Effectiveness of isolation measures with app support to contain COVID-19 epidemics: a parametric approach

Abstract

In this study, we analyze the effectiveness of measures aimed at finding and isolating infected individuals to contain epidemics like COVID-19, as the suppression induced over the effective reproduction number. We develop a mathematical model to compute the relative suppression of the effective reproduction number of an epidemic that such measures produce. This outcome is expressed as a function of a small set of parameters that describe the main features of the epidemic and summarize the effectiveness of the isolation measures. In particular, we focus on the impact when a fraction of the population uses a mobile application for epidemic control. Finally, we apply the model to COVID-19, providing several computations as examples, and a link to a public repository to run custom calculations. These computations display in a quantitative manner the importance of recognizing infected individuals from symptoms and contact-tracing information, and isolating them as early as possible. The computations also assess the impact of each variable on the mitigation of the epidemic.

Keywords: COVID-19; Contact tracing; Epidemic models.

Fig. 1

$R_t$ evolution in the homogeneous model, in an optimistic scenario

Fig. 2

${\text{Eff}}_{\infty }$ as a function of the time ${\mathrm{\Delta }}^{\text{A}\to \text{T}}$ from notification to positive testing

Fig. 3

${\text{Eff}}_{\infty }$ for some values of $p_{\text{sym}}$ and $\kappa$

Fig. 4

${\text{Eff}}_{\infty }$ for some rescalings of the distribution of ${\tau }^{\text{0,C}}$

Fig. 5

${\text{Eff}}_{\infty }$ for some values of $R_t^0$, for $t\ge 0$

Fig. 6

KPIs evolution in the optimistic scenario

Fig. 7

KPIs evolution in case of gradual adoption of the app

Fig. 8

${\text{Eff}}_{\infty }$ as a function of the efficiencies $s_{\text{sym}}^{\text{s,app}}$ and $s^{\text{c,app}}$

Fig. 9

${\text{Eff}}_{\infty }$ as a function of app adoption ${ϵ}_{\text{app}}$

Fig. 10

Schematic representation of $\mathrm{\Omega }$, $t^{\text{I}}$, and $\sigma$. Dots represent individuals $\omega \in \mathrm{\Omega }$