A point pattern model of the spread of foot-and-mouth disease.
The spatial spread of foot-and-mouth disease (FMD) is influenced by several sources of spatial heterogeneity: heterogeneity of the exposure to the virus, heterogeneity of the animal density and heterogeneity of the networks formed by the contacts between farms. A discrete space model assuming that farms can be reduced to points is proposed to handle these different factors. The farm-to-farm process of transmission of the infection is studied using point-pattern methodology. Farm management, commercial exchanges, possible airborne transmission, etc. cannot be explicitly taken into account because of lack of data. These latter factors are introduced via surrogate variables such as herd size and distance between farms. The model is built on the calculation of an infectious potential for each farm. This method has been applied to the study of the 1967-1968 FMD epidemic in UK and allowed us to evaluate the spatial variation of the probability of infection during this epidemic. Maximum likelihood estimation has been conducted conditional on the absence of data concerning the farms which were not infected during the epidemic. Model parameters have then been tested using an approximated conditional-likelihood ratio test. In this case study, results and validation are limited by the lack of data, but this model can easily be extended to include other information such as the effect of wind direction and velocity on airborne spread of the virus or the complex interactions between the locations of farms and the herd size. It can also be applied to other diseases where point approximation is convenient. In the context of an increase of animal density in some areas, the model explicitly incorporates the density and known epidemiological characteristics (e.g. incubation period) in the calculation of the probability of FMD infection. Control measures such as vaccination or slaughter can be simply introduced, respectively, as a reduction of the susceptible population or as a reduction of the source of infection.