Starting end of 2019 a novel strain of coronavirus SARS-CoV-2 originated in Wuhan, China and spread globally. The first confirmed cases were identified in December 2019 [11]. On January 30 infection was found in 19 countries and 7 818 cases were reported [12]. On March 11 WHO declared the pandemic [13]. Then, it was 118 319 confirmed cases and 4292 deaths [14]. Although most cases show no symptoms, the very high rate of infections in several countries resulted in a shortage of healthcare capacity due to a small number of beds equipped with respirators and oxygen as well as high morbidity among medical personnel [15]. Therefore many governments decided to introduce lockdown to slow-down COVID-19 spread. China decided to block the cities and to introduce strict quarantine for all residents of highly affected regions. The other preventive measures were: isolation of infected and suspected of being infected, social distancing. Such methods have proven effective in slowing down the spread of the virus and gave additional time for medical care adaptation [16]. The first two most affected countries were China and Italy. Several reports are forecasting how coronavirus infection rate is affected by preventive measures [17,18]. However, there is a limited number of publications considering timing in preventive regulations [5-7,19]. The most advanced model seems to be eSIR [6]. In the study comparing outbreak in Hunan, China and Italy eSIR model explains differences in the rate of infection, clearly identifying that 1-7 days delay in the country lockdown would result in even 5 times more infections [5]. As a consequence, the capacity for healthcare may be insufficient and the disease may spread to medical staff and store employees, which will further increase the extent of the epidemic. Therefore the introduction of preventive measures, even very broad and restrictive may prevent a population from health disaster and an elevated number of death cases as a consequence of a shortage in medical equipment. The question is how long such intensive preventive measures should last and when we can depart from strict social isolation, allow business activities and initiate a return to normal functioning. This is a negotiating factor between SARS-CoV-2 spread prevention and economic protection of people and the state. There is no country which may sustain months of lockdown without a threat of deep recession. Based on eSIR model, to prevent a substantial growth of COVID-19 cases Italy should continue lockdown by August 5.

We performed eSIR analysis for Poland using different scenarios of loosening lockdown regulations. The first preventive measures were introduced in Poland on March 12, a week after the first laboratory-confirmed case of COVID-19, when the outbreak was already spread in other European countries, with the particularly dangerous way in Italy. The timetable of a stepped lockdown in Poland is shown in Figure 2. Our model shows that preventive measures slowed down coronavirus spread in Poland in Figure 3 and Table 1. As shown, introducing and maintaining restrictive lockdown slows down the spread of the epidemic but the final effect depends on how long specific preventive measures will continue. On May 18 some precautions have been lifted and according to social observations, Polish change their behavior to further reduce the social distance. Our forecast shows that keeping preventive measures like before May 18 would keep epidemic under strict control with relatively low infectivity per day with the epidemic endpoint in December. However, starting May 18 we estimate that π(t) values will rise to 0.4, 0.6 or 0.8 depending on the social distance reduction resulting from changes in regulations and people’s behaviour. In the event of a significant reduction of precautions, our model shows a very significant increase in a daily number of infections with the peak falling between the end of September and December (Figure 3A-C) and more than 1 million people infected within one year. A significant local increase in the number of new cases was observed in the Silesia region due to coronavirus spread among miners [9]. This shows that some economic sectors and employee groups are particularly vulnerable because of the difficulty or even the inability to observe strict precautions. Our model shows that even slight lifting of preventive measures in Poland starting middle of May will result in an increase of the frequency of infection with peak time on the end of September or later (Figure 3).

Our forecast model was built on limited data availability; on May 22 in Poland was 719 571 tests performed in total since February 29, which is roughly 2% of the population tested. Spatial distribution of infected cases shows the possibility of a local outbreak model. However, there is no spatially fine-grained surveillance data for model tuning. Our model does not include the incubation period and the duration of infectivity. R0 in our forecast for Poland is high and exceeds 4 but is similar to that in Italy according to eSIR model, where R0 is adjusted according to the timetable of prevention [5]. On another hand, our calculated R0 in Poland may be overestimated due to the relatively low number of tests, which were mainly carried out on suspected people.

In conclusion, to our knowledge, this is the first model forecasting COVID-19 spread in Poland concerning the time-line of introduced preventive measures and its anticipated stepped withdrawn. The forecast shows that relatively early introduction of preventive measures in Poland caused a significant reduction in the epidemic rate in comparison with Italy or Spain. However, the future depends mostly on people behavior which is the most difficult factor to control. Loss of selfawareness and a significant reduction in social distance may result in a sharp increase in the daily incidence of SARS-CoV-2 infections and a shortage in a medical care capacity. Our model suggests that relatively rigorous precautions should be maintained in Poland until the end of September to keep the epidemic rate low.