Degree distribution dynamics for disease spreading with individual awareness

Abstract

Behavioral responses triggered by the perceived risk of experiencing the disease represent a key ingredient in the spread of epidemics across human population. In this paper, two forms of individual awareness (i.e., the risk perception of an emerging epidemic) are addressed: Contact awareness that increases with individual contact number, and local awareness that increases with the fraction of infected contacts. By extending the probability generating functionology, the author shows that it is possible to track the evolution of the degree distributions among susceptible and infected individuals when the underlying network of contacts is represented by a semi-random configuration model. It is hopefully to shed some light on the dynamic aspects of networked epidemiological models.