Abstract
In recent years our understanding of the processes which control and influence the dynamics of animal populations and lead to their often observed stability and resilience, has in certain areas been enhanced by theoretical studies of a mathematical nature (May, 1973).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anderson, R. M. (1974): “Mathematical models of the host — helminth parasite interactions” Ecological stability (Ed. by M. B. Usher and M. H. Williamson) pp 43–69 Chapman and Hall, London.
Anderson, R. M. and Whitfield, P. J. (1975): Survival characteristics of the free- living cercarial population of the ectoparasitic digenean Transversotrema patialensis. (Soparker, 1924). Parasitology 70, 295–310.
Anderson, R. M., Whitfield, P. J. and Wills, C. A. (1976): Experimental population dynamics of the ectoparasitic digenean Transversotrema patialense on the fish host Brachydanio rerio. In preparation.
Bailey, N. T. J. (1957): The mathemati cal theory of epidemics Griffin, London.
Boray, J. C. (1969): Experimental fascioliasis in Australia. Advances in Parasitology, 7, 96–210.
Bradley, D. J. (1971): Inhibition of Leishmanis donovani reproduction during chronic infections in mice. Trans. R. Soc. Trop. filed. Hyg. 65, 17–18.
Cohen, J. E. (1973a): Selective host mortality in a catalytic model applied to Schistosomiasis, Am. Natur., 107, 199–212.
Cohen, J. E. (1973b): Heterologous immunity in human malaria. Quant. Rev. Biol. 48, 467–489.
Cox, F. E. G. (1975): Enhanced Trypanosoma musculi infections in mice with concomitant malaria. Nature, 258, 148–149.
Crofton, H. D. (1971a): A quantitive approach to parasitism. Parasitology, 62, 179–193.
Crofton, H. D. (1971b): A model of host — parasite relation-ships. Parasitology, 63, 343–364.
Dietz, K., (1967): Epidemics and rumours: A survey. J. Roy. Statist. Soc. Ser. A, 130, 505–528.
Dietz, K., Molineaux, L. and Thomas, A. (1974): A malaria model tested in the African savannah. Bull. Wld. Hlth. Org. 50, 347–357.
Goffman, W. and Warren, K. 5. (1970): An application of the Kermack — McKendrick theory to the epidemiology of Schistosomiasis. Am. J. Trop. Wed,. Hyg. 19, 278–283.
Gray, A. R. (1962): The influence of antibody on serological variation in Trypanosoma brucei. Ann. Trop. Med. Parasit.56, 4–13.
Greenwood, M. and Yule, G. U. (1920): An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurence of multiple attacks of disease or of repeated accidents. J. Roy. Stat. Soc. 83, 255
Hockley, D. J. and McLaren, D. J. (1972): Schistosoma mansoni; changes in the outer membrane of the tegument during development from cercariae to adult worm. Int. J. Parasit. 3, 13
Jarrett, E. E. E., Jarrett, W. F. H. and Urquhart, G. M. (1968): Quantitative studies on the kinetics of establishment and expulsion of intestinal nematode populations in susceptible and immune hosts, Nippostrongylus brasiliensis in the rat. Parasitology, 58, 625–639.
Jenkins, D. C. and Phillipson, R. F. (1971): The kinetics of repeated low — level infections of Nippostrongylus brasiliensjs in the rat. Parasitology, 62, 457–466.
Kostitzin, V. A. (1934), Symbiose, parasitisme et evolution. Hermann, Paris.
Leslie, P. H. and Gower, J. C. (1960): The properties of a stochastic model for the predator — prey type interaction between two species. Biometrika, 47, 219–234
Leyton, M. K. (1968): Stochastic models in populations of helminthic parasites in the definitive host. 11 — Sexual mating functions. Math. Biosci. 3, 413–9.
Lotka, A. J. (1925): Elements of physical Biology. Williams and Wilkins, Baltimore.
May, R. M. (1973): Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton.
May, R. M., Conway, G. R., Hassell, M. P. and Southwood, T. R. E. (1974): Time delays, density dependence and single species oscillations. J. Anim. Ecol. 47, 907–15.
