Math. Model. Nat. Phenom.
Volume 15, 2020
Coronavirus: Scientific insights and societal aspects
|Number of page(s)||12|
|Published online||21 April 2020|
Dynamics of COVID-19 pandemic at constant and time-dependent contact rates
Department of Biosystems and Soft Matter, Institute of Fundamental Technological Research, Polish Academy of Sciences,
2 Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, 02-097 Warsaw, Poland.
* Corresponding author: email@example.com
Accepted: 5 April 2020
We constructed a simple Susceptible–Exposed–Infectious–Removed model of the spread of COVID-19. The model is parametrised only by the average incubation period, τ, and two rate parameters: contact rate, β, and exclusion rate, γ. The rates depend on nontherapeutic interventions and determine the basic reproduction number, R0 = β∕γ, and, together with τ, the daily multiplication coefficient in the early exponential phase, θ. Initial R0 determines the reduction of β required to contain the spread of the epidemic. We demonstrate that introduction of a cascade of multiple exposed states enables the model to reproduce the distributions of the incubation period and the serial interval reported by epidemiologists. Using the model, we consider a hypothetical scenario in which β is modulated solely by anticipated changes of social behaviours: first, β decreases in response to a surge of daily new cases, pressuring people to self-isolate, and then, over longer time scale, β increases as people gradually accept the risk. In this scenario, initial abrupt epidemic spread is followed by a plateau and slow regression, which, although economically and socially devastating, grants time to develop and deploy vaccine or at least limit daily cases to a manageable number.
Mathematics Subject Classification: 92D30
Key words: basic reproduction number / novel coronavirus
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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