Assessing the Impact of (Self)-Quarantine Through a Basic Model of Infectious Disease Dynamics

TL;DR

This paper introduces a novel differential equation model to evaluate the effects of (self)-quarantine on infectious disease spread, highlighting the limited impact of quarantine alone during early COVID-19 outbreak phases.

Contribution

The model departs from classic bilinear infection processes, incorporating non-differentiability at disease-free states, and provides insights into quarantine effectiveness using COVID-19 data.

Findings

Peak cases could be 200 times higher than reported.

Strong quarantine adherence reduces peak by 22%.

Early outbreak impact of quarantine is more significant.

Abstract

We introduce a system of differential equations to assess the impact of (self-)quarantine of symptomatic infectious individuals on disease dynamics. To this end we depart from using the classic bilinear infection process, but remain still within the framework of the mass-action assumption. From the mathematical point of view our model is interesting due to the lack of continuous differentiability at disease free steady states, which implies also that the basic reproductive number cannot be computed following established approaches for certain parameter values. However, we parametrise our mathematical model using published values from the COVID-19 literature, and analyse the model simulations. We also contrast model simulations against publicly available COVID-19 test data focusing on the first wave of the pandemic during March - July 2020 in the UK. Our simulations indicate that actual peak case numbers might have been as much as 200 times higher than the reported positive test cases during the first wave in the UK. We find that very strong adherence to self-quarantine rules yields (only) a reduction of 22$\%$ of peak numbers and delays the onset of the peak by approximately 30-35 days. However, during the early phase of the outbreak the impact of (self)-quarantine is much more significant. We also take into account the effect of a national lockdown in a simplistic way by reducing the effective susceptible population size. We find that in case of a 90$\%$ reduction of the effective susceptible population size, strong adherence to self-quarantine still only yields a 25$\%$ reduction of peak infectious numbers when compared to low adherence. This is due to the significant number of asymptomatic infectious individuals in the population.