COVID-19 statistics data is being provided by State Data Governance Information System and is publicly available. We retrieved the number of new confirmed COVID- 19 cases, number of positive tests, deaths from COVID-19 for each municipality of Lithuania (60 municipalities overall) from “COVID19 statistika dashboards” dataset [22]. We have analysed the period from 20/03/2020 to 20/06/2021 covering two quarantines applied in Lithuania.

In order to evaluate the effect of applied NPIs on the progression of the pandemics, we used following 8 NPIs: school closing, workplace closing, cancel of public events, restrictions on gatherings, closed public transport, stay at home requirements, restric- tions on internal movement, international travel controls. We used Oxford COVID-19 Government Response Tracker (OxCGRT) [14] to obtain the NPI data for Lithuania. This dataset consists of 23 government response measures and is being curated by over 200 Oxford University volunteers who are constantly retrieving and updating the data for each country in the world using reliable sources (e.g. governmental websites). NPI information for Lithuania is being updated based on the information provided in the website of Ministry of Health of The Republic of Lithuania [23].

The primary downloaded NPI data was in a form of ordinal variables ranging from 0 to 3 or 4, where the lowest level indicates the least strict intervention and the highest level marks the most strict restrictions (full data description can be found in [14]). We recoded the analysed NPIs into the binary variables as described below:

• 1 if School closing NPI value in original dataset is above 1 and 0 otherwise;

• 1 if Workplace closing NPI value in original dataset is above 1 and 0 otherwise;

• 1 if Cancel public events NPI value in original dataset is above 1 and 0 otherwise;

• 1 if Restrictions on gatherings NPI value in original dataset is above 3 and 0 otherwise;

• 1 if Close public transport NPI value in original dataset is above 1 and 0 oth- erwise;

• 1 if Stay at home requirements NPI value in original dataset is above 1 and 0 otherwise;

• 1 if Restrictions on internal movement NPI value in original dataset is above 1 and 0 otherwise;

• 1 if International travel controls NPI value in original dataset is above 1 and 0 otherwise.

For reproduction number estimates we used eight NPI binary variables during both quarantine periods. In addition, to describe the situation of second quarantine we use detailed information about 11 governmental interventions introduced in second quarantine as well. We retrieved the information about these 11 interventions from the COVID-19 website of Government of the Republic of Lithuania [24]. Dates and descriptions of applied interventions are presented in Table 1. The latter numbering of the governmental interventions we will use later in Fig. 1 and Fig. 2.

Table 1
Nationwide governmental interventions applied in Lithuania during the secondquarantine

We calculated the reproduction number using the method presented by Cori et al. [10]where the estimation shows the average number of secondary infections arising after time $\textcolor{red}{}t$ if conditions do not change during this time. This method requires only two inputs: the number of new cases and serial interval (time between the start of primary and secondary infections) distribution, and the following equation is used to calculate the estimate:

$R_t=\frac{I_t}{\hfill {\sum }_{s=1}^t{I}_{t-s}{\omega }_s}$

where $I_t$ is number of new cases at day $t$ , ${\omega }_s$ – current infectivity (probability that secondary infection will appear after $\textcolor{red}{}s$ days), $\textcolor{red}{}s$ – day when individual was infected. This calculation is implemented in EpiEstim R library [9], and is based on main three assumptions:

1. 1. Reproduction number is being estimated using all data from the time period with selected length so it is calculated at the end of this period;
2. 2. In order to achieve sufficient posterior coefficient of variation the accumulated number of new cases in the population or sample should reach minimal number of 11;
3. 3. New cases appear only locally and infection cannot be transmitted to other species.

According to Gostic et al. [13], all infections that have occurred during the first specified time period are lost in denominator. Therefore, this method presented by Cori might estimate very large$R_t$ values at the beginning of the time series.

Fig. 1.
Reproduction number and the non-pharmaceutical interventions applied at the specific moment in time.

Following the recommendations from Pan American Health Organization [19], serial interval of 4.8 days and standard deviation of 2.3 days with 3 days uncertainty were used for reproduction number estimation. The $R_t$ was estimated only when the accumulated number of new cases reached 11 for each municipality separately. If there was a smaller number of accumulated new cases in the municipality, it was assumed that the reproduction number in that municipality is below 1.

