A Spatial SIRS Boolean Network Model for the Spread of H5N1 Avian Influenza Virus among Poultry Farms

To predict the spread of Avian Influenza we propose a synchronous Susceptible-Infected-Recovered-Susceptible (SIRS) Boolean network of poultry farms, using probabilistic Boolean rules. Gravity models from transportation theory are used for the probability of infection of a node in one time step, taking into account farm sizes, distances between farms, and mean distance travelled by birds. Basic reproduction numbers are computed analytically and numerically. The dynamics of the network are analyzed and various statistics considered such as number of infected nodes or time until eradication of the epidemic. We conclude that mostly when large farms (eventually) become infected the epidemic is more encompassing, but for a farm that does not have a very large poultry population, the epidemic could be contained.