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      Exact properties of SIQR model for COVID-19

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      Physica a
      Elsevier B.V.

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          Abstract

          The SIQR model is reformulated where compartments for infected and quarantined are redefined so as to be appropriate to COVID-19, and exact properties of the model are presented. It is shown that the maximum number of infected at large depends strongly on the quarantine rate and that the quarantine measure is more effective than the lockdown measure in controlling the pandemic. The peak of the number of quarantined patients is shown to appear some time later than the time that the number of infected becomes maximum. On the basis of the expected utility theory, a theoretical framework to find out an optimum strategy in the space of lockdown measure and quarantine measure is proposed for minimizing the maximum number of infected and for controlling the outbreak of pandemic at its early stage.

          Highlights

          • Exact properties of the SIQR model appropriate to COVID-19 are obtained.

          • The peak of quarantined patients appears some time later than the peak of infected.

          • A theory is given to find out an optimum strategy to control COVID-19.

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          Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID19 mortality and healthcare demand

          The global impact of COVID-19 has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 H1N1 influenza pandemic. Here we present the results of epidemiological modelling which has informed policymaking in the UK and other countries in recent weeks. In the absence of a COVID-19 vaccine, we assess the potential role of a number of public health measures – so-called non-pharmaceutical interventions (NPIs) – aimed at reducing contact rates in the population and thereby reducing transmission of the virus. In the results presented here, we apply a previously published microsimulation model to two countries: the UK (Great Britain specifically) and the US. We conclude that the effectiveness of any one intervention in isolation is likely to be limited, requiring multiple interventions to be combined to have a substantial impact on transmission. Two fundamental strategies are possible: (a) mitigation, which focuses on slowing but not necessarily stopping epidemic spread – reducing peak healthcare demand while protecting those most at risk of severe disease from infection, and (b) suppression, which aims to reverse epidemic growth, reducing case numbers to low levels and maintaining that situation indefinitely. Each policy has major challenges. We find that that optimal mitigation policies (combining home isolation of suspect cases, home quarantine of those living in the same household as suspect cases, and social distancing of the elderly and others at most risk of severe disease) might reduce peak healthcare demand by 2/3 and deaths by half. However, the resulting mitigated epidemic would still likely result in hundreds of thousands of deaths and health systems (most notably intensive care units) being overwhelmed many times over. For countries able to achieve it, this leaves suppression as the preferred policy option. We show that in the UK and US context, suppression will minimally require a combination of social distancing of the entire population, home isolation of cases and household quarantine of their family members. This may need to be supplemented by school and university closures, though it should be recognised that such closures may have negative impacts on health systems due to increased absenteeism. The major challenge of suppression is that this type of intensive intervention package – or something equivalently effective at reducing transmission – will need to be maintained until a vaccine becomes available (potentially 18 months or more) – given that we predict that transmission will quickly rebound if interventions are relaxed. We show that intermittent social distancing – triggered by trends in disease surveillance – may allow interventions to be relaxed temporarily in relative short time windows, but measures will need to be reintroduced if or when case numbers rebound. Last, while experience in China and now South Korea show that suppression is possible in the short term, it remains to be seen whether it is possible long-term, and whether the social and economic costs of the interventions adopted thus far can be reduced.
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            Foundations of Social Theory

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              Author and article information

              Journal
              Physica A
              Physica A
              Physica a
              Elsevier B.V.
              0378-4371
              0378-4371
              21 November 2020
              21 November 2020
              : 125564
              Affiliations
              [1]Kyushu University, Nishiku, Fukuoka 819-0395, Japan
              [2]Research Institute for Science Education, Inc., Kitaku, Kyoto 603-8346, Japan
              Author notes
              [* ]Correspondence to: Kyushu University, Nishiku, Fukuoka 819-0395, Japan.
              Article
              S0378-4371(20)30862-1 125564
              10.1016/j.physa.2020.125564
              7680020
              33250562
              2f9d11ba-cce3-4ea0-9730-c4dfd8ef64aa
              © 2020 Elsevier B.V. All rights reserved.

              Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.

              History
              : 6 August 2020
              : 4 November 2020
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