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Mathematics 2018, 6(9), 143; https://doi.org/10.3390/math6090143

A Within-Host Stochastic Model for Nematode Infection

1
Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Calle Nicolás Cabrera 13-15, 28049 Madrid, Spain
2
Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds LS2 9JT, UK
*
Author to whom correspondence should be addressed.
Received: 25 June 2018 / Revised: 6 August 2018 / Accepted: 11 August 2018 / Published: 21 August 2018
(This article belongs to the Special Issue Stochastic Processes with Applications)
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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. View Full-Text
Keywords: host-parasite interaction; nematode infection; nonhomogeneous Poisson process; seasonal environment; Strang–Marchuk splitting approach host-parasite interaction; nematode infection; nonhomogeneous Poisson process; seasonal environment; Strang–Marchuk splitting approach
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Gómez-Corral, A.; López-García, M. A Within-Host Stochastic Model for Nematode Infection. Mathematics 2018, 6, 143.

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