20-1.12]
minimum ifrm 0.83 [0.34-1.77]
results (Figure 7 in the appendix).
Figure 5 shows an example of the 
growth curves with the assumption that 
after the NPIs are loosened, Rt increases 
to R5 = 1.5. We can notice that the curves 
are approximately parallel and that put-
ting off loosened NPIs (so-called delay) by 
each additional week means approximate-
ly 2.5 weeks longer until a critical value is 
reached; we arbitrarily set 500 newly in-
fected or 5 deaths per day as the critical 
values. For lower assumed values of R5, 
the distance between the curves is some-
what longer, with R5 = 1.25 it is already at 
4 weeks (in the more pessimistic model B 
it is on average a week shorter and only in-
creases with longer delays).
Figure 4: The actual (red columns) and the forecasted number of deaths (blue curve) for Slovenia, taking into account 
mean ifrm (model A: includes all countries, model B: Italy and Spain excluded).
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Figure 5: Forecast increase in the number of infected and deceased after the NPIs are loosened 
(assumed R5 = 1.5). Red arrows mark the distance between the curves when crossing the 500 
new infected per day or 5 deceased per day thresholds.
0
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597
ORIGINAL SCIENTIFIC ARTICLE
Estimation of the reproductive number and the outbreak size of SARS-CoV-2 in Slovenia
cantly affected by the exclusion of Spain 
and Italy from the analysis; model B has 
somewhat higher estimates of the share 
of infected; however, the difference at no 
point exceeds 0.2 percentage point.
The actual number and the forecasted 
number of deaths for Slovenia for the re-
viewed period is depicted in Figure 4 by 
the model used, along with the forecast-
ed number of deaths for the 7 days fol-
lowing the final date of the analysis. In 
both models, we can notice an agreement 
between the actual number and the fore-
casted number of deaths, and in model B, 
the forecast for the next 7 days is some-
what more pessimistic. Using different es-
timates of ifrm has very little effect on the 
Table 2: Estimated Rt (mean and [95 % CI]) at the adoption of various NPIs for Slovenia 
according to different scenarios.
Model Scenario ifrm R0 R1 R2 R3 R4
A mean ifrm 3.4 [2.0-5.0] 3.2 [1.9-4.8] 2.9 [1.7-4.5] 2.1 [1.1-3.2] 0.6 [0.3-0.9]
maximum ifrm 3.4 [1.9-5.1] 3.2 [1.8-4.8] 2.9 [1.6-4.5] 2.1 [1.1-3.5] 0.6 [0.3-0.9]
minimum ifrm 3.6 [2.1-5.1] 3.3 [2.1-4.8] 3.1 [1.8-4.5] 2.2 [1.1-3.3] 0.6 [0.4-0.9]
B mean ifrm 2.8 [1.7-4.4] 2.6 [1.6-4.0] 2.4 [1.5-3.8] 2 [1.1-3.0] 0.8 [0.5-1.2]
maximum ifrm 2.7 [1.6-4.1] 2.6 [1.5-3.8] 2.4 [1.3-3.7] 1.9 [1.0-3.0] 0.8 [0.4-1.2]
minimum ifrm 3 [1.9-4.4] 2.8 [1.8-4.2] 2.6 [1.5-4.0] 2.1 [1.3-3.3] 0.9 [0.5-1.3]
Table 3: The estimated (cumulative) share (%) 
of infected for Slovenia according to different 
scenarios.
Model Scenario ifrm Mean [ 95 % CI ]
A mean ifrm 0.53 [0.23-1.01]
maximum ifrm 0.45 [0.20-0.88]
minimum ifrm 0.66 [0.31-1.22]
B mean ifrm 0.66 [0.26-1.45]
maximum ifrm 0.53 [0.20-1.12]
minimum ifrm 0.83 [0.34-1.77]
results (Figure 7 in the appendix).
Figure 5 shows an example of the 
growth curves with the assumption that 
after the NPIs are loosened, Rt increases 
to R5 = 1.5. We can notice that the curves 
are approximately parallel and that put-
ting off loosened NPIs (so-called delay) by 
each additional week means approximate-
ly 2.5 weeks longer until a critical value is 
reached; we arbitrarily set 500 newly in-
fected or 5 deaths per day as the critical 
values. For lower assumed values of R5, 
the distance between the curves is some-
what longer, with R5 = 1.25 it is already at 
4 weeks (in the more pessimistic model B 
it is on average a week shorter and only in-
creases with longer delays).
Figure 4: The actual (red columns) and the forecasted number of deaths (blue curve) for Slovenia, taking into account 
mean ifrm (model A: includes all countries, model B: Italy and Spain excluded).
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Figure 5: Forecast increase in the number of infected and deceased after the NPIs are loosened 
(assumed R5 = 1.5). Red arrows mark the distance between the curves when crossing the 500 
new infected per day or 5 deceased per day thresholds.
