Skip to main content
Log in

The uniqueness of wave solutions for the deterministic non-reducible n-type epidemic

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

In a recent paper, [8], we investigated the existence of wave solutions for a model of the deterministic non-reducible n-type epidemic. In this paper we first prove two properties left as an open question in that paper. The uniqueness of the wave solutions at all speeds for which a wave solution exists is then established. Only an exceptional case is not covered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Aronson, D. G.: The asymptotic speed of propagation of a simple epidemic. Fitzgibbon, W. E., Walker, H. F., (eds.) Nonlinear Diffusion. Research Notes in Mathematics vol.14, 1–23. London-San Francisco-Melbourne: Pitman 1977

    Google Scholar 

  2. Bochner, S., Martin, W. T.: Several complex variables. Princeton: Princeton University Press 1948

    Google Scholar 

  3. Diekmann, O.: Run for your life. A note on the asymptotic speed of propagation of an epidemic. J. Diff. Eq. 33, 58–73 (1979)

    Google Scholar 

  4. Dieudonné, J.: Foundations of modern analysis. New York: Academic Press 1969

    Google Scholar 

  5. Kingman, J.F.C.: A convexity property of positive matrices. Q. J. Math. Oxford (2) 12, 283–284 (1961)

    Google Scholar 

  6. Lui, R.: A nonlinear integral operator arising from a model in population genetics, 1. Monotone initial data. Siam J. Math. Anal. 13 (No. 6), 913–937 (1982)

    Google Scholar 

  7. Miller, H. D.: A convexity property in the theory of random variables denned on a finite Markov chain. Ann. Math. Stat. 32, 1260–1270 (1961)

    Google Scholar 

  8. Radcliffe, J., Rass, L.: Wave solutions for the deterministic non-reducible n-type epidemic. J. Math. Biol. 7, 45–66 (1983)

    Google Scholar 

  9. Radcliffe, J., Rass, L.: Saddle point approximations in n-type epidemics and contact birth processes. (To appear in the Rocky Mountain Journal of Mathematics)

  10. Radcliffe, J., Rass, L., Stirling, W. D.: Wave solutions for the deterministic host-vector epidemic. Math. Proc. Cambridge Philos. Soc. 91, 131–152 (1982)

    Google Scholar 

  11. Thieme, H. R.: Asymptotic estimates of the solutions of nonlinear integral equations and asymptotic speeds for the spread of populations. J. Reine Angew. Math. 306, 94–121 (1979)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Radcliffe, J., Rass, L. The uniqueness of wave solutions for the deterministic non-reducible n-type epidemic. J. Math. Biology 19, 303–308 (1984). https://doi.org/10.1007/BF00277101

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00277101

Key words

Navigation