key: cord-0288537-cammib0l
authors: Zielinski, J.; Gruziel-Słomka, M.; Nowosielski, J. M.; Bartczuk, R. P.; Niedzielewski, K.; Semeniuk, M.; Gorski, Łukasz; Kisielewski, J.; Moszynski, A.; Radwan, M.; Kaczorek, A.; Rakowski, F.
title: The efficiency of dynamic regional lockdown approach in controlling the COVID-19 epidemic. Insights from the agent-based epidemiological model for Poland
date: 2021-09-12
journal: nan
DOI: 10.1101/2021.09.06.21263031
sha: 8b0c8aa44a1fb561f5d7559f4b418f00079bdf6f
doc_id: 288537
cord_uid: cammib0l

In this work properties of the dynamic regional lockdown approach to suppress the COVID-19 epidemic spread in Poland were investigated. In particular, an agent based model was used with the aim to indicate an optimal lockdown strategy, defined here as the one which minimizes mean lockdown time over regional unit provided health service is not overwhelmed. With this approach the lockdown extent was also considered by varying restrictions between complete regional school closure and/or significant social distancing in semi-public spaces. In result, a cooperative effect was discovered in the case when closure of schools was accompanied by severe restrictions of social contacts in semi-public spaces. Moreover, the regional lockdown approach implemented here on the level of counties (units of population around 100k) proofed to be successful, that is allowed to identify optimal entrance and release thresholds for lockdown. The authors believe that until significant portion of population is vaccinated such a strategy might be applied.

The COVID-19 epidemic, which probably started at the turn of 2019 and 2020, unfortunately does not end. Although there are 17 a few approved vaccines, vaccine supply remains an unresolved challenge. Moreover, some people refuse to be vaccinated for 18 various reasons. Due to the high infectivity of the SARS-CoV-2 virus and a large percentage of people with asymptomatic 19 course of illness (and therefore difficult to detect), the effective suppression of the disease requires use of drastic solutions, such 20 as lockdown or common quarantines. The consequences of these actions are dramatic for the economy, and it seems that many 21 countries will not be able to re-apply full lockdown due to the economic consequences. 22 It is therefore essential to look for the solutions that can help suppress the epidemic while reducing negative social effects. 23 It seems that most countries will have to implement some form of smart lockdowns -they must be strong enough to prevent 24 a sharp increase in number of infections, and weak enough not to cause a significant increase of unemployment. One of the 25 proposed solutions is a regional dynamic lockdown strategy. In essence, it comes down to the application of strong restrictions 26 in regions particularly strongly affected by the pandemic. After the number of infected decreases, restrictions should be relaxed 27 in a given region. 28 To assess the impact of the applied restrictions, and to understand the epidemic scenarios themselves, several typical 88 indices will be used, see Figure 1 . Crucial parameters for our purpose are those that directly describe the burden of epidemic 89 either on health system service -e.g. the interval when majority of available ICU beds are occupied or economy -e.g. the 90 length of the lockdown interval. An attack rate does not seem to be an essential criterion for decision making on lockdown 91 introduction, taking into account that majority of cases are asymptomatic or have a mild course of infection. However, it carries 92 the information on the level of immunity in the society, assuming the recovered agents become immune. Example results -from simulation with entrance and release threshold values equal 12 and 10, respectivelydescribing the indices used in this paper: the attack rate during the first semester, the first wave, or the entire school year, Figure 1a ; the interval over which the demand for ICU beds exceeded 90% of the supply, Figure 1b ; the interval of the first wave defined via R e f f , Figure 1c ; the interval of a full -countrywide -lockdown, Figure 1d . The vertical, dashed lines mark the start (black, dashed) or the ends of certain intervals described in the legend of Figure 1a The impact of lockdown entrance threshold 94 In this section, we consider the effect of lockdown entrance threshold (LET) on ICU overload time, and attack rate.

The attack rate till Dec., 3rd (see Figure 2a ) strongly depends on LET for simulations with school closure applied (diamonds) 96 or with school closure accompanied by restriction imposed on public spaces (squares). On the other hand, it weakly depends on 97 LET for simulations with public spaces restricted (circles). One can observe almost 4-fold increase in the attack rate between 98 simulations with LET 2 and 24 and both contexts restricted, and about 2.5-fold increase in simulations with only schools closed.

Clearly, the higher the lockdown entrance threshold value, the later lockdown is reached. This applies to both individual 100 counties, and countrywide lockdown -the state in which the entry threshold has been exceeded in all counties. What may 101 seem a bit surprising, the difference in the time of reaching the national lockdown for LET = 4 and LET = 24 is only 3 weeks, 102 regardless of the strength of the lockdown, see Figure 2b . This is a consequence of the exponential nature of the epidemic and 103 its suppression by regional lockdowns. However, for a very high entry threshold, national lockdown may occur later than the 104 ICU overcapacity. This would lead to mass deaths due to lack of available care. Thus, the introduction of a strong national 105 lockdown would be almost certain, regardless of earlier assumptions made by the government.

As one can see, closing of schools reduces the number of infections much more than closing of the street context (public 107 places). This is due to the large number of households in Poland where three generations live together. This means that children 108 who are infected at school and often pass infection asymptomatically, infect a significant number of household members. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. dependent. However, the relationship between attack rate and LET should be universal. The higher the LET, the higher the 114 attack rate. Furthermore the stronger the lockdown is, the more attack rate depends on the LET. 

and R e f f (t) for LET=LRT (middle).

