This is a preprint, and has not been peer-reviewed.

Omer Karin¹, Yinon M. Bar-On², Tomer Milo¹, Itay Katzir¹, Avi Mayo¹, Yael Korem¹, Avichai Tendler¹, Boaz Dudovich³, Eran Yashiv⁴, Amos J. Zehavi₅, Nadav Davidovitch⁶, Ron Milo², Uri Alon¹,*

¹Dept. Molecular Cell Biology,²Dept. Plant and Environmental Sciences, Weizmann Institute of Science, Rehovot Israel 76100, ³Applied Materials, Rehovot, Israel, ⁴The Eitan Berglas School of Economics, Tel Aviv University, ₅Dept. of Public Policy and Dept. of Political Sciences, Tel Aviv University, Israel, ⁶Dept. of Health Systems Management, Ben-Gurion University, Beer-Sheva, Israel. OK and YBO equal contributors.

*correspondences to: uri.alon@weizmann.ac.il

Many countries have applied lockdowns that help suppress COVID-19, but with devastating economic consequences. Here we propose exit strategies from lockdown that provide sustainable, albeit reduced, economic activity. We use mathematical models to show that a cyclic schedule of 4-day work and 10-day lockdown, or similar variants, can, in certain conditions, suppress the epidemic while providing part-time employment. The cycle reduces the reproduction number R by a combination of reduced exposure time and an anti-phasing effect in which those infected during work days reach peak infectiousness during lockdown days. The number of work days can be adapted in response to observations. Throughout, full epidemiological measures need to continue including hygiene, physical distancing, compartmentalization and extensive testing and contact tracing. A cyclic exit strategy is a conceptual framework, which, when combined with other interventions to control the epidemic, can offer the beginnings of predictability to many economic sectors.

Current non-pharmaceutical interventions to suppress COVID-19 use testing, contact tracing, physical distancing, mask use, identification of regional outbreaks, compartmentalization down to the neighborhood and company level, and population-level quarantine at home known as lockdown (Flaxman, Mishra, Gandy, Unwin, et al. 2020; Ferguson et al. 2020; C. J. Wang, Ng, and Brook 2020; Chen et al. 2020). The aim is to flatten the infection curve and prevent overload of the medical system until a vaccine becomes available.

Lockdown is currently in place in many countries. It has a large economic and social cost, including unemployment on a massive scale. Once a lockdown has reduced the number of critical cases to a desired goal, a decision must be reached on how to exit it responsibly. The main concern is the risk of resurgence of the epidemic. One strategy proposes reinstating lockdown when a threshold number of critical cases is exceeded in a resurgence, and stopping lockdown again once cases drop below a low threshold (Kissler et al. 2020; Ferguson et al. 2020) (Fig 1A,S1). While such an “adaptive triggering” strategy can prevent healthcare services from becoming overloaded, it leads to economic uncertainty and continues to accumulate cases with each resurgence.

Fig. 1 | Cyclic work-lockdown strategy can control the epidemic, prevent resurgences and offer predictable part-time employment. a) Exit from lockdown carries the risk of resurgence of the epidemic, with need to re-enter prolonged lockdown. b) A cyclic work-lockdown strategy prevents resurgences by keeping the average R<1. It thus allows an earlier exit from lockdown, and provides a clear part-time work schedule. Transmission rates provide R in lockdown and work days of R_L=0.6 and R_W =1.5 respectively.

Here we carefully propose an exit strategy from lockdown that can prevent resurgence of the epidemic while allowing sustained, albeit reduced, economic activity. The strategy can be implemented at a point where lockdown has succeeded in stabilizing the number of daily critical cases to a value that the health system can support. Hereafter when we say ‘lockdown’ we mean population-level quarantine at home, together with all other available interventions such as testing and social distancing.

The basic idea is to keep the effective reproduction number R, defined as the average number of people infected by each infected individual, below 1. When R is below 1, the number of infected people declines exponentially, a basic principle of epidemiology.

To reduce R below 1, we propose a cyclic schedule with k continuous days of work followed by n continuous days of lockdown (see also Bin et al, 2020). As shown below, 4 days of work and 10 days of lockdown is a reasonable cycle that allows a repeating 2-week schedule. Epidemiological measures should be used and improved throughout, including rapid testing, contact isolation and compartmentalization of workplaces and regions. The cyclic strategy can thus be considered as a component of the evolving policy toolkit that can be combined with other interventions.

