Dynamics of COVID-19 pandemic at constant and time-dependent contact rates

• Published in: Mathematical modelling of natural phenomena 2020, Vol.15, p.28
• Main Authors: Kochańczyk, Marek, Grabowski, Frederic, Lipniacki, Tomasz
• Format: Article
• Language: English
• Subjects: Coronaviruses; COVID-19; Epidemics; Multiplication; Pandemics; Risk acceptance; Social behavior; Time dependence; Vaccines
• ISSN: 0973-5348; 1760-6101
• DOI: 10.1051/mmnp/2020011

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, R 0 = β / γ , and, together with τ , the daily multiplication coefficient in the early exponential phase, θ . Initial R 0 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.