On Macdonald's model for schistosomiasis

Abstract

An attempt is made to reconstruct the specifics of the model in Macdonald's 1965 paper based on some manuscripts. The resulting model is not conclusive as discrepancies occur between this formulation and Macdonald's results. Assuming the formulation is adequate, the values of parameters yielding Macdonald's standard situation are provided. A way of studying the equilibrium behaviour of the model is outlined. The mathematical nature of the properties observed by Macdonald is studied. The model is altered to admit aggregated distributions of worms in hosts and to permit different death rates of infected and uninfected snails. The dynamics are found to depend strongly on the death rate of infected snails.