By “work days” we mean release from lockdown with strict hygiene and physical distancing measures on the same k weekdays for everyone. The nature of the release from lockdown can be tuned. It can include the entire population including schools, except for quarantined infected individuals and people in risk groups who may be in quarantine. More conservatively, it can include workers in selected sectors of the economy. Remote work should be encouraged for sectors that can work from home.

Recently a cyclic strategy called alternating quarantine was proposed in which the population is divided into two sets of households that work on alternating weeks, namely a 7-work:7-lockdown schedule in two shifts (Meidan et al. (2020)). Here we examine this strategy under varying k, i.e. two groups, each with a k-work:(14-k)-lockdown schedule, working in a staggered manner on alternating weeks (Fig 2,Fig S6). The staggered strategy has the advantage that production lines can work throughout the month, and transmission during workdays is reduced due to lower density. The non-staggered strategy has the advantage that lockdown days are easier to enforce.

Fig. 2 | Staggered cyclic work-lockdown strategy in which the population is divided into two groups of households that work on alternating weeks. Shown is I(t) from the SEIR-Erlang deterministic model with mean latent period of 3 days and mean infectious period 4 days (Bar-On et al. 2020). Transmission rates in lockdown and work give R_L=0.6 and R_W =1.5 respectively. Density compensation is φ=1.5 and non-compliance is η=0.1 (see Methods).

The cyclic strategies reduce the mean R by two effects: restriction and antiphasing. The restriction effect is a reduction in the time T that an infectious person is in contact with many others, compared to the situation with no lockdown(Bin et al, 2020). For example, a 4-day work:10-day lockdown cycle reduces T to 2/7 T ≈ 0.3T.

The antiphasing effect uses the timescales of the virus against itself (Fig. 3). Most infected people are close to peak infectiousness for about 3–5 days, beginning ≈3 days after being exposed (Li et al. 2020; He et al. 2020). A proper work-lockdown cycle, such as a 4-work:10-lockdown schedule, allows most of those infected during work days to reach maximal infectiousness during lockdown, and thus avoid infecting many others. Those with symptoms can be infectious for longer (He et al. 2020), but remain hospitalized, isolated or (self-)quarantined along with their household members, preventing secondary infections outside the household.

The staggered strategy also reduces transmission by virtue of reduced density during work days (Methods).

Fig. 3 | The cyclic exit strategy is aided by placing peak infectiousness in the lockdown days. SARS-CoV-2 has an average latent (non-infectious) period of about 3 days. A 14-day cycle in which people enter lockdown after 3 or 4 work days benefits from this property. Even those infected on the first day of work spend most of their latent period at work and reach peak infectiousness during lockdown. This reduces the number of secondary infections.

The cyclic strategy can be synergistically combined with rapid testing and contact isolation. Household-level testing at the end of the lockdown period and before return to work or school can help shorten infection chains.

Simulations using a variety of epidemiological models, including SEIR models and stochastic network-based simulations, show that a cyclic strategy can suppress the epidemic provided that the lockdown is effective enough (Fig. 4, Table 1). A 4–10 cycle seems to work well for a range of parameters and is robust to uncertainties in the model (Fig. S2, S3).

The transmission parameters during work days and lockdown days can be described by the effective replication numbers that describe extended periods of work and lockdown conditions, R_W and R_L, respectively. Lockdown need only be as strong as that achieved in most European countries, with R_L=0.6–0.8 (Imperial college, 2020)(Salje, et al 2020) in order to support a cyclic strategy with 4 work days, when measures are enforced during workdays providing R_W=1.5 (Table 1). If lockdown is as strong as in some Chinese cities, with estimated R_L~0.3 (C. Wang et al. 2020)(Leung et al, 2020), the same work-day R_W can support up to 7–8 work days per two week cycle (Fig S3); in this case, a 4 workday cycle can suppress the epidemic even if workday R_W is as large as in the early days of the epidemic in Europe, R_W=3–4 (Flaxman, Mishra, Gandy, and Others 2020). Ideally, measures will eventually bring down R during workdays below 1, as in South Korea’s control of the epidemic in early 2020, making lockdown unnecessary.

Fig. 4 | Cyclic strategy with k workdays and 14-k lockdown days controls the epidemic for a range of effective replication numbers at work and lockdown. Each region shows the maximal number of work days in a 14-day cycle that provide decline of the epidemic. Simulation used a SEIR-Erlang deterministic model with mean latent period of 3 days and infectious periods of 4 days. Results are robust to uncertainty in model parameters (Fig S2).

