A model of transmission of a viral epidemic among schools within a shoal of pilchards

Abstract

Populations of animals are not uniformly distributed in space, but exhibit a variety of levels of organisation. The structure of this organisation has major implications for the interactions of animals, including the transmission of diseases. For example, clupeoid fishes form large shoals that subdivide into schools. Pilchards are forage fish that dominate the link in the food chain between plankton (both zoo- and phyto-) and larger fish, birds and mammals. In 1995, and again in 1998/1999, epidemics of a herpesvirus reduced stocks of Australian pilchards along 5000 km of coastline by up to 70%. As a part of a suite of studies into these phenomena, we have developed a model of the effect of the subdivision of shoals of the pilchard into schools on the transmission of this disease. Subdividing the population into schools can reduce the rate of transmission of infection. It may also make transmission rate independent of the shoal's population. However, viral transmission at the shoal level is shown to be only weakly sensitive to the details of local mixing processes between schools at realistic mixing rates. Schools do not serve as refuges to avoid the epidemic nor do they disrupt its large (hundreds to thousands of kilometres) scale spread. We can incorporate schooling into epidemic models simply by reducing the transmission rate by the number of schools in the shoal. Since we estimate infection transmission rate from the rate of spread of disease at large scale, we are implicitly already doing this in models without a schooling structure.