Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T10:09:27.662Z Has data issue: false hasContentIssue false
  • English
  • Français

A study of the role of the transmission mechanism in macroparasite aggregation

Part of: Markov processes Applications

Published online by Cambridge University Press:  14 July 2016

Julian Herbert  and
Valerie Isham
Julian Herbert*
Affiliation:
University College, London
Valerie Isham*
Affiliation:
University College, London
*
1Postal address: Department of Statistical Science, University College, London, UK. Email: [email protected]
1Postal address: Department of Statistical Science, University College, London, UK. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The dynamics of host-macroparasite infections pose considerable challenges for stochastic modelling because of the need to take into account a large number of relevant factors and many nonlinear interactions between them. This paper focuses attention on the infection transmission process and the effects of specific modelling assumptions about the mechanisms involved. Some dramatically simplified linear models are considered; they are based on multidimensional linear birth and death processes, and are designed to illuminate qualitative effects of interest. Both single and compound infections are allowed. It is shown that such simple models can generate and increase dispersion of parasite counts, even among homogeneous hosts.

Keywords

Aggregationbirth-death processescompound infectionsepidemic modelsmacroparasitesmultidimensional branching processesoverdispersiontransmission dynamics

MSC classification

Primary: 62P10: Applications to biology and medical sciences
Secondary: 60J85: Applications of branching processes 92D30: Epidemiology
Type
Other stochastic models
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 249 - 262
Copyright
Copyright © Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adke, S. (1964). Multi-dimensional birth and death processes. Biometrics 20, 212–216.CrossRefGoogle Scholar
Adler, F. and Kretzschmar, M. (1992). Aggregation and stability in parasite-host models. Parasitology 104, 199–205.CrossRefGoogle ScholarPubMed
Anderson, R. and May, R. (1978). Regulation and stability of host-parasite population interactions, I: Regulatory processes. J. Animal Ecology 47, 219–247.CrossRefGoogle Scholar
Anderson, R. and May, R. (1985). Helminth infections of humans: mathematical models, population dynamics and control. Adv. Parasitology 24, 1–101.CrossRefGoogle ScholarPubMed
Anderson, R. and May, R. (1991). Infectious Diseases of Humans: Dynamics and Control. Oxford University Press.CrossRefGoogle Scholar
Barbour, A. and Kafetzaki, M. (1993). A host-parasite model yielding heterogeneous parasite loads. J. Math. Biol. 31, 157–176.Google Scholar
Barbour, A., Heesterbeek, J. and Luchsinger, C. (1996). Threshold and initial growth rates in a model of parasitic infection. Ann. Appl. Probab. 6, 1045–1074.CrossRefGoogle Scholar
Damaggio, M. and Pugliese, A. (1996). The degree of aggregation of parasite distributions in epidemic models. Z. Angew. Math. Mech. 76 S2, 425–428.Google Scholar
Grenfell, B., Dietz, K. and Roberts, M. (1995a). Modelling the immuno-epidemiology of macroparasites in wildlife host populations. In Ecology of Infectious Diseases in Natural Populations , eds Grenfell, B. and Dobson, A., Cambridge University Press, 362–383.CrossRefGoogle Scholar
Grenfell, B., Wilson, K., Isham, V., Boyd, H. and Dietz, K. (1995b). Modelling patterns of parasite aggregation in natural populations: trichostrongylid nematode-ruminant interactions as a case study, Parasitology 111, S135–S151.CrossRefGoogle ScholarPubMed
Herbert, J. (1998). Stochastic Processes for Parasite Dynamics. PhD Thesis, University of London.Google Scholar
Herbert, J. and Isham, V. (2000). Stochastic host-parasite population models, J. Math. Biol. 40, 343–371.CrossRefGoogle Scholar
Hudson, P. and Dobson, A. (1995). Macroparasites: observed patterns. In Ecology of Infectious Diseases in Natural Populations , eds Grenfell, B. and Dobson, A., Cambridge University Press, 144–176.CrossRefGoogle Scholar
Isham, V. (1995). Stochastic models of host-macroparasite interaction. Ann. Appl. Probab. 5, 720740.Google Scholar
Kretzschmar, M. (1989). A renewal equation with a birth-death process as a model for parasitic infections. J. Math. Biol. 27, 191–221.CrossRefGoogle Scholar
Kretzschmar, M. and Adler, F. (1993). Aggregated distributions in models for patchy populations. Theor. Pop. Biol. 43, 1–30.CrossRefGoogle ScholarPubMed
Mode, C. (1962). Some multi-dimensional birth and death processes and their applications in population genetics. Biometrics 18, 543–567.CrossRefGoogle Scholar
Nasell, I. (1985). Hybrid Models of Tropical Infections (Lecture Notes in Biomathematics 59). Springer, Berlin.CrossRefGoogle Scholar
Pugliese, A., Rosa, R. and Damaggio, M. L. (1998). Analysis of a model for macroparasitic infection with variable aggregation and clumped infections. J. Math. Biol. 36, 419–447.Google Scholar
Roberts, M. (1995). A pocket guide to host-parasite models. Parasitology Today ll, 383–391.CrossRefGoogle Scholar
Roberts, M., Smith, G. and Grenfell, B. (1995). Mathematical models for macroparasites of wildlife. In Ecology of Infectious Diseases in Natural Populations , eds Grenfell, B. and Dobson, A., Cambridge University Press, 177–208.CrossRefGoogle Scholar
Shanbhag, D. (1972). On a vector valued birth and death process. Biometrics 28, 417–425.CrossRefGoogle ScholarPubMed
Shaw, D. (1994). Distributions of Macroparasites in Naturally-fluctuating Host Populations. PhD Thesis, University of Cambridge.Google Scholar
Shaw, D. and Dobson, A. (1995). Patterns of macroparasite abundance and aggregation in wildlife populations: a quantitative review. Parasitology 111, S111–S133.CrossRefGoogle ScholarPubMed
Tallis, G. and Leyton, M. (1966). A stochastic approach to the study of parasite populations. J. Theor. Biol. 13, 251–260.CrossRefGoogle Scholar
Tallis, G. and Leyton, M. (1969). Stochastic models of populations of helminthic parasites in the definitive host, I. Math. Biosciences 4, 39–48.Google Scholar
Wassom, D., Dick, T., Arnason, N., Strickland, D. and Grundmann, A. (1986). Host genetics: a key factor in regulating the distribution of parasites in natural host populations. J. Parasitology 72, 334–337.CrossRefGoogle ScholarPubMed
Woolhouse, M. E. J. (1995). The interpretation of immunoepidemiological data for helminth infections. In Models for Infectious Human Diseases: Their Structure and Relation to Data , eds Isham, V. and Medley, G., Cambridge University Press, 200–203.Google Scholar