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      COVID-19 epidemic control using short-term lockdowns for collective gain

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          Abstract

          While many efforts are currently devoted to vaccines development and administration, social distancing measures, including severe restrictions such as lockdowns, remain fundamental tools to contain the spread of COVID-19. A crucial point for any government is to understand, on the basis of the epidemic curve, the right temporal instant to set up a lockdown and then to remove it. Different strategies are being adopted with distinct shades of intensity. USA and Europe tend to introduce restrictions of considerable temporal length. They vary in time: a severe lockdown may be reached and then gradually relaxed. An interesting alternative is the Australian model where short and sharp responses have repeatedly tackled the virus and allowed people a return to near normalcy. After a few positive cases are detected, a lockdown is immediately set. In this paper we show that the Australian model can be generalized and given a rigorous mathematical analysis, casting strategies of the type short-term pain for collective gain in the context of sliding-mode control, an important branch of nonlinear control theory. This allows us to gain important insights regarding how to implement short-term lockdowns, obtaining a better understanding of their merits and possible limitations. Effects of vaccines administration in improving the control law’s effectiveness are also illustrated. Our model predicts the duration of the severe lockdown to be set to maintain e.g. the number of people in intensive care under a certain threshold. After tuning our strategy exploiting data collected in Italy, it turns out that COVID-19 epidemic could be e.g. controlled by alternating one or two weeks of complete lockdown with one or two months of freedom, respectively. Control strategies of this kind, where the lockdown’s duration is well circumscribed, could be important also to alleviate coronavirus impact on economy.

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          Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study

          Summary Background Since December, 2019, Wuhan, China, has experienced an outbreak of coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Epidemiological and clinical characteristics of patients with COVID-19 have been reported but risk factors for mortality and a detailed clinical course of illness, including viral shedding, have not been well described. Methods In this retrospective, multicentre cohort study, we included all adult inpatients (≥18 years old) with laboratory-confirmed COVID-19 from Jinyintan Hospital and Wuhan Pulmonary Hospital (Wuhan, China) who had been discharged or had died by Jan 31, 2020. Demographic, clinical, treatment, and laboratory data, including serial samples for viral RNA detection, were extracted from electronic medical records and compared between survivors and non-survivors. We used univariable and multivariable logistic regression methods to explore the risk factors associated with in-hospital death. Findings 191 patients (135 from Jinyintan Hospital and 56 from Wuhan Pulmonary Hospital) were included in this study, of whom 137 were discharged and 54 died in hospital. 91 (48%) patients had a comorbidity, with hypertension being the most common (58 [30%] patients), followed by diabetes (36 [19%] patients) and coronary heart disease (15 [8%] patients). Multivariable regression showed increasing odds of in-hospital death associated with older age (odds ratio 1·10, 95% CI 1·03–1·17, per year increase; p=0·0043), higher Sequential Organ Failure Assessment (SOFA) score (5·65, 2·61–12·23; p<0·0001), and d-dimer greater than 1 μg/mL (18·42, 2·64–128·55; p=0·0033) on admission. Median duration of viral shedding was 20·0 days (IQR 17·0–24·0) in survivors, but SARS-CoV-2 was detectable until death in non-survivors. The longest observed duration of viral shedding in survivors was 37 days. Interpretation The potential risk factors of older age, high SOFA score, and d-dimer greater than 1 μg/mL could help clinicians to identify patients with poor prognosis at an early stage. Prolonged viral shedding provides the rationale for a strategy of isolation of infected patients and optimal antiviral interventions in the future. Funding Chinese Academy of Medical Sciences Innovation Fund for Medical Sciences; National Science Grant for Distinguished Young Scholars; National Key Research and Development Program of China; The Beijing Science and Technology Project; and Major Projects of National Science and Technology on New Drug Creation and Development.
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            Characteristics of and Important Lessons From the Coronavirus Disease 2019 (COVID-19) Outbreak in China: Summary of a Report of 72 314 Cases From the Chinese Center for Disease Control and Prevention

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              The COVID‐19 epidemic

