The numerical and programming methods used to implement models of the spread and impact of a major epidemic disease: pilchard herpesvirus, Australia 1995 and 1998/1999

Viral epidemics killed 60e75% of Australia’s pilchards in 1995 and again in 1998/1999. The spread and impact of these epidemics depended upon features with relevant spatial scales of centimetres to continental and time scales of minutes to years or decades. A suite of models was developed to analyse different aspects of the spread and impact of the epidemics. No single model had to describe all scales, but models of epidemic spread required resolution of features on scales of minutes to months and kilometers to continental scale. This paper details the approaches used to solve the numerical problems presented by attempts to model the epidemics and their impacts and the computer programs used to solve the numerical methods. A phase-duration model of infection required the development of numerically efficient ‘conveyer-belt’ implementation and a novel analytical solution of epidemic wave velocity. An existing age-structure model was adapted to simulate post-epidemic recovery. The potential for management of the epidemics, in the light of modelling results, is discussed.