The linear stability and basic reproduction numbers for autonomous FDEs

Xiao-Qiang Zhao

doi:10.3934/dcdss.2023082

Article Contents

2024, Volume 17, Issue 2: 708-719. Doi: 10.3934/dcdss.2023082

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The linear stability and basic reproduction numbers for autonomous FDEs

Xiao-Qiang Zhao

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada

Dedicated to Professor Yihong Du on the occasion of his 60th birthday

Received: February 2023

Revised: April 2023

Early access: April 17, 2023

Published online: April 17, 2023

Research is supported in part by the NSERC of Canada (RGPIN-2019-05648).

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Abstract

In this paper, we first prove the stability equivalence between a linear autonomous and cooperative functional differential equation (FDE) and its associated autonomous and cooperative system without time delay. Then we present the theory of basic reproduction number $ \mathcal{R}_0 $ for general autonomous FDEs. As an illustrative example, we also establish the threshold dynamics for a time-delayed population model of black-legged ticks in terms of $ \mathcal{R}_0 $.

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Mathematics Subject Classification: 34K06, 34K30, 37C65, 37L15, 92D25.

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