The uniqueness of Atkinson and Reuter's epidemic waves
- 1 July 1977
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 82 (1) , 127-130
- https://doi.org/10.1017/s0305004100053755
Abstract
Atkinson and Reuter(1) consider travelling wave solutions for the deterministic epidemic, with or without removals, spreading along the line. In the case where there are no removals, they reformulate the problem in terms of the solutions X(·) to the integral equation which satisfy X(− ∞) = − ∞, X( + ∞) = 0, X(u) < 0 for u ∈ (− ∞, ∞), where is the left hand tail of the contact distribution, and where ʗ > 0 is the velocity of the wave corresponding to X. They show that no solution is possible unless converges for λ > 0 sufficiently small, and that any solution X must satisfy for some C > 0. They then prove the following existence theorems.This publication has 2 references indexed in Scilit:
- Deterministic epidemic waves of critical velocityMathematical Proceedings of the Cambridge Philosophical Society, 1977
- Deterministic epidemic wavesMathematical Proceedings of the Cambridge Philosophical Society, 1976