Stochastic host-parasite interaction models

Journal of Mathematical Biology

Volumn 40, Issue 4, 2000, Pages 343-371

  Herbert, Julian ^a   Isham, Valerie ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Epidemic model; Helminths; Macroparasites; Moment closure approximations; Multivariate negative binomial distribution; Parasite induced mortality

Indexed keywords

ANIMAL; ANIMAL PARASITOSIS; ARTICLE; BINOMIAL DISTRIBUTION; BIOLOGICAL MODEL; COMPARATIVE STUDY; DRUG RESISTANCE; HELMINTH; HOST PARASITE INTERACTION; IMMUNOLOGY; PARASITOLOGY; POISSON DISTRIBUTION; PROBABILITY; SHEEP; SHEEP DISEASE; STATISTICAL MODEL;

ANIMALS; BINOMIAL DISTRIBUTION; DRUG RESISTANCE; HELMINTHIASIS, ANIMAL; HELMINTHS; HOST-PARASITE RELATIONS; LINEAR MODELS; MARKOV CHAINS; MODELS, BIOLOGICAL; POISSON DISTRIBUTION; SHEEP; SHEEP DISEASES;

EID: 0034168871     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850050184     Document Type: Article

References (29)

1. Adler, F. and Kretzschmar, M. (1992), Aggregation and stabilty in parasite-host models, Parasitology 104, 199-205
2. Anderson, R. and Gordon, D. (1982), Processes influencing the distribution of parasite numbers within host populations with special emphasis on parasite-induced host mortalities, Parasitology 85, 373-398
3. Anderson, R. and May, R. (1978), Regulation and stability of host-parasite population interactions. I. Regulatory processes, J. Animal Ecology 47, 219-247
4. Anderson, R. and May, R. (1985), Helminth infections of humans: Mathematical models, populations dynamics and control, Advances in Parasitology 24, 1-101
5. Anderson, R. and May, R. (1991), Infectious Diseases of Humans: Dynamics and Control, OUP, Oxford
6. Barbour, A. and Kafetzaki, M. (1993), A host-parasite model yielding heterogeneous parasite loads, J. Math. Biol. 31, 157-176
7. Barbour, A., Heesterbeek, J. and Luchsinger, C. (1996), Threshold and initial growth rates in a model of parasitic infection, Ann. Appl. Prob. 6, 1045-1074
8. Chan, M. S. and Isham, V. (1998), A stochastic model of schistosomiasis immuno-epidemiology, Math. Biosciences 151, 179-198
9. Grenfell, B., Dietz, K. and Roberts, M. (1995a), Modelling the immuno-epidemiology of macroparasites in wildlife host populations, in B. Grenfell and A. Dobson, eds, Ecology of Infectious Diseases in Natural Populations, CUP, Cambridge
10. 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
11. Isham, V. (1993), Stochastic models for epidemics with special reference to AIDS, Ann. Appl. Prob. 3, 1-27
12. Isham, V. (1995), Stochastic models of host-macroparasite interaction, Ann. Appl. Prob. 5, 720-740
13. Johnson, N., Kotz, S. and Balakrishnan, N. (1997), Discrete Multivariate Distributions, Chapman and Hall, London
14. Kretzschmar, M. (1989a), A renewal equation with a birth-death process as a model for parasitic infections, J. Math. Biol. 27, 191-221
15. Kretzschmar, M. (1989b), Persistent solutions in a model for parasitic infections, J. Math. Biol. 27, 549-573
16. Kretzschmar, M. (1993), Comparison of an infinite dimensional model for parasitic diseases with a related 2-dimensional system, J. Mathematical Analysis and Applications 176, 235-260
17. Kretzschmar, M. and Adler, F. (1993), Aggregated distributions in models for patchy populations, Theoretical Population Biology 43, 1-30
18. Michael, E., Grenfell, B., Isham, V., Denham, D. and Bundy, D. (1998), Modelling variability in lymphatic filariasis: macrofilarial dynamics in the brugia pahangi cat model, Proceedings of the Royal Society of London Series B - Biological Sciences 265, 155-165
19. Nåsell, I. (1985), Hybrid Models of Tropical Infections, number 59 in Lecture Notes in Biomathematics, Springer, Berlin
20. Patil, G. G. and Joshi, S. W. (1968), A Dictionary and Bibliography of Discrete Distributions, Oliver and Boyd Ltd, Edinburgh
21. Pugliese, A., Rosa, R. and Damaggio, M. (1998), Analysis of a model for macroparasite infection with variable aggregation and clumped input, J. Mathematical Biology 36 S2, 419-447
22. Quinnell, R., Grafen, A. and Woolhouse, M. (1995), Changes in parasite aggregation with age: a discrete infection model, Parasitology 111, 635-644
23. Shaw, D. (1994), Distributions of macroparasites in naturally-fluctuating host populations, PhD thesis, University of Cambridge
24. Shaw, D. and Dobson, A. (1995), Patterns of macroparasite abundance and aggregation in wildlife populations: a quantitative review, Parasitology 111, S111-S133
25. Smith, G., Grenfell, B. T., Isham, V. and Cornell, S. (1999), Anthelmintic resistance revisited: under-dosing, chemoprophylactic strategies, and mating probabilities., Int. J. Parasitology 29, 77-91
26. Tallis, G. and Leyton, M. (1966), A stochastic approach to the study of parasite populations, J. Theor. Biol. 13, 251-260
27. Tallis, G. and Leyton, M. (1969), Stochastic models of populations of helminthic parasites in the definitive host. I, Math. Biosciences 4, 39-48
28. Whittle, P. (1957), On the use of the normal approximation in the treatment of stochastic processes, J. R. Statist. Soc. B19, 268-281
29. Woolhouse, M. E. J. (1995), The interpretation of immunoepidemiological data for helminth infections, in V. Isham and G. Medley, eds, Models for Infectious Human Diseases: their Structure and Relation to Data, CUP, Cambridge