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

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

At any given time t, a person k is classified as susceptible, S k ðtÞ, infected, I k ðtÞ, or recovered, R k ðtÞ, to the disease under consideration. Disease risk awareness among susceptible individuals spreads after public health officials make the deliberate decision to stress vigorously the risk of infection, as it may be the case under an influenza epidemic or other health emergency. The model assumes that the decision to promote risk prevention starts once a pre-determined prevalence level P à , at time t à , has been reached. Health authorities start to spread information about a pathogen's outbreak, information that gets communicated by those individuals, actively aware, in the network, with different degrees of efficiency. The spread of information is a function of chance (probability model) and economical/educational level. The state of active informationcommunicator is assumed to be temporary, with individuals moving into a"passive" state, indifferent, after a short period of time. Before time t à every susceptible individual is unaware of the information campaigns but for times s > t à , members of S k ðsÞ may change status from unaware (S u k ðsÞ) to aware (S a k ðsÞ), then moving, with some probability, into the indifferent class (S i k ðsÞ).