              The current outbreak of the novel coronavirus SARS‐CoV‐2 (coronavirus disease 2019; previously 2019‐nCoV), epi‐centred in Hubei Province of the People’s Republic of China, has spread to many other countries. On 30. January 2020, the WHO Emergency Committee declared a global health emergency based on growing case notification rates at Chinese and international locations. The case detection rate is changing daily and can be tracked in almost real time on the website provided by Johns Hopkins University 1 and other forums. As of midst of February 2020, China bears the large burden of morbidity and mortality, whereas the incidence in other Asian countries, in Europe and North America remains low so far. Coronaviruses are enveloped, positive single‐stranded large RNA viruses that infect humans, but also a wide range of animals. Coronaviruses were first described in 1966 by Tyrell and Bynoe, who cultivated the viruses from patients with common colds 2. Based on their morphology as spherical virions with a core shell and surface projections resembling a solar corona, they were termed coronaviruses (Latin: corona = crown). Four subfamilies, namely alpha‐, beta‐, gamma‐ and delta‐coronaviruses exist. While alpha‐ and beta‐coronaviruses apparently originate from mammals, in particular from bats, gamma‐ and delta‐viruses originate from pigs and birds. The genome size varies between 26 kb and 32 kb. Among the seven subtypes of coronaviruses that can infect humans, the beta‐coronaviruses may cause severe disease and fatalities, whereas alpha‐coronaviruses cause asymptomatic or mildly symptomatic infections. SARS‐CoV‐2 belongs to the B lineage of the beta‐coronaviruses and is closely related to the SARS‐CoV virus 3, 4. The major four structural genes encode the nucleocapsid protein (N), the spike protein (S), a small membrane protein (SM) and the membrane glycoprotein (M) with an additional membrane glycoprotein (HE) occurring in the HCoV‐OC43 and HKU1 beta‐coronaviruses 5. SARS‐CoV‐2 is 96% identical at the whole‐genome level to a bat coronavirus 4. SARS‐CoV‐2 apparently succeeded in making its transition from animals to humans on the Huanan seafood market in Wuhan, China. However, endeavours to identify potential intermediate hosts seem to have been neglected in Wuhan and the exact route of transmission urgently needs to be clarified. The initial clinical sign of the SARS‐CoV‐2‐related disease COVID‐19 which allowed case detection was pneumonia. More recent reports also describe gastrointestinal symptoms and asymptomatic infections, especially among young children 6. Observations so far suggest a mean incubation period of five days 7 and a median incubation period of 3 days (range: 0–24 days) 8. The proportion of individuals infected by SARS‐CoV‐2 who remain asymptomatic throughout the course of infection has not yet been definitely assessed. In symptomatic patients, the clinical manifestations of the disease usually start after less than a week, consisting of fever, cough, nasal congestion, fatigue and other signs of upper respiratory tract infections. The infection can progress to severe disease with dyspnoea and severe chest symptoms corresponding to pneumonia in approximately 75% of patients, as seen by computed tomography on admission 8. Pneumonia mostly occurs in the second or third week of a symptomatic infection. Prominent signs of viral pneumonia include decreased oxygen saturation, blood gas deviations, changes visible through chest X‐rays and other imaging techniques, with ground glass abnormalities, patchy consolidation, alveolar exudates and interlobular involvement, eventually indicating deterioration. Lymphopenia appears to be common, and inflammatory markers (C‐reactive protein and proinflammatory cytokines) are elevated. Recent investigations of 425 confirmed cases demonstrate that the current epidemic may double in the number of affected individuals every seven days and that each patient spreads infection to 2.2 other individuals on average (R0) 6. Estimates from the SARS‐CoV outbreak in 2003 reported an R0 of 3 9. A recent data‐driven analysis from the early phase of the outbreak estimates a mean R0 range from 2.2 to 3.58 10. Dense communities are at particular risk and the most vulnerable region certainly is Africa, due to dense traffic between China and Africa. Very few African countries have sufficient and appropriate diagnostic capacities and obvious challenges exist to handle such outbreaks. Indeed, the virus might