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      On the use of growth models to understand epidemic outbreaks with application to COVID-19 data

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          Abstract

          The initial phase dynamics of an epidemic without containment measures is commonly well modelled using exponential growth models. However, in the presence of containment measures, the exponential model becomes less appropriate. Under the implementation of an isolation measure for detected infectives, we propose to model epidemic dynamics by fitting a flexible growth model curve to reported positive cases, and to infer the overall epidemic dynamics by introducing information on the detection/testing effort and recovery and death rates. The resulting modelling approach is close to the Susceptible-Infectious-Quarantined-Recovered model framework. We focused on predicting the peaks (time and size) in positive cases, active cases and new infections. We applied the approach to data from the COVID-19 outbreak in Italy. Fits on limited data before the observed peaks illustrate the ability of the flexible growth model to approach the estimates from the whole data.

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          Most cited references20

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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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            Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy

            In Italy, 128,948 confirmed cases and 15,887 deaths of people who tested positive for SARS-CoV-2 were registered as of 5 April 2020. Ending the global SARS-CoV-2 pandemic requires implementation of multiple population-wide strategies, including social distancing, testing and contact tracing. We propose a new model that predicts the course of the epidemic to help plan an effective control strategy. The model considers eight stages of infection: susceptible (S), infected (I), diagnosed (D), ailing (A), recognized (R), threatened (T), healed (H) and extinct (E), collectively termed SIDARTHE. Our SIDARTHE model discriminates between infected individuals depending on whether they have been diagnosed and on the severity of their symptoms. The distinction between diagnosed and non-diagnosed individuals is important because the former are typically isolated and hence less likely to spread the infection. This delineation also helps to explain misperceptions of the case fatality rate and of the epidemic spread. We compare simulation results with real data on the COVID-19 epidemic in Italy, and we model possible scenarios of implementation of countermeasures. Our results demonstrate that restrictive social-distancing measures will need to be combined with widespread testing and contact tracing to end the ongoing COVID-19 pandemic.
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              Log-normal Distributions across the Sciences: Keys and Clues

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                Author and article information

                Contributors
                Role: ConceptualizationRole: Formal analysisRole: MethodologyRole: Writing – original draftRole: Writing – review & editing
                Role: Writing – review & editing
                Role: ConceptualizationRole: Funding acquisitionRole: MethodologyRole: SupervisionRole: ValidationRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS One
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                2020
                20 October 2020
                20 October 2020
                : 15
                : 10
                : e0240578
                Affiliations
                [001] Laboratoire de Biomathématiques et d’Estimations Forestières, Faculté des Sciences Agronomiques, Université d’Abomey-Calavi, Abomey-Calavi, Bénin
                Universita degli Studi di Catania, ITALY
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Author information
                https://orcid.org/0000-0002-3685-3043
                https://orcid.org/0000-0002-0574-8793
                https://orcid.org/0000-0002-6965-4331
                Article
                PONE-D-20-25923
                10.1371/journal.pone.0240578
                7575103
                33079964
                075252eb-54d4-4abb-8c0c-050cb8bdd0d9
                © 2020 Frédéric Tovissodé et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 18 August 2020
                : 29 September 2020
                Page count
                Figures: 1, Tables: 5, Pages: 14
                Funding
                The authors received no specific funding for this work.
                Categories
                Research Article
                Medicine and Health Sciences
                Medical Conditions
                Infectious Diseases
                Viral Diseases
                Covid 19
                Medicine and Health Sciences
                Epidemiology
                People and Places
                Population Groupings
                Ethnicities
                European People
                Italian People
                Medicine and Health Sciences
                Diagnostic Medicine
                Virus Testing
                Research and Analysis Methods
                Mathematical and Statistical Techniques
                Mathematical Functions
                Curve Fitting
                Biology and Life Sciences
                Population Biology
                Population Metrics
                Death Rates
                Medicine and Health Sciences
                Public and Occupational Health
                People and places
                Geographical locations
                Europe
                European Union
                Italy
                Custom metadata
                All relevant data are within the manuscript and its Supporting Information files.
                COVID-19

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                Uncategorized

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