Abstract
A model has been formulated in [6] to describe the spatial spread of an epidemic involving n types of individual, and the possible wave solutions at different speeds were investigated. The final size and pandemic theorems are now established for such an epidemic. The results are relevant to the measles, host-vector, carrier-borne epidemics, rabies and diseases involving an intermediate host. Diseases in which some of the population is vaccinated, and models that divide the population into several strata are also covered.
Similar content being viewed by others
References
Diekmann, O.: Thresholds and travelling waves for the geographical spread of infection. J. Math. Biol. 6, 109–130 1978
Essén, M.: Studies on a convolution inequality. Ark Mat. 5, 113–152 (1963)
Gantmacher, F. R.: The theory of matrices, Vol. 2. New York: Chelsea 1959
Krasnosel'skii, M. A.: Positive solutions of operator equations. Groningen: Noordhoff 1964
Ostrowski, A. M.: Solutions of equations and systems of equations. New York: Academic Press 1966
Radcliffe, J., Rass, L.: Wave solutions for the deterministic non-reducible n-type epidemic. J. Math. Biol. 17, 45–66 (1983)
Radclifie, J., Rass, L.: The spatial spread of the deterministic host-vector epidemic. (To appear in Math. Biosciences.)
Thieme, H. R.: A model for the spread of an epidemic. J. Math. Biol. 4, 337–351 1977
Thieme, H. R.: The asymptotic behaviour of solutions of non-linear integral equations. Math. Z. 157, 141–154 (1977)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Radcliffe, J., Rass, L. The spatial spread and final size of the deterministic non-reducible n-type epidemic. J. Math. Biology 19, 309–327 (1984). https://doi.org/10.1007/BF00277102
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00277102