State-scale and premises-scale gravity models for the spread of highly pathogenic avian influenza (H5N1) in Nigeria and Ghana were used to provide a basis for risk maps for future epidemics and to compare and rank plausible culling and vaccination strategies for control. Maximum likelihood methods were used to fit the models to the 2006–2007 outbreaks. The sensitivity and specificity of the state-scale model-generated probabilities that any given state would be involved in an epidemic were each 57 %. The premises-based model indicated that reactive, countrywide vaccination strategies, in which the order in which flocks are vaccinated was strictly determined by known risk factors for infection, were more effective in reducing the final size of the epidemic and the epidemic impact than vaccinating flocks at random or ring vaccination. The model suggests that an introduction of highly pathogenic avian influenza (H5N1) into Ghana had a high chance (84 %) of causing a major outbreak. That this did not happen was most probably a result of the very swift Ghanaian response to news of the first introductions.

A stochastic, spatial, discrete-time, SEIR model of avian influenza epidemics among poultry farms in Pennsylvania is formulated. Using three different spatial scales wherein all the birds within a single farm, ZIP code, or county are clustered into a single point, we obtain three different views of the epidemics. For each spatial scale, two parameters within the viral-transmission kernel of the model are estimated using simulated epidemic data. We show that simulated epidemics modeled using data collected on the farm and ZIP-code levels behave similar to the actual underlying epidemics, but this is not true using data collected on the county level. Such analyses of data collected on different spatial scales are useful in formulating intervention strategies to control an ongoing epidemic (e.g., vaccination schedules and culling policies).

SUMMARY We formulate a stochastic, spatial, discrete-time model of viral “Susceptible, Exposed, Infectious, Recovered” animal epidemics and apply it to an avian influenza epidemic in Pennsylvania in 1983–84. Using weekly data for the number of newly infectious cases collected during the epidemic, we find estimates for the latent period of the virus and the values of two parameters within the transmission kernel of the model. These data are then jackknifed on a progressive weekly basis to show how our estimates can be applied to an ongoing epidemic to generate continually improving values of certain epidemic parameters.

Three different estimators are presented for the types of parameters present in mathematical models of animal epidemics. The estimators make use of data collected during an epidemic, which may be limited, incomplete, or under collection on an ongoing basis. When data are being collected on an ongoing basis, the estimated parameters can be used to evaluate putative control strategies. These estimators were tested using simulated epidemics based on a spatial, discrete-time, gravity-type, stochastic mathematical model containing two parameters. Target epidemics were simulated with the model and the three estimators were implemented using various combinations of collected data to independently determine the two parameters.