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

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

Infection final size is a function of network topology and prevalence threshold, P à , and the basic reproduction number R 0 . We observed that for Erd} os-R enyi and Small-world networks under small value of R 0 , an optimal P à can be found for which the infection final size is minimized. This optimal point is the value that provides the best outcome under the prevalence P à at the time, t à , the time when temporary protection was promoted by aware susceptible individuals, Fig. 5a and 5b. The existence of this optimal P à is because of lack of enough infected cases to spread the infection for prevalence less than P à , and lack of enough susceptible individuals to protect themselves against the infection for prevalence bigger than P à . This trend is observed for more homogeneous network structures as the infection spreads more slowly than in heterogeneous networks such as Scale-free ones. For Scale-free network, for which there is no epidemic threshold, a monotonic increasing function final size is observed, a function of the prevalence threshold P à , there is no optimal point P à that minimizes infection final size, Fig. 5c .