Table 1. Effective replication numbers for a 4–10 cyclic strategy in several scenarios. R_W and R_L are the replication numbers that would be observed in continuous periods of work and lockdown, respectively.

An important consideration is that the cyclic strategy is adaptive, and can be tuned when conditions change and the effects of the approach are monitored.

For example, weather conditions may affect R (Kissler et al. 2020), as well as advances in regional monitoring and case tracing. If one detects, for example, that a 4:10 strategy leads to an increasing trend in cases, one can shift to a cycle with fewer work days. Conversely, if a strong decreasing trend is observed, one can shift to more work days and gain economic benefit (Fig 5). In certain scenarios, 7 days of work or more in two weeks can be achieved (Fig S3,S8). Generally, small changes in work and knockdown transmission (R_W and R_L) have only a mild effect on the average R in the cyclic strategy , as shown in Fig S7.

Fig. 5 | The cyclic strategy can be tuned according to the trends in case numbers over weeks. (a) If average R is above 1, cases will show a rising trend, and number of work days in the cycle can be reduced to achieve control. (b) Number of work days per cycle can be increased when control meets a desired health goal.

Measures will be required during the work days to ensure that people do not excessively compensate for the lockdown periods by having so many more social connections that R is significantly increased. This may include sound epidemiological measures such as the continuation of banning large social events and clear communication campaigns by the health authorities to enhance adherence to hygiene and physical distancing. Extensive rapid testing and contact tracing should be developed and extended in parallel (Linnarsson 2020).

The economic benefits of a cyclic strategy include part-time employment to millions who have been put on leave without pay or who have lost their jobs. This mitigates massive unemployment and business bankruptcy during lockdown. Prolonged unemployment during lockdown and the recession that is expected to follow can reduce worker skill (Krebs 2007; Edin and Gustavsson 2008; Davis and von Wachter 2011; Schmieder, von Wachter, and Bender 2016; Carlsson-Szlezak, Reeves, and Swartz 2020) and carries major societal drawbacks (Nichols, Mitchell, and Lindner 2013). Unemployment also has detrimental health effects which include exacerbation of existing physical and mental illnesses. High levels of unemployment have been associated with increases in morbidity and mortality (Roelfs et al. 2011).

The cyclic strategy offers a measure of economic predictability, potentially enhancing consumer and investor confidence in the economy which is essential for growth and recovery (Akerlof and Shiller 2010; Keynes 2018). It can also be equitable and transparent in terms of who gets to exit lockdown.

For these reasons, a cyclic strategy can be maintained for far longer than continuous lockdown. This allows time for developing a vaccine, treatment, effective testing and buildup of herd immunity without overwhelming health care capacity.

The cyclic strategy does not seem to have a long-term cost in terms of COVID-19 cases compared to a start-stop lockdown policy triggered by resurgences. Comparing the two strategies shows that in the mid-term and long term, the start-stop strategy accumulates more cases due to resurgences (Fig. 5). This does not depend heavily on parameters: the fundamental reason is that new cases arise during each resurgence. Thus, a strategy that restarts lockdown with every resurgence uses feedback to effectively keep average R close to 1, and continues to accumulate cases. In contrast, the cyclic strategy keeps average R below one, and thus prevents resurgences.

Fig. 6 | The cumulative number of cases under a cyclic strategy is lower at long times than in a strategy that restarts lockdown when the epidemic re-surges. Cumulative number of cases is shown for the simulations of Fig 1a (red) and Fig1b (blue). Even though exit from lockdown occurred earlier in the cyclic strategy case, the cumulative number of cases associated with this strategy is lower in the long term than the accumulated cases when lockdown is released and then restarted once the epidemic re-surges. The relative benefit of the cyclic strategy is further increased by considering non-COVID-19-related health consequences of extended lockdown during resurgences, prevented by the cyclic strategy.

The cyclic strategy can apply at many scales: to a company, a school, a town or an entire country. Regions or organizations that adopt this strategy are predicted to resist infections from the outside. An infection entering from the outside cannot spread widely because average R<1. After enough time, if this is applied globally, there is even a possibility for the epidemic to be eradicated, in the absence of mutations or unknown reservoirs.

The cyclic strategy can work in regions with insufficient testing capacity, as long as the lockdown phases provide low enough transmission. This may apply to a large part of the earth’s population.

On April 24, Reuters reported that Austria will use a variant of the staggered cyclic strategy to reopen its schools on May 18, 2020, with two groups attending school 5 days every two weeks (Reuters,2020). Mexico city has announced a 4:10 cycle starting June 15. Several companies have adopted similar strategies.

