Figure 1.

Probabilistic model for the spread of influenza within a social network, using a ‘S-I-R’ (susceptible-infected-recovered) schema. (i) Each day is considered as a collection of nodes that represent the patients in the hospital on that day. Individual patients are either infected, or not infected (one of ‘Susceptible’ or ‘Recovered’), and transition between states based on their state at the previous time step, as well as the state of their incoming nodes, connected by either room-sharing or healthcare workers-sharing links. (ii) The infected state is divided into sub-states (I₁ through I_D) that reflect the number of days remaining during which the patient is infectious. Patient transitions between the various states are governed by the probabilities shown. L_i,t is the set of incoming links for patient i on day t. j_ℓ is the source patient of link ℓ. I_i,t is a binary variable indicative of infection, where I_i,t=1 (infected) if q_i,t∈{I₁, … ,I_D}, and 0 (not infected) if q_i,t∈{S,R}. q_∗,t denotes the set of states for all patients on day t. Solid arrows represent deterministic transitions, while dashed arrows represent probabilistic transitions (see text for details). HCW, healthcare worker.