Many countries have applied lockdown that helped 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. We do not call for immediate adoption of this policy, but rather to consider it as 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 (NPI) 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 ( 1 -4 ) . 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 ( 2 , 5 ) ( 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.

Stress activates a complex network of hormones known as the hypothalamic-pituitary-adrenal (HPA) axis. The HPA axis is dysregulated in chronic stress and psychiatric disorders, but the origin of this dysregulation is unclear and cannot be explained by current HPA models. To address this, we developed a mathematical model for the HPA axis that incorporates changes in the total functional mass of the HPA hormone-secreting glands. The mass changes are caused by HPA hormones which act as growth factors for the glands in the axis. We find that the HPA axis shows the property of dynamical compensation, where gland masses adjust over weeks to buffer variation in physiological parameters. These mass changes explain the experimental findings on dysregulation of cortisol and ACTH dynamics in alcoholism, anorexia, and postpartum. Dysregulation occurs for a wide range of parameters and is exacerbated by impaired glucocorticoid receptor (GR) feedback, providing an explanation for the implication of GR in mood disorders. These findings suggest that gland-mass dynamics may play an important role in the pathophysiology of stress-related disorders.

Hormones control the major biological functions of stress response, growth, metabolism, and reproduction. In animals, these hormones show pronounced seasonality, with different set-points for different seasons. In humans, the seasonality of these hormones remains unclear, due to a lack of datasets large enough to discern common patterns and cover all hormones. Here, we analyze an Israeli health record on 46 million person-years, including millions of hormone blood tests. We find clear seasonal patterns: The effector hormones peak in winter−spring, whereas most of their upstream regulating pituitary hormones peak only months later, in summer. This delay of months is unexpected because known delays in the hormone circuits last hours. We explain the precise delays and amplitudes by proposing and testing a mechanism for the circannual clock: The gland masses grow with a timescale of months due to trophic effects of the hormones, generating a feedback circuit with a natural frequency of about a year that can entrain to the seasons. Thus, humans may show coordinated seasonal set-points with a winter−spring peak in the growth, stress, metabolism, and reproduction axes.

Summary Cortisol is a major human stress hormone, secreted within minutes of acute stress. Cortisol also has slower patterns of variation: a strong circadian rhythm and a seasonal rhythm. However, longitudinal cortisol dynamics in healthy individuals over timescales of months has rarely been studied. Here, we measured longitudinal cortisol in 55 healthy participants using 12 cm of hair, which provides a retrospective measurement over one year. Individuals showed (non-seasonal) fluctuations averaging about 22% around their baseline. Fourier analysis reveals dominant slow frequencies with periods of months to a year. These frequencies can be explained by a mathematical model of the hormonal cascade that controls cortisol, the HPA axis, when including the slow timescales of tissue turnover of the glands. Measuring these dynamics is important for understanding disorders in which cortisol secretion is impaired over months, such as mood disorders, and to test models of cortisol feedback control.

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Hormones control the major biological functions of stress response, growth, metabolism and reproduction. In animals these hormones show pronounced seasonality, with different set-points for different seasons. In humans, the seasonality of these hormones remains unclear, due to a lack of datasets large enough to discern common patterns and cover all hormones. Here, we analyze an Israeli health record on 46 million person-years, including millions of hormone blood tests. We find clear seasonal patterns: the effector hormones peak in winter-spring, whereas most of their upstream regulating pituitary hormones peak only months later, in summer. This delay of months is unexpected because known delays in the hormone circuits last hours. We explain the precise delays and amplitudes by proposing and testing a mechanism for the circannual clock: the gland masses grow with a timescale of months due to trophic effects of the hormones, generating a feedback circuit with a natural frequency of about a year that can entrain to the seasons. Thus, humans may show coordinated seasonal set-points with a winter-spring peak in the growth, stress, metabolism and reproduction axes.

11Stress activates a complex network of hormones known as the Hypothalamic-Pituitary-Adrenal 12 (HPA) axis. The HPA axis is dysregulated in chronic stress and psychiatric disorders, but the 13 origin of this dysregulation is unclear and cannot be explained by current HPA models. To 14 address this, we developed a new mathematical model for the HPA axis that incorporates 15 changes in the total functional mass of the HPA hormone-secreting glands. The mass changes 16 are caused by the HPA hormones which act as growth factors for the glands in the axis. We 17find that the HPA axis shows the property of dynamical compensation, where gland masses 18 adjust over weeks to buffer variation in physiological parameters. These mass changes explain 19 the experimental findings on dysregulation of cortisol and ACTH dynamics in alcoholism, 20 anorexia and postpartum. Dysregulation occurs for a wide range of parameters, and is 21 exacerbated by impaired glucocorticoid receptor (GR) feedback, providing an explanation for 22 the implication of GR in mood disorders. These findings suggest that gland-mass dynamics 23 may play an important role in the pathophysiology of stress-related disorders. 24 25 Author Summary 26The HPA axis is a neuroendocrine axis that is activated in response to stressors. The classical 27 description of this axis includes three hormones that act in a cascade, with the final hormone 28 cortisol inhibiting the two upstream hormones, ACTH and CRH. This classical picture has 29 timescales of hours due to hormone half-lives, and cannot explain phenomena on the scale of 30 weeks to months associated with this axis, such as the dysregulation observed in depression, 31 alcohol addiction, postpartum, and other conditions. Here, we use a minimal-model approach 32to add to the classical model two known interactions in which CRH and ACTH not only 33 regulate downstream hormones, but also act as growth factors for the cells that secrete these 34hormones. This creates a physiological circuit that can maintain total cell mass and buffer 35 parameter changes. It has a fragility in which after prolonged stress, the total cell functional 36 masses grow and take weeks to return to baseline. This is sufficient to explain the specific 37 dynamics of hormone dysregulation found in several contexts. It also quantifies the effect of 38 the cortisol (glucocorticoid) receptor on resilience to prolonged stress. Our findings suggest 39 that interactions between hormones and cell functional mass may play an important role in 40 HPA axis regulation on the timescale of weeks to months. 41 42 43 44