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      Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan

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          Abstract

          We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability of the disease free equilibrium in terms of the basic reproduction number, and we investigate the sensitivity of the model with respect to the variation of each one of its parameters. Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China.

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          Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission

          P van den Driessche, James Watmough (2002)
          Article 0 comments Cited 666 times – based on 0 reviews     Review now
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            Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China

            Benjamin F. Maier, Dirk Brockmann (2020)
            The recent outbreak of COVID-19 in Mainland China was characterized by a distinctive subexponential increase of confirmed cases during the early phase of the epidemic, contrasting an initial exponential growth expected for an unconstrained outbreak. We show that this effect can be explained as a direct consequence of containment policies that effectively deplete the susceptible population. To this end, we introduce a parsimonious model that captures both, quarantine of symptomatic infected individuals as well as population-wide isolation practices in response to containment policies or behavioral changes and show that the model captures the observed growth behavior accurately. The insights provided here may aid the careful implementation of containment strategies for ongoing secondary outbreaks of COVID-19 or similar future outbreaks of other emergent infectious diseases.
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              A mathematical model for simulating the phase-based transmissibility of a novel coronavirus

              Tian-Mu Chen, Jia Rui, Qiu-Peng Wang … (2020)
              Background As reported by the World Health Organization, a novel coronavirus (2019-nCoV) was identified as the causative virus of Wuhan pneumonia of unknown etiology by Chinese authorities on 7 January, 2020. The virus was named as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) by International Committee on Taxonomy of Viruses on 11 February, 2020. This study aimed to develop a mathematical model for calculating the transmissibility of the virus. Methods In this study, we developed a Bats-Hosts-Reservoir-People transmission network model for simulating the potential transmission from the infection source (probably be bats) to the human infection. Since the Bats-Hosts-Reservoir network was hard to explore clearly and public concerns were focusing on the transmission from Huanan Seafood Wholesale Market (reservoir) to people, we simplified the model as Reservoir-People (RP) transmission network model. The next generation matrix approach was adopted to calculate the basic reproduction number (R 0) from the RP model to assess the transmissibility of the SARS-CoV-2. Results The value of R 0 was estimated of 2.30 from reservoir to person and 3.58 from person to person which means that the expected number of secondary infections that result from introducing a single infected individual into an otherwise susceptible population was 3.58. Conclusions Our model showed that the transmissibility of SARS-CoV-2 was higher than the Middle East respiratory syndrome in the Middle East countries, similar to severe acute respiratory syndrome, but lower than MERS in the Republic of Korea.
              Article 0 comments Cited 268 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Journal ID (nlm-ta): Chaos Solitons Fractals
                Journal ID (iso-abbrev): Chaos Solitons Fractals
                Title: Chaos, Solitons, and Fractals
                Publisher: Elsevier Ltd.
                ISSN (Print): 0960-0779
                ISSN (Electronic): 0960-0779
                Publication date PMC-release: 27 April 2020
                Publication date (Electronic): 27 April 2020
                Electronic Location Identifier: 109846
                Affiliations
                [a ]Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, Aveiro 3810-193, Portugal
                [b ]Departamento de Matemática Aplicada II, E. E. Aeronáutica e do Espazo, Campus de Ourense, Universidade de Vigo, Ourense 32004, Spain
                [c ]Instituto de Matematicas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
                Author notes
                [* ]Corresponding author.
                Article
                Publisher ID: S0960-0779(20)30246-0 Publisher ID: 109846
                DOI: 10.1016/j.chaos.2020.109846
                PMC ID: 7184012
                PubMed ID: 32341628
                SO-VID: 97a3c3b4-2e01-44fc-80f7-799843b84c22
                Copyright © © 2020 Elsevier Ltd. All rights reserved.
                License:

                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
                Date received : 18 April 2020
                Date accepted : 22 April 2020
                Categories
                Subject: Article

                Keywords: mathematical modeling of covid-19 pandemic,wuhan case study,basic reproduction number,stability,sensitivity analysis,numerical simulations,34d05,92d30
                Data availability:
                Keywords: mathematical modeling of covid-19 pandemic, wuhan case study, basic reproduction number, stability, sensitivity analysis, numerical simulations, 34d05, 92d30

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