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Non-monotone waves of a stage-structured SLIRM epidemic model with latent period
Published online by Cambridge University Press: 15 September 2020
Abstract
We propose and investigate a stage-structured SLIRM epidemic model with latent period in a spatially continuous habitat. We first show the existence of semi-travelling waves that connect the unstable disease-free equilibrium as the wave coordinate goes to − ∞, provided that the basic reproduction number $\mathcal {R}_0 > 1$ and $c > c_*$ for some positive number $c_*$. We then use a combination of asymptotic estimates, Laplace transform and Cauchy's integral theorem to show the persistence of semi-travelling waves. Based on the persistent property, we construct a Lyapunov functional to prove the convergence of the semi-travelling wave to an endemic (positive) equilibrium as the wave coordinate goes to + ∞. In addition, by the Laplace transform technique, the non-existence of bounded semi-travelling wave is also proved when $\mathcal {R}_0 > 1$ and $0 < c < c_*$. This indicates that $c_*$ is indeed the minimum wave speed. Finally simulations are given to illustrate the evolution of profiles.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 5 , October 2021 , pp. 1407 - 1442
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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