The first 100 days: Modeling the evolution of the COVID-19 pandemic

Efthimios Kaxiras; Georgios Neofotistos; Eleni Angelaki

doi:10.1016/j.chaos.2020.110114

The first 100 days: Modeling the evolution of the COVID-19 pandemic

Chaos Solitons Fractals. 2020 Sep:138:110114. doi: 10.1016/j.chaos.2020.110114. Epub 2020 Jul 10.

Authors

Efthimios Kaxiras^{1

2}, Georgios Neofotistos^{1

3}, Eleni Angelaki^{4

3}

Affiliations

¹ Institute for Applied Computational Science, Harvard J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.
² Department of Physics, Harvard University, Cambridge, MA, USA.
³ Department of Physics, University of Crete, Heraklion, Greece.
⁴ Harvard J.A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA,USA.

Abstract

A simple analytical model for modeling the evolution of the 2020 COVID-19 pandemic is presented. The model is based on the numerical solution of the widely used Susceptible-Infectious-Removed (SIR) populations model for describing epidemics. We consider an expanded version of the original Kermack-McKendrick model, which includes a decaying value of the parameter β (the effective contact rate), interpreted as an effect of externally imposed conditions, to which we refer as the forced-SIR (FSIR) model. We introduce an approximate analytical solution to the differential equations that represent the FSIR model which gives very reasonable fits to real data for a number of countries over a period of 100 days (from the first onset of exponential increase, in China). The proposed model contains 3 adjustable parameters which are obtained by fitting actual data (up to April 28, 2020). We analyze these results to infer the physical meaning of the parameters involved. We use the model to make predictions about the total expected number of infections in each country as well as the date when the number of infections will have reached 99% of this total. We also compare key findings of the model with recently reported results on the high contagiousness and rapid spread of the disease.

Keywords: COVID-19; Compartmental model; Modeling pandemic evolution.