The cyclic strategy has several caveats. It can not suppress the epidemic if the reproduction number during lockdown days is larger than one. The strategy also depends on the assumption that transmission is, on average, nearly proportional to exposure time (Methods), whereas in reality a fraction of transmissions may be very rapid. Avoiding large events with high rapid transmission potential is thus important. Since many unknowns remain for modelling this epidemic, careful monitoring is required to see if the strategy is working (as in Fig 5).

With these considerations in mind, a cyclic strategy can serve as a less risky step than full reopening of the economy and can thus be tried earlier to minimize damage caused by lockdown. The exact nature of the intervention must be tuned to optimize economy and minimize infection. The cyclic strategy can be synergistically combined with other approaches to suppress the epidemic. The general message is that we can tune lockdown exit strategies to balance the health pandemic and the economic crisis.

Methods:

SEIR model: The deterministic SEIR model is dS /dt=-βSI, dE /dt=βSI-σE, dI / dt=σE-γI, where S,E and I are the susceptible, exposed (noninfectious) and infectious fractions. Reference parameters for COVID-19 (Bar-On et al. 2020) are σ=0.33/day; γ=0.25/day , and S=1 is used to model situations far from herd immunity. The values used for β are defined in each plot where R=β/γ. The analytical solution for cyclic strategies is in (SI).

SEIR-Erlang model: The SEIR model describes an exponential distribution of the lifetimes of the exposed and infectious compartments. In reality these distributions show a mode near the mean. To describe this, we split E and I into two artificial serial compartments each with half the mean lifetime of the original compartment (Champredon, Dushoff, and Earn 2018). This describes Erlang-distributed lifetimes (the distribution of the sum of two exponentially distributed random variables) with the same mean transition rates as the original SEIR model. Thus, dS/dt=-βSI, dE₁/dt=βSI-2σE₁, dE₂ /dt=2σE₁–2σE₂, dI₁ /dt=2σE₂–2γI₁, dI₂ /dt=2γI₁ -2γI₂ , where I=I₁ +I₂ , and R=β/γ . In the figures we used a worst-case assumption of no herd immunity, namely S~1. Herd immunity further reduces case numbers. Case numbers are in arbitrary units, and can describe large or small outbreaks. The deterministic simulation describes a fully-mixed population. Population structure typically reduces overall outbreak peak size (House and Keeling 2011) compared to a fully mixed situation with the same mean transmission rate, but includes the possibility of high attack rates in certain sub-populations. For example, a stochastic simulation on a network shows a larger range of conditions for a cyclic strategy to work than in a deterministic model (compare Fig 4 and Fig S5),

Staggered cyclic strategy, SEIR-Erlang model: We model two groups, A and B, with a susceptible, exposed and infectious compartment for each group. The SEIR-Erlang model for group A is:

dS_A,1/dt = -f_A(S_A,I_A,t)

dE_A,1/dt =f_A(S_A,I_A,t) — 2σE_A,1

dE_A2/dt = 2σ(E_A,1- E_A,2)

dI_A1/dt = 2σE_A,2–2γI_A,1

dI_A2/dt = 2γ(I_A,1- I_A,2)

I_A=I_A,1+I_A,2

with analogous equations for group B. We assume that each group consists of half of the population. This causes density at work to be reduced (Barzel, et al, 2020). For ease of comparison to the non-staggered case, we refer to the replication numbers of a single fully mixed population with a cyclic strategy, namely R=R_W on work days and R=R_L during lockdown. In the staggered case, during lockdown, as opposed to work, individuals from a group interact primarily with their own household. The density in the household is not affected by dividing the population into two staggered work groups. Hence, the effective R remains R_L.

f_A(S_A, I_A, t=A lockdown day)=2 R_L S_A I_A

Where the factor of 2 normalizes S_A=0.5. During work days, we can estimate the number of transmissions at work and not at home by R_W-R_L. This gives the following equation:

f_A(S_A,I_A,t=A work day)=(2 R_L+(R_W-R_L))S_A I_A

With analogous equations for group B.

We next model cross-transmission between the groups. Due to the expected difficulty of enforcing a staggered work schedule as compared to a non-staggered cycle strategy, we assume a leakage term due to a fraction of individuals from each group that does not adhere to their lockdown. These non-adheres instead interact with the other group during the other groups’ work days.

