Homophily in the adoption of digital proximity tracing apps shapes the evolution of epidemics

We study how homophily of human physical interactions affects the impact of digital proximity tracing on the epidemic evolution. Analytical and numerical results show the existence of different dynamical regimes with respect to the mixing rate between adopters and nonadopters, revealing a rich phenomenology in terms of the reproduction number as well as the attack rate. We corroborate our findings with Monte Carlo simulations on different real contact networks. Our results indicate that depending on infectivity and adoption, mixing between adopters can be beneficial as well as detrimental for disease control.

Figure 1

(a) Reproduction number $R$ normalized with respect to the basic reproduction number $R_0$ for different values of adoption $T$ below $T^{*}$. Dots indicate the minimum at ${\alpha }^{*}$, while the dashed line shows its variation for $T\in [0.1,0.55]$. (b) Numerical solution of the dynamics for the attack rate as a function of $\alpha$ and $R_0$. The solid line indicates the threshold ${\alpha }_c^{-}$ for which $R=1$. Colored, dashed lines denote the dynamical regimes: critical, intermediate, and saturated. Adoption was fixed as $T=0.7$. For these parameter values we have ${\alpha }_c^{+}>1$. (c) Top panels show the attack rate and the reproduction number for the different regimes defined in (b). The specific attack rates for adopters and nonadopters are reported in the bottom panels. Black diamonds indicate ${\alpha }_c^{-}$, at which $R=1$.

Figure 2

Attack rate as a function of the reproduction number $R$ for different values of adoption $T$. The size of the points interpolates between $\alpha =0$ and $\alpha =1$. We fixed the basic reproduction number as $R_0=1.5$.

Figure 3

Dependence of the attack rate on $\alpha$ as resulting from Monte Carlo simulations for the three dynamical regimes and four different real-world networks. Each column refers to a different network, while rows indicate the critical, intermediate, and saturated regime, respectively, from top to bottom. Note that different values of $\alpha$ can be accessed depending on adoption $T$ and structural constraints of the network. Dots indicate the median value, whereas the ribbon indicates first and third quartiles. Each point is obtained by averaging over $4\times {10}^4$ runs. From left to right, the networks have 780, 636, 212, and 226 nodes. For the saturated and critical regimes we fixed $T=0.30$ and $T=0.90$, respectively. In the intermediate regime, $T$ was fixed as 0.75, 0.72, 0.67, and 0.69 for the different networks (left to right). Specific to each network we set $\beta$ as 0.030, 0.085, 0.110, and 0.090.