 ## Pairwise SIS approximation model (page 285) The simplest form of a pair-based approximation model is used to capture disease spread through a network of contacts (see Section 7.6 of this chapter). In its most basic form, this pair-wise model assumes an equal number of contacts per individual and no clustering; this approximation therefore corresponds most closely to the random network, although adaptations that capture clustering or heterogeneities are possible.
The method operates by modelling the number of susceptible-infected pairs in the network as well as simply the number of individuals. In principle to calculate the behaviour of pairs we need to know about triples: where the arrows indicate the direction of transmission. However, by making a suitable approximation, we can formulate a set of equations that capture the spatial correlations due to network structure and yet only contain one extra state variable: Parameters
 n is the number of connections per individual in the population τ is the transmission rate across a contact γ is the recovery rate for infectious individuals [Y](0) is the  initial number of infected individuals in the population. Obviously [X](0)=N-[Y](0) [XY](0) is the initial number of X-Y pairs; we set [XY](0)=n[X][Y]/N N is the number of individuals in the population.

Requirements.
All parameters must be positive.

Files
Python ProgramMATLAB Code.

 Questions and comments to: M.J.Keeling@warwick.ac.uk or rohani@uga.edu Princeton University Press Our research web pages: Matt Keeling      Pejman Rohani