Effect of delayed awareness and fatigue on the efficacy of self-isolation in epidemic control

The isolation of infectious individuals is a key measure of public health for the control of communicable diseases. However, involving a strong perturbation of daily life, it often causes psychosocial distress, and severe financial and social costs. These may act as mechanisms limiting the adoption of the measure in the first place or the adherence throughout its full duration. In addition, difficulty of recognizing mild symptoms or lack of symptoms may impact awareness of the infection and further limit adoption. Here we study an epidemic model on a network of contacts accounting for limited adherence and delayed awareness to self-isolation, along with fatigue causing overhasty termination. The model allows us to estimate the role of each ingredient and analyze the tradeoff between adherence and duration of self-isolation. We find that the epidemic threshold is very sensitive to an effective compliance that combines the effects of imperfect adherence, delayed awareness and fatigue. If adherence improves for shorter quarantine periods, there exists an optimal duration of isolation, shorter than the infectious period. However, heterogeneities in the connectivity pattern, coupled to a reduced compliance for highly active individuals, may almost completely offset the effectiveness of self-isolation measures on the control of the epidemic.

Figure 1

Schematic representation of compartments and transition rates of the model.

Figure 2

Dependence of the epidemic threshold on the quarantine duration $T_Q$ for various values of the parameter $c$ in Eq. (8). Vertical lines indicate the optimal values from Eq. (9). $T=1$, $T_U=0.2$, and $\langle k\rangle =0.6$.

Figure 3

Epidemic threshold ${\lambda }_c$ as a function of the system size $N$ for $\gamma =2.25$ and several values of $p_Q$. Dashed lines represent the theoretical prediction, Eq (16), while symbols are the numerical estimates, obtained from the peak of the susceptibility [32]. $T=1$, $T_U=0.25$, $T_Q=1$.

Figure 4

Epidemic threshold ${\lambda }_c$ as a function of $T_Q$ for $T=1$, $T_U=0.2$ and various $p_Q$. Symbols are the results of numerical simulations, dashed lines are the predictions of HMF theory, dotted lines are the predictions of QMF theory.

Figure 5

Epidemic threshold ${\lambda }_c$ as a function of $T_Q$ for $T=1$, $p_Q=0.7$ and various $T_U$. Dashed lines are the predictions of HMF theory and dotted lines are the predictions of QMF theory while symbols are the results of numerical simulations.

Figure 6

Density of individuals in the various compartments in the stationary state as a function of $\lambda$ for $T=1$, $T_U=0.2$, $T_Q=0.33$, and $p_Q=0.7$.

Figure 7

Epidemic threshold as a function of $T_Q$ for $T=1$, $T_U=0.25$. In the heterogeneous case (circles and bottom lines) $p_Q\left(k\right)=k_{\min }/k$. In the homogeneous case (squares and top lines) $p_Q$ is the same for all nodes: $p_Q=\langle p_Q\left(k\right)\rangle =0.66$. Dashed lines are for the HMF predictions, whereas dotted lines are for the QMF ones.

Figure 8

Epidemic threshold as a function of $p_Q$ for $T=1$, $T_U=0.25$. In the heterogeneous case (circles and bottom lines) $T_Q\left(k\right)=(T-T_U)(k_{\max }-k)/(k_{\max }-k_{\min })$. In the homogeneous case (squares and top lines) $T_Q$ is the same for all nodes $T_Q=\langle T_Q\left(k\right)\rangle =0.71$. Dashed lines are for the HMF predictions, whereas dotted lines are for the QMF ones.