As one may notice (see Figure 3 ), both LET and LRT strongly influence the times of the beginning and end of successive 122 waves of epidemics. A stronger lockdown means a greater risk of next epidemic waves coming soon. Someone might consider 123 this a disadvantage of strong lockdown or an advantage of a weak one. However, this is an apparent benefit resulting from the 124 ineffectiveness of a weak lockdown. Weak lockdown, as well as its absence, lead to a high R e f f value, long first wave and a 125 large number of infections in short time, and thus unacceptably many deaths.

As one can see, in the case of a strong lockdown, especially for a high LET value, the occurrence times of subsequent 127 4/11

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The copyright holder for this this version posted September 12, 2021. ; https://doi.org/10.1101/2021.09.06.21263031 doi: medRxiv preprint epidemic waves strongly depend on the LRT. This means that the times when the first wave ends, and the next waves occur depend on government decisions. On the other hand, governments have no influence on the starting time of the first wave. 129 Moreover, as shown in the previous section, the choice of particular LET can shift the beginning of the first lockdown just by 130 few weeks.

Searching for an optimal lockdown strategy. 132 In many countries, completely different lockdown strategies have been chosen, which means that choosing the optimal one is 133 not easy. On the one hand, we all know that too long lockdowns are socially unacceptable. On the other hand, the capacity of 134 health systems must not be exceeded. These needs seem contradictory.

In order to find the optimal lockdown strategy, we ran the model with different LET and LRT threshold values. The simulation 136 results are presented on Fig. 4 . As one can see, in the case of a weak lockdown (just closing public places or schools only, see means that some poviats will have to apply a repeated, short lockdown. The cost seems low.

More detailed analysis of lockdowns 148 An important feature of the proposed scheme is the regionalization of lockdowns, as it allow to prevent the introduction of civil 149 restrictions where and when they are not not necessary. Therefore, the transition of regional lockdowns into a countrywide . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Brazil shows the scale of the vaccine shortage. Therefore, for many countries, a different, realistic strategy is needed.

For economic and social reasons, governments are defending themselves against ordering strong and long lockdowns. It is 169 obvious to most people that the more costly (economically and socially) lockdown is, the more effective it is. So a dilemma 170 arises whether to sacrifice people's lives or the economy and, among others, the psyche of children. In this study we have shown 171 that a possible strong, regional and short lockdown allows governments to avoid the above dilemma. Strong lockdown, even if 172 it does not eradicate the epidemic, may suppress it enough to allow for the lockdown release. Of course, a strong lockdown 173 itself has many unpleasant consequences. Therefore, it is crucial to avoid introducing lockdowns when and where they are not 174 necessary. Therefore, they should be introduced and lifted at the appropriate moment and only in parts of the country where it 175 is necessary. In our opinion, the strategy is the optimal method of epidemic management until the population is vaccinated.

This section briefly describes the agent-based model used in this paper.

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The results presented in this work were obtained with the usage of an agent based model. Initially, the model was developed to 180 explain influenza epidemic in Poland 1 . Similarly to influenza, Covid-19 is an infectious airborne disease. In order to adapt the 181 model for simulation of the Covid-19 epidemic spread a number of modifications, and new features were introduced.

Epidemic spread takes place within the virtual society of Poland 16 . The virtual society consists of 36 million geo-referenced software agents. Agents meet in various contexts where they can contract the disease. Each agent is assigned to exactly one geo-referenced household context. A workplace, a preschool, a school, a university, a large university, a street, and a travel are the other context categories present in the model. Contexts are characterised by contacting rates (CRs), which are model parameters. One can therefore model the imposing and lifting of governmental restrictions by changing the CRs. Every agent attends contexts he/she belongs to, and after a full day the probability of infection for each susceptible agent is calculated. The probability, expressed simply as: 

The first important extension of the model is the introduction of asymptomatic infected agents. The motivation is to take into account COVID-19 cases which do not exhibit any (obvious) symptoms of the disease for the whole course of the infection. We assume that infectiousness of an asymptomatic agent is multiplied by parameter a (i.e. a = 0.1) with respect to a symptomatic agent. The proportion of asymptomatic and symptomatic agents varies across agents age category. With the above, the context infectivities become:

where c stands for a household, a workplace, a preschool, a school, a university, a large university, a street, or a travel. For a household, the f parameter is assumed to be 1. The total infectivity, I, that enters the Eq. 1 is just:

where w c are the contacting rates within a given context, and the sum goes over all the contexts a given agent visited/attended 188 during a given day. Table 1 variable. It represents the isolation and quarantine enforced by the state authorities in contrary to coefficient f which is related Table 1 .

L A S HNI HPI HI D R 4 7 5 10 13 7 ∞ ∞ Table 2 Model calibration 217 The were open in real life was necessary to determine CRs of the schools context).

The final values of CR multipliers are listed in Table 3 . Table 3 Supplementary materials 250 To show how the epidemic is spreading across the country, we present an example animation. It is a visualization of lock down 251 counties for example thresholds LET = LRT = 12. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. 

Additional information 305 Competing interests (mandatory statement).

Authors have no competing interests as defined by Nature Research, or other interests that might be perceived to influence 307 the interpretation of the article. 308

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