  The spread of an infectious disease depends on intrinsic properties of the
disease as well as the connectivity and actions of the population. This study
investigates the dynamics of an SIR type model which accounts for human
tendency to avoid infection while also maintaining preexisting, interpersonal
relationships. Specifically, we use a network model in which individuals
probabilistically deactivate connections to infected individuals and later
reconnect to the same individuals upon recovery. To analyze this network model,
a mean field approximation consisting of a system of fourteen ordinary
differential equations for the number of nodes and edges is developed. This
system of equations is closed using a moment closure approximation for the
number of triple links. By analyzing the differential equations, it is shown
that, in addition to force of infection and recovery rate, the probability of
deactivating edges and the average node degree of the underlying network
determine if an epidemic occurs.
