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      Compartmental Models of the COVID-19 Pandemic for Physicians and Physician-Scientists

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          Abstract

          As the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection spreads globally, physicians and physician-scientists are confronted with an enlarging body of literature about the nature of this pandemic. Understanding the current epidemiological models for disease spread, mortality, and recovery is more important than ever before. One of the most relevant mathematical models relating to the spread of a pandemic is the susceptible-infectious-removed (SIR) model. Other models worth exploring are the susceptible-exposed-infectious-removed (SEIR) and the susceptible-unquarantined-quarantined-confirmed (SUQC) model.

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          Modeling the epidemic dynamics and control of COVID-19 outbreak in China

          Shilei Zhao, Hua. Chen (2020)
          Background The coronavirus disease 2019 (COVID-19) is rapidly spreading in China and more than 30 countries over last two months. COVID-19 has multiple characteristics distinct from other infectious diseases, including high infectivity during incubation, time delay between real dynamics and daily observed number of confirmed cases, and the intervention effects of implemented quarantine and control measures. Methods We develop a Susceptible, Un-quanrantined infected, Quarantined infected, Confirmed infected (SUQC) model to characterize the dynamics of COVID-19 and explicitly parameterize the intervention effects of control measures, which is more suitable for analysis than other existing epidemic models. Results The SUQC model is applied to the daily released data of the confirmed infections to analyze the outbreak of COVID-19 in Wuhan, Hubei (excluding Wuhan), China (excluding Hubei) and four first-tier cities of China. We found that, before January 30, 2020, all these regions except Beijing had a reproductive number R > 1, and after January 30, all regions had a reproductive number R < 1, indicating that the quarantine and control measures are effective in preventing the spread of COVID-19. The confirmation rate of Wuhan estimated by our model is 0.0643, substantially lower than that of Hubei excluding Wuhan (0.1914), and that of China excluding Hubei (0.2189), but it jumps to 0.3229 after February 12 when clinical evidence was adopted in new diagnosis guidelines. The number of unquarantined infected cases in Wuhan on February 12, 2020 is estimated to be 3,509 and declines to 334 on February 21, 2020. After fitting the model with data as of February 21, 2020, we predict that the end time of COVID-19 in Wuhan and Hubei is around late March, around mid March for China excluding Hubei, and before early March 2020 for the four tier-one cities. A total of 80,511 individuals are estimated to be infected in China, among which 49,510 are from Wuhan, 17,679 from Hubei (excluding Wuhan), and the rest 13,322 from other regions of China (excluding Hubei). Note that the estimates are from a deterministic ODE model and should be interpreted with some uncertainty. Conclusions We suggest that rigorous quarantine and control measures should be kept before early March in Beijing, Shanghai, Guangzhou and Shenzhen, and before late March in Hubei. The model can also be useful to predict the trend of epidemic and provide quantitative guide for other countries at high risk of outbreak, such as South Korea, Japan, Italy and Iran. Supplementary Materials The supplementary materials can be found online with this article at 10.1007/s40484-020-0199-0.
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            An SEIR model of influenza A virus infection and reinfection within a farrow-to-finish swine farm

            Fatima Etbaigha, Allan R. Willms, Zvonimir Poljak (2018)
            Influenza A virus (IAV) in swine is a pathogen that causes a threat to the health as well as to the production of swine. Moreover, swine can spread this virus to other species including humans. The virus persists in different types of swine farms as evident in a number of studies. The core objectives of this study are (i) to analyze the dynamics of influenza infection of a farrow-to-finish swine farm, (ii) to explore the reinfection at the farm level, and finally (iii) to examine the effectiveness of two control strategies: vaccination and reduction of indirect contact. The analyses are conducted using a deterministic Susceptible-Exposed-Infectious-Recovered (SEIR) model. Simulation results show that the disease is maintained in gilts and piglets because of new susceptible pigs entering the population on a weekly basis. A sensitivity analysis shows that the results are not sensitive to variation in the parameters. The results of the reinfection simulation indicate that the virus persists in the entire farm. The control strategies studied in this work are not successful in eliminating the virus within the farm.
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              A Path-Specific SEIR Model for use with General Latent and Infectious Time Distributions

              Aaron T. Porter, Jacob Oleson (2013)
              Most current Bayesian SEIR (Susceptible, Exposed, Infectious, Removed (or Recovered)) models either use exponentially distributed latent and infectious periods, allow for a single distribution on the latent and infectious period, or make strong assumptions regarding the quantity of information available regarding time distributions, particularly the time spent in the exposed compartment. Many infectious diseases require a more realistic assumption on the latent and infectious periods. In this article, we provide an alternative model allowing general distributions to be utilized for both the exposed and infectious compartments, while avoiding the need for full latent time data. The alternative formulation is a path-specific SEIR (PS SEIR) model that follows individual paths through the exposed and infectious compartments, thereby removing the need for an exponential assumption on the latent and infectious time distributions. We show how the PS SEIR model is a stochastic analog to a general class of deterministic SEIR models. We then demonstrate the improvement of this PS SEIR model over more common population averaged models via simulation results and perform a new analysis of the Iowa mumps epidemic from 2006.
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                Author and article information

                Contributors
                Anas Abou-Ismail:
                ORCID: http://orcid.org/0000-0002-7918-0416
                a.a.ismael.2010@gmail.com
                Journal
                Journal ID (nlm-ta): SN Compr Clin Med
                Journal ID (iso-abbrev): SN Compr Clin Med
                Title: Sn Comprehensive Clinical Medicine
                Publisher: Springer International Publishing (Cham )
                ISSN (Electronic): 2523-8973
                Publication date (Electronic): 4 June 2020
                Pages: 1-7
                Affiliations
                Palm Springs, CA 92264 USA
                Author information
                http://orcid.org/0000-0002-7918-0416
                Article
                Publisher ID: 330
                DOI: 10.1007/s42399-020-00330-z
                PMC ID: 7270519
                PubMed ID: 32838137
                SO-VID: 15b12a6b-2df8-4659-861c-5e552c6217b3
                Copyright © © Springer Nature Switzerland AG 2020
                License:

                This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.

                History
                Date accepted : 19 May 2020
                Categories
                Subject: Covid-19

                Keywords: covid-19,susceptible,infectious,recovered,mathematical model,quarantine,basic reproductive number,herd immunity,sir,seir,sis,suqc
                Data availability:
                Keywords: covid-19, susceptible, infectious, recovered, mathematical model, quarantine, basic reproductive number, herd immunity, sir, seir, sis, suqc

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