0
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4 Discussion and conclusions
Our calculations show that the NPIs for 
limiting the spread infection in reviewed 
countries were successful, as we estimate 
that the current reproductive number of 
the infection in Slovenia is below 1, re-
gardless of the model used. With model A 
(taking into account all 12 countries) 1 is 
not included in the 95% credibility inter-
val, while in model B, where we intention-
ally included less data (by excluding Ita-
ly and Spain), the upper limit of the 95% 
credibility interval is above 1.
When interpreting these results, it must 
be emphasised that they are based on a 
very strong assumption that the effective-
ness of the NPIs in Slovenia was the same 
as in other countries. Here we could be 
concerned whether the estimated decline 
of Rt for Slovenia is not just an artefact of 
the model, as the data for Slovenia for as-
sessing the model has less weight because 
of the small number of deaths. With this 
in mind, we conducted sensitivity analysis 
in which we exponentially increased the 
number of deaths in Slovenia for the to-
tal reviewed period. The estimated Rt was 
still decreasing in accordance with the as-
sumption of the model; however, both the 
initial Rt and the Rt after the final NPIs, 
were at significantly higher levels (above 
3), from which we can conclude that the 
model is sensitive enough.
We can note from our results that the 
impact of excluding Spain and Italy from 
the analysis is negligible. In this case, our 
estimates of Rt before the NPIs are lower, 
and after the NPIs they are higher than if 
all countries were to be taken into account. 
This can be the result of the fact that the 
nature of the pandemic and the effective-
ness of the NPIs in Spain and Italy were 
different than elsewhere, or that it can be 
merely a reflection of a different phase of 
the epidemic in these two countries with 
regard to the rest.
Both models provide similar forecasts 
regarding the number of deaths for the 
598
PUBLIC HEALTH (OCCUPATIONAL MEDICINE)
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next 7 days after 13 April, with the fore-
casts of model B being somewhat more 
pessimistic. In the period between 14 
April and 18 April, we had on average 3 
deaths per day (in these 5 days the daily 
number of deceased were 1, 5, 0, 5 and 
4; this data is not final and is subject to 
change), which is in line with the fore-
casts of both models. Because of the small 
absolute numbers in Slovenia, random 
variation is larger, and it takes longer to 
be able to differentiate between random 
variability and actual trends. Therefore, 
even when taking into account the data on 
the number of deceased for the period be-
tween 14 and 18 April (not included in the 
model), it is currently not possible to con-
clude which model fits the data better. Be-
cause of the short time that passed in most 
countries between the adoption of differ-
ent NPIs, this analysis is not sufficient to 
evaluate the effect of any individual NPIs, 
but merely their cumulative effect. It can 
present a potential problem to assume that 
an effect of a NPI on Rt is immediate. We 
verified the effect of this assumption by 
adding another artificial NPI (10 days for a 
full lockdown); however, this did not have 
a significant impact on the result.
We also tested the alternative option, 
where we assumed a full lockdown only on 
30 March (model C, more detailed results 
in appendix, Figure 8). When interpreting 
these results, one has to understand the 
limits of the model. The absence of a spike 
after the NPIs on 20 March is a conse-
quence of the model and not its estimate, 
while the strong impact of the fact that in 
other countries the reproductive number 
did not meaningfully decline without a 
total lockdown should also be taken into 
account. Model C can provide reasonably 
high estimate of the reproductive number 
(1.54; 95% CI [1–2.28]) for the period be-
tween 16 and 30 March. The model then 
attempts to correct this high estimate and 
bring it in line with the actual number of 
deceased because of the great downward 
leap and a very low value in the last inter-
val (R4 = 0.47; 95 % CI [0.29–0.79]). De-
spite this low final value, the estimate of 
the total number of infected is significant-
ly higher in model C than in model A, and 
very similar to model B, with the forecasts 
of the number of deceased in the following 
days also being very similar.
The data on the cumulative share of 
the infected (0.53% and 0.66% consider-
ing model A and model B or C, respec-
tively) shows that in Slovenia we are still 
very far from achieving herd immunity. At 
the same time, the number of potential-
ly infected individuals is relatively high, 
and therefore we can expect that if NPIs 
were partially loosed, this would lead to 
another increase in the virus reproduc-
tive number and thereby in the number of 
infected. If the new reproductive number 
(R5) is similar to the one before the NPIs, 
then current NPIs were pointless, as the 
number of newly infected will achieve the 
highest values within a week. If the roll-
out of loosening NPIs would be slower, the 
key question is, how long it is sensible to 
persist until the NPIs start to be loosened, 
so that the time until the need to re-in-
tensify the NPIs can be as long as possi-
ble. Our results show that every additional 
week of the so-called delay in the loosen-
ing the NPIs (which increases the repro-
ductive number to R5 = 1.5) extends the 
period until a critical level is reached by 
approximately 2.5 weeks, and with a lower 
R5 value, this time is further extended.