soon affect Africa. WHO has identified 13 top‐priority countries (Algeria, Angola, Cote d’Ivoire, the Democratic Republic of the Congo, Ethiopia, Ghana, Kenya, Mauritius, Nigeria, South Africa, Tanzania, Uganda, Zambia) which either maintain direct links to China or a high volume of travel to China. Recent studies indicate that patients ≥60 years of age are at higher risk than children who might be less likely to become infected or, if so, may show milder symptoms or even asymptomatic infection 7. As of 13. February 2020, the case fatality rate of COVID‐19 infections has been approximately 2.2% (1370/60363; 13. February 2020, 06:53 PM CET); it was 9.6% (774/8096) in the SARS‐CoV epidemic 11 and 34.4% (858/2494) in the MERS‐CoV outbreak since 2012 12. Like other viruses, SARS‐CoV‐2 infects lung alveolar epithelial cells using receptor‐mediated endocytosis via the angiotensin‐converting enzyme II (ACE2) as an entry receptor 4. Artificial intelligence predicts that drugs associated with AP2‐associated protein kinase 1 (AAK1) disrupting these proteins may inhibit viral entry into the target cells 13. Baricitinib, used in the treatment of rheumatoid arthritis, is an AAK1 and Janus kinase inhibitor and suggested for controlling viral replication 13. Moreover, one in vitro and a clinical study indicate that remdesivir, an adenosine analogue that acts as a viral protein inhibitor, has improved the condition in one patient 14, 15. Chloroquine, by increasing the endosomal pH required for virus‐cell fusion, has the potential of blocking viral infection 15 and was shown to affect activation of p38 mitogen‐activated protein kinase (MAPK), which is involved in replication of HCoV‐229E 16. A combination of the antiretroviral drugs lopinavir and ritonavir significantly improved the clinical condition of SARS‐CoV patients 17 and might be an option in COVID‐19 infections. Further possibilities include leronlimab, a humanised monoclonal antibody (CCR5 antagonist), and galidesivir, a nucleoside RNA polymerase inhibitor, both of which have shown survival benefits in several deadly virus infections and are being considered as potential treatment candidates 18. Repurposing these available drugs for immediate use in treatment in SARS‐CoV‐2 infections could improve the currently available clinical management. Clinical trials presently registered at ClinicalTrials.gov focus on the efficacy of remdesivir, immunoglobulins, arbidol hydrochloride combined with interferon atomisation, ASC09F+Oseltamivir, ritonavir plus oseltamivir, lopinavir plus ritonavir, mesenchymal stem cell treatment, darunavir plus cobicistat, hydroxychloroquine, methylprednisolone and washed microbiota transplantation 19. Given the fragile health systems in most sub‐Saharan African countries, new and re‐emerging disease outbreaks such as the current COVID‐19 epidemic can potentially paralyse health systems at the expense of primary healthcare requirements. The impact of the Ebola epidemic on the economy and healthcare structures is still felt five years later in those countries which were affected. Effective outbreak responses and preparedness during emergencies of such magnitude are challenging across African and other lower‐middle‐income countries. Such situations can partly only be mitigated by supporting existing regional and sub‐Saharan African health structures.
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                Author and article information

                Journal
                Annu Rev Control
                Annu Rev Control
                Annual Reviews in Control
                Elsevier Ltd.
                1367-5788
                1367-5788
                26 November 2021
                26 November 2021
                Affiliations
                [1]Department of Information Engineering, University of Padova, Padova, Italy
                Author notes
                [* ]Corresponding author.
                Article
                S1367-5788(21)00092-4
                10.1016/j.arcontrol.2021.10.017
                8616743
                34849089
                1f71ac23-95a8-4dd6-80ec-6886eafe1ee4
                © 2021 Elsevier Ltd. 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
                : 3 May 2021
                : 29 October 2021
                Categories
                Article

                compartmental models,sars-cov-2,epidemic spread,nonlinear control theory,sliding modes

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