Infectious disease control using contact tracing in random and scale-free networks

Abstract

Contact tracing aims to identify and isolate individuals that have been in contact with infectious individuals. The efficacy of contact tracing and the hierarchy of traced nodes-nodes with higher degree traced first-is investigated and compared on random and scale-free (SF) networks with the same number of nodes N and average connection K. For values of the transmission rate larger than a threshold, the final epidemic size on SF networks is smaller than that on corresponding random networks. While in random networks new infectious and traced nodes from all classes have similar average degrees, in SF networks the average degree of nodes that are in more advanced stages of the disease is higher at any given time. On SF networks tracing removes possible sources of infection with high average degree. However a higher tracing effort is required to control the epidemic than on corresponding random networks due to the high initial velocity of spread towards the highly connected nodes. An increased latency period fails to significantly improve contact tracing efficacy. Contact tracing has a limited effect if the removal rate of susceptible nodes is relatively high, due to the fast local depletion of susceptible nodes.

Figure 1

Possible transitions among the five different classes and the corresponding rates of transitions.

Figure 2

Time evolution of the proportion of infectious nodes for random (a) and scale-free (SF), (b) networks in the absence of tracing with r_SE=0.015,0.0215,…,0.08 and Lat_P=3.5.

Figure 3

Final epidemic size representing the number of nodes that became infectious during the whole epidemic, plotted as a function of r_SE in the absence of tracing. Continuous line corresponds to random networks and dashed line to SF networks. The latency period is Lat_P=3.5.

Figure 4

Proportion of infected nodes removed by tracing for random (a) and SF (b) networks for r_SE=0.15 and Lat_P=3.5.

Figure 5

Proportion of infected nodes removed by tracing for random (a) and SF (b) networks for r_SE=0.15 and Lat_P=10.0.

Figure 6

Average degree of new infectious nodes, and average degree of susceptible and infected nodes removed by tracing versus time for random (a) and SF (b) networks for r_SE=0.15, Lat_P=10.0 and $r_{SR}=r_{ER}=r_{IR}=0.5$.

Figure 7

The daily average degree and number (inset) of new infectious nodes versus time for different levels of tracing (r_ER=r_IR=0.5 and 1.6). Results obtained using SF networks for r_SE=0.15, Lat_P=10.0 and r_SR=0.5.