We can conclude that the current NPIs 
have an effective impact on slowing down 
the course of the epidemic. Based on the 
model, it seems that it is sensible to persist 
with the NPIs for at least a few weeks. It is 
currently impossible to assess the impact 
of loosening the NPIs, as this data is not 
yet available.
In this light, it is especially interesting to 
monitor and compare data with the Swed-
ish experiment, where the adopted NPIs 
are significantly milder. According to our 
estimates, the virus reproductive number 
in Sweden after all the implemented NPIs 
is approximately 2. Consequently, the esti-
mated share of infected in Sweden (12.9%) 
599
ORIGINAL SCIENTIFIC ARTICLE
Estimation of the reproductive number and the outbreak size of SARS-CoV-2 in Slovenia
is the highest among the 12 countries that 
were included in the analysis. How much 
of this is an artefact of the model, cannot 
be estimated at this time (similarly to the 
model C), because the official data on the 
infected is not usable. Time will tell which 
of the paths will be more successful in the 
long run.
5 Acknowledgment
The authors would like to thank the 
Slovenian Research Agency (ARRS) for 
financial support (programme P3–0154, 
project J3–1761 and for financing the 
young researcher Damjan Manevski).
6 Appendix
6.1 Explanation of selected dates of NPIs
The listed dates of implementations of NPIs from Table 1 were chosen in accor-
dance with the definitions that were given in the Flaxman et al. study (7), page 14. The 
appropriate dates for Slovenia are as follows (Figure 6):
• 9 March is the date when strict instructions for self-isolation of those with symp-
toms for SARS-CoV-2 came into effect, and the infrastructure for testing potential 
cases across the country was already established (13); 
• On 10 March, all public events in closed spaces for more than 100 people were 
banned (and in open spaces, for more than 500 people) (14);
• On 16 March, all primary and secondary schools in Slovenia were closed (15);
• On 16 March, the NPI was implemented instructing the population to avoid per-
sonal contact as much as possible, with most shops and services closing down and 
most work to be done remotely, along with a stop to public transportation services 
(16);
• On 20 March, the prohibition of public gatherings, meaning that in public, people 
can only move individually, and only if they have urgent business, and for excep-
tions listed in the ordinance (16).
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6.2 Results of models A and B while taking into account the lowest and the highest 
value of ifrm
Figure 6: Estimates for Slovenia.
Left image: forecasted and actual number of new cases per day. Middle image: forecasted and actual number of deaths per 
day. Right image: Rt at the adoption of different NPIs for Slovenia in different scenarios (A: all countries while taking into 
account the maximum ifrm, B: all countries while taking into account the minimum ifrm, C: excluding Italy and Spain, while 
taking into account the maximum ifrm, D: excluding Italy and Spain while taking into account the minimum ifrm).
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Measures
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Measures
Complete lock-down
Public events banned
School closure
Self-isolation
Social distancing
50%
95%
Figure 7: Actual and forecast number of deaths for Slovenia under different scenarios.
A: all countries while taking into account the maximum ifrm, B: all countries while taking into account the minimum ifrm, C: 
excluding Italy and Spain, while taking into account the maximum ifrm, D: excluding Italy and Spain while taking into account 
the minimum ifrm).
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601
ORIGINAL SCIENTIFIC ARTICLE
Estimation of the reproductive number and the outbreak size of SARS-CoV-2 in Slovenia
6.2 Results of models A and B while taking into account the lowest and the highest 
value of ifrm
Figure 6: Estimates for Slovenia.
Left image: forecasted and actual number of new cases per day. Middle image: forecasted and actual number of deaths per 
day. Right image: Rt at the adoption of different NPIs for Slovenia in different scenarios (A: all countries while taking into 
account the maximum ifrm, B: all countries while taking into account the minimum ifrm, C: excluding Italy and Spain, while 
taking into account the maximum ifrm, D: excluding Italy and Spain while taking into account the minimum ifrm).
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Measures
Complete lock-down
Public events banned
School closure
Self-isolation
Social distancing
50%
95%
Figure 7: Actual and forecast number of deaths for Slovenia under different scenarios.
A: all countries while taking into account the maximum ifrm, B: all countries while taking into account the minimum ifrm, C: 
excluding Italy and Spain, while taking into account the maximum ifrm, D: excluding Italy and Spain while taking into account 
the minimum ifrm).
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Date
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Date
6.3 Results of model C (complete lockdown only on 30 March, 12 countries mean value 
of ifrm)
Figure 8: Estimates for Slovenia under the model C.
Left image: forecasted and actual number of new cases per day. Middle image: forecasted and actual number of deaths per 
day. Right image: Rt with the adoption of different NPIs for Slovenia.
0
500
1000
1500
0
2
4
6
0
1
2
3
4
C Measures
Complete lock-down
Public events banned
School closure
Self-isolation
Social distancing
50%
95%
 2
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R t
602
PUBLIC HEALTH (OCCUPATIONAL MEDICINE)
Zdrav Vestn | November – December 2020 | Volume 89 | https://doi.org/10.6016/ZdravVestn.3068
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