A Within-Host Stochastic Model for Nematode Infection

dc.contributor.authorGómez-Corral, Antonio
dc.contributor.authorLópez-García, M.
dc.descriptionThis article belongs to the Special Issue Stochastic Processes with Applications
dc.description.abstractWe 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 t0, 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 (sub index 0) when these strategies should be applied.
dc.description.departmentDepto. de Estadística e Investigación Operativa
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.sponsorshipMinisterio de Economía y Competitividad (MINECO)
dc.identifier.citation1. Sutherland, I.; Scott, I. Gastrointestinal Nematodes of Sheep and Cattle. Biology and Control; Wiley-Blackwell: Chichester, UK, 2010. 2. Taylor, M.A.; Coop, R.L.; Wall, R.L. Veterinary Parasitology, 3rd ed.; Blackwell: Oxford, UK, 2007. 3. Bjørn, H.; Monrad, J.; Nansen, P. Anthelmintic resistance in nematode parasites of sheep in Denmark with special emphasis on levamisole resistance in Ostertagia circumcincta. Acta Vet. Scand. 1991, 32, 145–154. [PubMed] 4. Entrocasso, C.; Alvarez, L.; Manazza, J.; Lifschitz, A.; Borda, B.; Virkel, G.; Mottier, L.; Lanusse, C. Clinical efficacy assessment of the albendazole ivermectin combination in lambs parasited with resistant nematodes. Vet. Parasitol. 2008, 155, 249–256. [CrossRef] [PubMed] 5. Stear, M.J.; Doligalska, M.; Donskow-Schmelter, K. Alternatives to anthelmintics for the control of nematodes in livestock. Parasitology 2007, 134, 139–151. [CrossRef] [PubMed] 6. Hein, W.R.; Shoemaker, C.B.; Heath, A.C.G. Future technologies for control of nematodes of sheep. N. Z. Vet. J. 2001, 49, 247–251. [CrossRef] [PubMed] 7. Knox, D.P. Technological advances and genomics in metazoan parasites. Int. J. Parasitol. 2004, 34, 139–152. [CrossRef] [PubMed] 8. Sayers, G.; Sweeney, T. Gastrointestinal nematode infection in sheep—A review of the alternatives to anthelmintics in parasite control. Anim. Health Res. Rev. 2005, 6, 159–171. [CrossRef] [PubMed] 9. Waller, P.J.; Thamsborg, S.M. Nematode control in ‘green’ ruminant production systems. Trends Parasitol. 2004, 20, 493–497. [CrossRef] [PubMed] 10. Smith, G.; Grenfell, B.T.; Isham, V.; Cornell, S. Anthelmintic resistance revisited: Under-dosing, chemoprophylactic strategies, and mating probabilities. Int. J. Parasitol. 1999, 29, 77–91. [CrossRef] 11. Praslicka, J.; Bjørn, H.; Várady, M.; Nansen, P.; Hennessy, D.R.; Talvik, H. An in vivo dose-response study of fenbendazole against Oesophagostomum dentatum and Oesophagostomum quadrispinulatum in pigs. Int. J. Parasitol. 1997, 27, 403–409. [CrossRef] 12. Coles, G.C.; Roush, R.T. Slowing the spread of anthelmintic resistant nematodes of sheep and goats in the United Kingdom. Vet. Res. 1992, 130, 505–510. [CrossRef] 13. Prichard, R.K.; Hall, C.A.; Kelly, J.D.; Martin, I.C.A.; Donald, A.D. The problem of anthelmintic resistance in nematodes. Aust. Vet. J. 1980, 56, 239–250. [CrossRef] [PubMed] 14. Anderson, R.M.; May, R.M. Infectious Diseases of Humans: Dynamics and Control; Oxford University Press: Oxford, UK, 1992. 