Epidemics on networks: Reducing disease transmission using health emergency declarations and peer communication

Azizi, Asma; Montalvo, Cesar; Espinoza, Baltazar; Kang, Yun; Castillo-Chavez, Carlos

To determine the effectiveness of awareness spread, we compare the prevalence over time in the absence and presence of awareness. Fig. (4) shows the results for network structures G E , G W , and G S . We observe that all networks, with or without awareness, support an outbreak for the chosen parameters (that is, the probability of extinction is low or the results are conditioned on non-extinction). Due to a lack of epidemic threshold for Scale-free network (Chowell & Castillo-Chavez, 2003; May & Lloyd, 2001; Moreno, Pastor-Satorras, & Vespignani, 2002) , we always observe an outbreak with severity that depends on the initial infected index. For the other network structures, we observe an epidemic threshold depends on the network topology; specifically, on the average number of neighbors and the levels of heterogeneity in the number of neighbors (mean and variance of degree distribution) (Kiss et al., 2017) . For example, for the case of Small-world networks Moore et al. (Moore & Newman, 2000) derived an analytic expression for the percolation threshold p c , above which there will be an outbreak. For the case when the network is homogeneous (Erd} os-R enyi network), the epidemic threshold is proportional to the average number of neighbors (average degree) (Pastor-Satorras, Castellano, Van Mieghem, & Vespignani, 2015) . Hence, for our simulation for both networks G E and G W we approximated the basic reproduction number using epidemic take-offs, when we had an outbreak, that is, whenever R 0 > 1 (probability of extinction for the parameters used seemed to be negligible).