The spread of a parasitic infection in a spatially distributed host population (Q1184668)

The author studies a stochastic model for the spread of a parasitic disease in a spatially distributed host population and describes how one obtains a deterministic model in terms of a partial differential equation and an integro-differential equation in the limit when the size \(N_ h\) of the host population, the size \(N_ p\) of the parasite population, and the ratio \(N_ p/N_ h\) tend to infinity. The hosts are assumed to occupy fixed spatial positions and the parasites are mobile but can propagate within the hosts only. The paper is based on, and extends previous work of the author [Z. Wahrscheinlichkeitstheor. Verw. Geb. 69, 279-322 (1985; Zbl 0549.60071), Probab. Theory Relat. Fields 74, 591-616 (1987; Zbl 0592.60064), ibid. 82, 565-586 (1989; Zbl 0659.60134), and Ann. Probab. 18, 290-318 (1990; Zbl 0711.92014)]. A number of hints about possible extensions and modifications of the model are given.