When group B is in lockdown, infectious non-adherers from group B can infect individuals from group A who are in their work days. This rate is modeled as proportional to the replication number for people infected at work and not at home, R_W-R_L:

f_A(S_A,I_A,t=A work day, B lockdown day)=(2 R_L+(R_W-R_L))γ S_A I_A+η(R_W-R_L)γ S_A I_B

When individuals from group A are in lockdown and non-adhere, they can be infected from individuals from group B on group B work days. We also add a higher-order term for susceptible non-adherent individuals from group A that meet non-adherent infectious individuals from group A during group A lockdown:

f_A(S_A , I_A, t=A lockdown day, B work day)=2 R_L γ S_A I_A+η (R_W-R_L) γ S_A I_B+2 η² (R_W-R_L) γ S_A I_A

When both groups are in lockdown at the same time, there are only higher order terms for cross transmission:

f_A(S_A , I_A, t=A lockdown day, B lockdown day)=2 R_L γ S_A I_A+2 η² (R_W-R_L) γ S_A I_B+2 η² (R_W-R_L) γ S_AI_A

Note that for complete leakage η=1 and under symmetry assumptions I_A=I_B, the equations become identical to the case of a single fully mixed population:

f_A(S_A, I_A, S_B, I_B, t=A work day)=2 R_W γ S_A I_A

f_A(S_A, I_A, S_B, I_B, t=A lockdown day)=2 R_L γ S_A I_A

So far, we assumed that density at work is half that of the non-staggered case. However, in practice, compensatory mechanisms might lead to a higher effective density. For example, people might cluster to maintain a level of social interaction, or certain work-day situations may require a fixed density of individuals. These effects can be modeled by adding a density compensation parameter φ which re-scales the work-day infection rate. This number is φ=2 for complete compensation of transmission where density at work is not affected by partitioning, or φ=1 is the staggered model above with half the density at work. We obtain the following equations:

f_A(S_A,I_A,t=A work day, B lockdown day)=(2 R_L+φ(R_W-R_L))γ S_A I_A+ηφ(R_W-R_L) γ S_A I_B

f_A(S_A , I_A, t=A lockdown day, B lockdown day)=2 R_L γ S_A I_A+2 η² φ(R_W-R_L) γ S_A I_B+2 η² φ(R_W-R_L) γ S_AI_A

With analogous equations for group B.

Stochastic SEIR model on social networks with epidemiological measures: We also simulated a stochastic SEIR process on social contact networks. Each node i represents an individual and can be in a susceptible, exposed, infected or removed state (i.e. quarantined, recovered or dead). Lifetime in the E and I states is drawn from an Erlang distribution with means TE and TI. The total transmission rate of a node i is drawn from a long tailed distribution to account for super-spreaders. The probability of infection per social link j, q_ij, is set either constant for all links connected to node i or drawn from an exponential distribution to account for heterogeneity in infection rates. Node states are updated at each time step. Network models include Erdos-Renyi and small world networks. During lockdown, a fraction of the links are inactivated (same links for each lockdown phase).

Linearity of transmission risk with exposure time: In order for restriction of exposure time to be effective, probability of infection must drop appreciably when exposure time is reduced. This requires a low average infection probability per unit time per social contact, q, so that probability of infection, p=1-exp(-qT), does not come close to 1 for exposure time T on the order of days. For COVID-19, an infected person infects on the order of R=3 people on average during the infectious period of mean duration D=4 days. If the mean number of social contacts is C, which is estimated at greater than 10, one has q~DR/C<0.1/day. Thus infection probability on the scale of hours to a few days is approximately linear with exposure time: 1-exp(-qT)~ qT. This is consistent with the observation that infected people do not typically infect their entire household, with attack rates on the order of 0.1–0.3 (Bi at al., 2020, Jing et al., 2020, Liu et al.,2020, Wang et al., 2020). It also matches linearity observed in influenza transmission (Cui et al. 2011). We also tested a scenario using network models in which some contacts have much higher q than others (exponentially distributed q between links). A mildly lower R in lockdown is required to provide a given benefit of the cyclic strategy than when q is the same for all links.

An economic perspective on the cyclic exit strategy is available here:

https://medium.com/@urialonw/economic-perspective-on-the-cyclic-exit-strategy-for-covid-19-b70aa0ff1a13

Fig. S1: Reinstating lockdown based on case number threshold leads to uncertainty in the timing of new lockdown. SEIR-Erlang model simulation showing the initial growth phase of an epidemic in the first two weeks, triggering a lockdown of 7 weeks. Lockdown is reinstated once a threshold of cases is exceeded. We show three scenarios with different effective reproduction numbers after lockdown is first lifted (R_W=1.4, R_W=2.0 and R_W=2.8), leading to a wide distribution of the time at which the case threshold is crossed and lockdown is reinstated.