15. Marion, G.; Renshaw, E.; Gibson, G. Stochastic effects in a model of nematode infection in ruminants. IMA J. Math. Appl. Med. Biol. 1998, 15, 97–116. [CrossRef] [PubMed] 16. Cornell, S.J.; Isham, V.S.; Grenfell, B.T. Stochastic and spatial dynamics of nematode parasites in farmed ruminants. Proc. R. Soc. B Biol. Sci. 2004, 271, 1243–1250. [CrossRef] [PubMed] 17. Roberts, M.G.; Grenfell, B.T. The population dynamics of nematode infections of ruminants: Periodic perturbations as a model for management. IMA J. Math. Appl. Med. Biol. 1991, 8, 83–93. [CrossRef] [PubMed] 18. Roberts, M.G.; Grenfell, B.T. The population dynamics of nematode infections of ruminants: The effect of seasonality in the free-living stages. IMA J. Math. Appl. Med. Biol. 1992, 9, 29–41. [CrossRef] [PubMed] 19. Allen, L.J.S. An Introduction to Stochastic Processes with Applications to Biology; Pearson Education: Hoboken, NJ, USA, 2003. 20. Gómez-Corral, A.; López García, M. Control strategies for a stochastic model of host-parasite interaction in a seasonal environment. J. Theor. Biol. 2014, 354, 1–11. [CrossRef] [PubMed] 21. Abbott, K.A.; Taylor, M.; Stubbings, L.A. Sustainable Worm Control Strategies for Sheep, 4th ed.; A Technical Manual for Veterinary Surgeons and Advisers; SCOPS: Worcestershire, UK, 2012. Available online: (accessed on 1 June 2018). 22. Uriarte, J.; Llorente, M.M.; Valderrábano, J. Seasonal changes of gastrointestinal nematode burden in sheep under an intensive grazing system. Vet. Parasitol. 2003, 118, 79–92. [CrossRef] [PubMed] 23. Faragó, I.; Havasi, A.; Horváth, R. On the order of operator splitting methods for time-dependent linear systems of differential equations. Int. J. Numer. Anal. Model. Ser. B 2011, 2, 142–154. 24. Nasreen, S.; Jeelani, G.; Sheikh, F.D. Efficacy of different anthelmintics against gastro-intestinal nematodes of sheep in Kashmir Valley. VetScan 2007, 2, 1. 25. Kassai, T. Veterinary Helminthology; Butterworth-Heinemann: Oxford, UK, 1999. 26. Barger, I.A. Genetic resistance of hosts and its influence on epidemiology. Vet. Parasitol. 1989, 32, 21–35. [CrossRef] 27. Barger, I.A.; Le Jambre, L.F.; Georgi, J.R.; Davies, H.I. Regulation of Haemonchus contortus populations in sheep exposed to continuous infection. Int. J. Parasitol. 1985, 15, 529–533. [CrossRef] 28. Dobson, R.J.; Waller, P.J.; Donald, A.D. Population dynamics of Trichostrongylus colubriformis in sheep: The effect of infection rate on the establishment of infective larvae and parasite fecundity. Int. J. Parasitol. 1990, 20, 347–352. [CrossRef] 29. Bailey, J.N.; Kahn, L.P.; Walkden-Brown, S.W. Availability of gastro-intestinal nematode larvae to sheep following winter contamination of pasture with six nematode species on the Northern Tablelands of New South Wales. Vet. Parasitol. 2009, 160, 89–99. [CrossRef] [PubMed] 30. Valderrábano, J.; Delfa, R.; Uriarte, J. Effect of level of feed intake on the development of gastrointestinal parasitism in growing lambs. Vet. Parasitol. 2002, 104, 327–338. [CrossRef] 31. Grennan, E.J. Lamb Growth Rate on Pasture: Effect of Grazing Management, Sward Type and Supplementation; Teagasc Research Centre: Athenry, Ireland, 1999.
dc.relation.projectID(MTM2014-58091-P and BES-2009-018747)
dc.rightsAtribución 3.0 España
dc.rights.accessRightsopen access
dc.subject.keywordHost-parasite interaction
dc.subject.keywordNematode infection
dc.subject.keywordNonhomogeneous Poisson process
dc.subject.keywordseasonal environment
dc.subject.keywordStrang–Marchuk splitting approach.
dc.subject.ucmMatemáticas (Matemáticas)
dc.subject.ucmEstadística aplicada
dc.subject.ucmProcesos estocásticos
dc.subject.ucmParasitología (Medicina)
dc.subject.unesco12 Matemáticas
dc.subject.unesco1208.08 Procesos Estocásticos
dc.subject.unesco3207.12 Parasitología
dc.subject.unesco2404 Biomatemáticas
dc.titleA Within-Host Stochastic Model for Nematode Infection
dc.typejournal article
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