Abstract
We propose a stochastic model for the development of gastrointestinal nematode infection in growing lambs under the assumption that nonhomogeneous Poisson processes govern the acquisition of parasites, the parasite-induced host mortality, the natural (no parasite-induced) host mortality and the death of parasites within the host. By means of considering a number of age-dependent birth and death processes with killing, we analyse the impact of grazing strategies that are defined in terms of an intervention instant t 0 , which might imply a move of the host to safe pasture and/or anthelmintic treatment. The efficacy and cost of each grazing strategy are defined in terms of the transient probabilities of the underlying stochastic processes, which are computed by means of Strang–Marchuk splitting techniques. Our model, calibrated with empirical data from Uriarte et al and Nasreen et al., regarding the seasonal presence of nematodes on pasture in temperate zones and anthelmintic efficacy, supports the use of dose-and-move strategies in temperate zones during summer and provides stochastic criteria for selecting the exact optimum time instant t 0 when these strategies should be applied.
Highlights
Gastrointestinal (GI) nematodes are arguably the major cause of ill health and poor productivity in grazing sheep worldwide, especially in young stock
We develop a mathematical model for the within-host GI nematode infection dynamics, to compare the effectiveness and cost of various worm control strategies, which are related to pasture management practices and/or strategic treatments based on the use of a single anthelmintic drug
The efficacy and cost of each grazing strategy are defined in terms of the transient probabilities of each of the underlying stochastic processes; that is, the probability that the parasite load of the infected host is at any given level at each time instant, given that a particular control strategy has been applied at the intervention instant t0
Summary
Gastrointestinal (GI) nematodes are arguably (see [1,2]) the major cause of ill health and poor productivity in grazing sheep worldwide, especially in young stock. We develop a mathematical model for the within-host GI nematode infection dynamics, to compare the effectiveness and cost of various worm control strategies, which are related to pasture management practices and/or strategic treatments based on the use of a single anthelmintic drug. The efficacy and cost of each grazing strategy are defined in terms of the transient probabilities of each of the underlying stochastic processes; that is, the probability that the parasite load of the infected host is at any given level at each time instant, given that a particular control strategy has been applied at the intervention instant t0.
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