Fig S2. The cyclic strategy is insensitive to variations in the model parameters. The SEIR-Erlang model has two free parameters, the lifetimes of the latent and infectious periods, given by T_E=1/σ and T_I=1/γ. The reference parameters used in the main text are T_E=3 days, and T_I=4 days based on the COVID-19 literature (Bar-On et al. 2020). The panels show the regions in which effective R<1 with (A) T_E=3d and T_I=2d, (B) T_E=1.5d and T_I=4d, (c ) T_E=1.5d and T_I=2d, (D) T_E=3d and T_I=6d, (E) T_E=4.5 d and T_I=4d, and (F) T_I=6d, T_E=4.5 d. These and similar parameter variations make small differences to the phase plots.

Fig. S3 A SIR deterministic model captures some of the effects. The SIR model (right panel) lacks the exposed (non-infectious) compartment. It shows that the cyclic lockdown strategies can control the epidemic, but at smaller parameter regions for each given strategy than the SEIR-Erlang model (left panel). The difference is biggest at large ratios of R at work and lockdown, where SEIR-Erlang has an advantage. The SIR model is dS/dt=-SI,dI/dt=SI-I. The replication number is R=β/γ . The value of γ does not affect this plot. We used S=1. Effective R in the SIR model is the average R weighted by the fraction of time for work and lockdown. For analytical work on optimal epidemic control in the SIR model see [https://osf.io/rq5ct/]. In the large panel, the regions for cyclic startegies with k=1 to k=9 work days in two weeks are shown. Note that the axes in this plot are inverted with respect to Fig 3.

Fig. S4 Stochastic simulation of a 4-work-10-lockdown cyclic strategy using a SEIR process simulated on a contact network. Infected nodes versus time from a simulation run using the SEIRSplus package from the Bergstrom lab, https://github.com/ryansmcgee/seirsplus. Contact network has a power-law-like degree distribution with two exponential tails, with mean degree of 15, N=10⁴ nodes, sigma=gamma=1/3.5 days, beta=0.95 till day 14, lockdown beta=0.5 with mean degree 2 (same edges removed every lockdown period), work day beta=0.7. Probability of meeting a non-adjacent node randomly at each time-step instead of a neighbor node is p=1 before day 14, in lockdown p=0, workday p=0.3. Testing is modeled to quarantine 1% of infected nodes per day, with no contact tracing. Shaded regions are lockdown periods, light gray regions are workdays. Initial conditions were 10 exposed and 10 infected nodes.

Fig S5. A stochastic simulation on a small-world network shows an expanded range in which the epidemic is controlled by a cyclic strategy. A custom simulator uses a stochastic SEIR process on a social network . The social network is small-world with with N=104 , mean degree C=16 and fraction of long-range connections p=1-R_L /R_W. Time-steps are one day. In work days transmission occurs along edges, with probability q_W=R_W /(C T_I). In lockdown days, the long range links of each node are inactivated (the same links are inactivated every day), with remaining links signifying the household. Transitions between exposed, infectious and removed states are determined by Erlang (shape=2) distributed times determined for each node at the beginning of the simulation.

Fig S6. Staggered cyclic strategies control the epidemic for various degrees of density compensation and non-compliance. Each region shows the maximal number of work days in a 14-day cycle that provide decline of the epidemic. Simulation used a SEIR-Erlang deterministic model with mean latent period of 3 days and infectious periods of 4 days. Density compensation φ and non-compliance (cross transmission) η parameters were as follows: (a) φ=1,η=0.1 (b) φ=1.5,η=0.1 (c) φ=1,η=0.3 (d) φ=1.5,η=0.3. Code can be found at https://github.com/omerka-weizmann/2_day_workweek.

Fig S7. The effective reproduction number Re for different work:lockdown cycles. The Re values are computed by the SEIR-Erlang deterministic model with parameters of Fig 1b. Note that Re changes gradually, so that even if R_W and R_L change slightly, the effects on Re are mild.

Fig S8. Effective reproduction number grows with the number of work days in a two week period. It declines with stringency of work-day measures (lower R_W). Form SEIR-Erlang simulations with parameters of Fig 1b.

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