The dynamics of reproduction number and the restrictions applied were analysed from the 20/03/2020 till the 20/06/2021 covering two quarantines applied in Lithuania. The first quarantine was declared in 16/03/2020 and have ended in 16/06/2020. From Fig. 1 one can observe that the estimated R values were very high during the summer season of 2020 but the number of new cases was at low level. This result confirms the feature of selected method that high R values were estimated at the beginning of the pandemics. The effect of specific NPI which is 100% effective can only be observed after some time delay. This is due to the process of clinical infection progression and when the infected individual starts to spread the virus [18]. The num- ber of new cases have started to increase after the summer season, while the applied restrictions were still loosened up. This acceleration of the virus spread evoked the governmental response and resulted in strengthened restrictions with second quaran- tine in 7/11/2020 (marked with the first vertical red line and number 1 in Fig. 1). After that the reproduction number started to lower, however it has decreased and became lower than 1 only when the additional restrictions of internal movement and requirement to stay at home were applied in 16/12/2020 (marked with the second vertical red line and number 2 in Fig. 1). From February 2021 the reproduction number have started to increase and have exceeded the value of 1. However, the situation in the last several months has improved and together with the steadily decreasing number of new cases governmental restrictions are being lifted (green vertical lines in Fig. 1).

Fig. 2.
The dynamics of percentage of Lithuanian municipalities with R > 1. Red vertical lines mark the applied governmental restrictions, while green vertical lines show when the restrictions were loosened up. Descriptions of the governmental interventions numbers can be found in Table 1.

Figure 1 shows the dynamics of 7-day reproduction number median (black curve) with 95% credible interval (blue curves). The red and gray tiles in the background show whether the eight NPIs (listed on the right side of the graph) were applied (On – red background color)/not applied (Off – gray background color) at the specific moment in time. Red vertical lines mark the added governmental restrictions, while green vertical lines show the days when governmental restrictions have been relieved. Red horizontal dashed line marks $\textcolor{red}{}\mathrm{R=1}$. The descriptions of nationwide governmental interventions marked with numbers and vertical lines in this figure can be found in Table 1.

Unequal proportions of new cases of COVID-19 in different municipalities of Lithua- nia suggested estimating the number of reproduction separately for each municipality. Therefore, we have estimated the reproduction number for each municipality sepa- rately. As there are 60 municipalities in Lithuania, we cannot present results for each municipality due to limited space. So we calculated the proportion of municipalities with$\textcolor{red}{}\mathrm{R>1}$, that is, which part of the country was a source of virus spread. Analysing the reproduction number in separate municipalities of Lithuania we obtained that more than 75% of municipalities had $\textcolor{red}{}\mathrm{R>1}$ at the beginning of the second quarantine (it is illustrated in Fig. 2). This number started to decrease only when stricter governmental restrictions were applied in 16/12/2020. Therefore, we performed a more detailed analysis of the situation of municipalities in the second quarantine in two periods – before and after the restriction introduced on 16/12/2021. For both periods, we compared the estimate of $\textcolor{red}{}{R}_t$ at the end of the period compared to the beginning (shown in Fig. 3, where the top panel is for the pre-restriction period and the bottom panel for the post-restriction period).

From the top Fig. 3 we can see that the $R_t$ has lowered in 47 out of 60 municipalities and even decreased below 1 in 5 municipalities (orange arrows) when the second quarantine was applied in 07/11/2020. Indeed, the decrease of $R_t$ was wider spread only when the internal movement ban was applied in 16/12/2020:$R_t$ has diminished in 45 out of 60 municipalities and it has decreased below 1 in 44 out of 60 municipalities (orange arrows at the bottom in Fig. 3). During the period from 16/12/2020 till 02/02/2021 the $R_t$ has decreased for 5 municipalities in which the$R_t$ value was below 1 at the beginning of this period (green arrows at the bottom Fig. 3). In this figure arrows directed to the right and left are showing whether the reproduction number was increasing or decreasing, accordingly, during this period. The green colour shows municipalities that had $R_t$ below 1 at the beginning and have it at the end of the period; orange colour marks municipalities that had$R_t$ above 1 at the beginning and has decreased below 1 at the end of the period; red colour shows where$R_t$ did not decrease below 1 in all periods.

The applied restrictions had a short effect and the situation in municipalities started to deprive till the May of 2021. The possible effect of population’s immunity formation and vaccination process itself might be one of the influencing factor for the decrease of viral spread till the end of the analysed period.