Abstract
An S→I→S epidemic transmitted by two similar strains of parasite acting on a host population of three genotypes which differ in their reaction to the disease is modelled and analyzed. Singular perturbation techniques are used to reduce the original system of nine differential equations to a coupled system of two equations describing the slowtime coevolution of gene frequency and parasite strain frequency.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Anderson, R. M., May R. M.: Coevolution of hosts and parasites, Preprint
Beck, K. C., Keener, J. P., Ricciardi, P.: The effect of epidemics on genetic evolution. J. Math. Biol. (1983)
Gillespie, J. H.: Natural selection for resistance to epidemics. Ecology 56, 493–495 (1975)
Hoppensteadt, F. C.: Singular perturbations on the infinite interval. Trans. Amer. Math. Soc. 123, 521–535 (1966)
Kemper, J. T.: The evolutionary effect of endemic infectious disease. Preprint
Levin, S. A.: Some approaches to the modelling of coevolutionary interactions. Coevolution. Chicago: U. Chicago Press, in press
Levin, S. A., Pimental, D.: Selection of intermediate rates of increase in parasite-host systems. Am. Nat. 117, 308–315 (1981)
Levin, S. A., Udovic, J. D.: A mathematical model of coevolving populations. Am. Nat. 111, 657–675 (1977)
Lewis, J. W.: On the coevolution of pathogen and host, in two parts. J. Theoret. Biology 93 927–985 (1981)
Saunders, I. W.: Epidemics in competition. J. Math. Biol. 11, 311–318, (1981)
Author information
Authors and Affiliations
Additional information
Karen Christine Beck died June 25, 1983 at home.
Born February 8, 1952 in Madison, Wisconsin, She received a B.A. degree in 1974 from Luther College, Decorah, Iowa and a Ph.D. in mathematics in 1980 from the University of Iowa. Since that time she has been an instructor in the Mathematics Department at the University of Utah. She was to become an Assistant Professor at the University of Texas, Arlington, beginning Autumn, 1983. Dr. Beck's areas of specialization in mathematics were Mathematical Analysis and Mathematical Biology. She published numerous research articles that resolved various problems in these areas.
Rights and permissions
About this article
Cite this article
Beck, K. Coevolution: Mathematical analysis of host-parasite interactions. J. Math. Biology 19, 63–77 (1984). https://doi.org/10.1007/BF00275931
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00275931