Mcdonald, G. (1950): The analysis of infection rates in diseases in which superinfection occurs. Trop. Dis. Bull. 47, 907–915.
Mcdonald, G. (1957): The epidemiology and control of malaria Oxford University Press, London.
McKendrick, A. G. (1926): Application of mathematics to medical problems. Proc. Edinb. Math. Soc. 44, 98–130.
Michel, J. F. (1967): Regulation of egg output of populations of Ostertagia ostertagi. Nature, 215, 1001–1002.
Mulligan, W., Urquhart, G. M., Jennings, F. W. and Neilson, J. T. M. (1965): Immuno ogical studies of Nippostrongylus brasiliensis infections in the rat, the self- cure phenomenon. Expt. Parasit. 16, 341
Narain, B. (1965): Survival of the first stage larvae and infective larvae of Bunostomum trqnocephalum Rudolphi, 1808. Parasitology, 55, 551–558.
Nassell, I. and Hirsch, W. M. (1972): A mathemati al model of some helminthic infections. Com. Pure Appl. Math. 25, 459–77.
Nassell, I. and Hirsch, W. M. (1973): The transmission dynamics of Schistosomiasis. Com. Pure Appl. Math. 26, 359–453.
Nice, N. G. and Wilson, R. A. (1974): A study of the effect of temperature on the growth of Fasciola hepatica in Lymnaea truncatula Parasitology, 68, 47–56.
Ollerenshaw, C. B. (1971): Forecasting liver fluke disease in Englang and Wales 1958–1968, with a comment on the influence of climate on the incidence of the disease in some other countries. Vet. Med. Rev. 213, 289–312.
Omerod, W. E. (1973): The initial stages of infection with Trypanosoma lewisi: control of parasitaemia by the host. Immunity to protozoa (Eds. P. C. C. Garnham, A. E. Pierce and I. Roitt). pp 213 — Blackwell Scientific publications, Oxford.
Pan, C. T. (1965): Studies on the host parasite relationship between Schistosoma mansoni and the snail Australorbis glabratus. Am. J. Trop. Med. Hyg. 14, 931–976.
Pearl, R. and Read, L. J. (1920): On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proc. Nat. Acad. Sci. U. S. A. 6, 273–288.
Phillips, S. M., Reid, W. A., Bruce, J. I., Hedlund, K., Colvin, R. C., Campbell, R., Diggs, C. L. and Sedun, E. H. (1975): The cellular and humoral immune response to Schistosoma mansoni infections in inbred rats. 1 Mechanisms during initial exposure. Cell Immun. 19, 99–116.
Pielou, E. C. (1969): An Introduction to Mathematical Ecology, Wiley Interscience, New York.
Rose, J. H. (1956): The bionomics of the free living larvae of Dictyocaulus viviparous. J. Comp. Path. Ther. 66, 228–240.
Smithers, S. R., Terry, R. J. and Hockley, D. J. (1969): Host antigens in Schistosomiasis. Proc. Roy. Soc. 171, 483
Tallis, G. M. and Leyton, M. (1969): Stochastic nodels of populations of helminthic parasites in the definitive host — 1 Math. Biosci. 4, 39–48.
Viens, P., Targett, G. A. T., Leuchars, E. and Davies, A. J. S. (1974): The immunological response of mice to Trypanosoma musculi 1. Initial control of the infection and the effect of T- cell deprivation. Clin. Exp. Immunol. 16, 279–294.
Wakelin, D. (1975): Genetic control of immune responses to parasitic infections of Trichuris muris in inbred and random bred strains of mice. Parasitology, 71, 5V–60.
Wangersky, P. J. and Cunningham, W. J. (1956): On time lags in equations of growth. Proc. nat. Acad. Sci. U.S.A. 42, 699–702.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1976 Springer-Verlag Berlin · Heidelberg
About this paper
Cite this paper
Anderson, R.M. (1976). Some Simple Models of the Population Dynamics of Eucaryotic Parasites. In: Berger, J., Bühler, W.J., Repges, R., Tautu, P. (eds) Mathematical Models in Medicine. Lecture Notes in Biomathematics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93048-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-93048-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07802-9
Online ISBN: 978-3-642-93048-5
eBook Packages: Springer Book Archive