## Individual based FMD model (page 274)

Individual-based models can encompass a wide range of model forms, and can be designed to include a variety of complex and detailed host behavior that could not be readily expressed within the other model types. As the name suggests, these models consider the dynamics of individuals that occupy a spatial landscape. As an additional example, we extend the SIR model (program 7.5) to the specific case of foot-and-mouth infection in the UK.  In this example, farms are the individual units and the transmission kernal is given by a polynomial function that fits the data. Each farm has an associated number of cattle and sheep which determine its susceptiblity to infection and the rate that it transmits infection once infectious. The rate at which a susceptible farm is infected is given by:

where the sum is over all infectious individuals (labelled j), dij is the distance between individuals i and j, and KT is the transmission kernel. Sus and Trans measure the susceptiblity and transmissibility of individual farms, governed by the number of livestock of each species Ni,l and the species specific characteristics. Ni,l is log-normally distributed to match the UK livestock census data.
In order to capture more realism, the infectious status of farms is assumed to be determined by the time since infection; hence farms spend exactly 5 days in the exposed class and 6 days in the infectious class. Farms report infection on day 10 and are culled on day 12; on day 13 ring culling around infected farms takes place.

Parameters
 Size is the length of the 2-D square in which simulations take place, measured in kilometers N is the population size, randomly distributed in 2-D sl is the susceptiblity of species l. ssheep = 1, scow = 10.5 tl is the transmissiblity of species l. tsheep = 5.1 × 10-7, tcow = 7.7 × 10-7 Ring is the size of the ring cull (in km) around each reported farm. Y(0) is the number of initially infected individuals
All rates are specified in days.

Requirements.
All parameters must be positive.

Files
MATLAB 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