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

Understanding individual decisions in a world where communications and information move instantly via cell phones and the internet, contributes to the development and implementation of policies aimed at stopping or ameliorating the spread of diseases. In this manuscript, the role of official social network perturbations generated by public health officials to slow down or stop a disease outbreak are studied over distinct classes of static social networks. The dynamics are stochastic in nature with individuals (nodes) being assigned fixed levels of education or wealth. Nodes may change their epidemiological status from susceptible, to infected and to recovered. Most importantly, it is assumed that when the prevalence reaches a pre-determined threshold level, P*, information, called awareness in our framework, starts to spread, a process triggered by public health authorities. Information is assumed to spread over the same static network and whether or not one becomes a temporary informer, is a function of his/her level of education or wealth and epidemiological status. Stochastic simulations show that threshold selection P* and the value of the average basic reproduction number impact the final epidemic size differentially. For the Erdős-Rényi and Small-world networks, an optimal choice for P* that minimize the final epidemic size can be identified under some conditions while for Scale-free networks this is not case.