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00000 n 0000754070 00000 n 0000754257 00000 n 0000754447 00000 n 0000754656 00000 n 0000754858 00000 n 0000754994 00000 n 0000755105 00000 n 0000755225 00000 n 0000755342 00000 n 0000755455 00000 n 0000755554 00000 n 0000755661 00000 n 0000755699 00000 n 0000755866 00000 n trailer << /Size 642 /Root 640 0 R /Info 641 0 R /ID [ ] >> startxref 756133 %%EOF 640 0 obj <>]>>/PageMode/UseOutlines/Pages 603 0 R/Type/Catalog>> endobj 642 0 obj <>stream 2020-09-14T15:29:33+08:00 LaTeX with hyperref 2020-09-14T15:30:43+08:00 2020-09-14T15:30:43+08:00 infectious disease; recovery age; relapse; patch; dispersal; non-locality pdfTeX-1.40.19 Unknown This is MiKTeX-pdfTeX 2.9.6839 (1.40.19) True (http://creativecommons.org/licenses/by/4.0) application/pdf Dongxue Yan Xingfu Zou In this paper, with the assumption that infectious individuals, once recovered for a period of fixed length, will relapse back to the infectious class, we derive an epidemic model for a population living in a two-patch environment (cities, towns, or countries, etc.). The model is given by a system of delay differential equations with a fixed delay accounting for the fixed constant relapse time and a non-local term caused by the mobility of the individuals during the recovered period. We explore the dynamics of the model under two scenarios: (i) assuming irreducibility for three travel rate matrices; (ii) allowing reducibility in some of the three matrices. For (i), we establish the global threshold dynamics in terms of the principal eigenvalue of a $2 \times 2$ matrix. For (ii), we consider three special cases so that we can obtain some explicit results, which allow us to explicitly explore the impact of the travel rates. We find that the role that the travel rate of recovered and infectious individuals differs from that of susceptible individuals. There is also an important difference between case (i) and (ii): under (ii), a boundary equilibrium is possible while under (i) it is impossible. Dynamics of an epidemic model with relapse over a two-patch environment infectious disease recovery age relapse patch dispersal non-locality 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License uuid:c80776ee-9254-437a-9143-ceb219cb8dfd uuid:5d375e73-624c-4687-b906-0fc12047a982 endstream endobj 643 0 obj <> endobj xref 0 1 0000000000 65535 f 640 1 0000769135 00000 n 642 2 0000769310 00000 n 0000775493 00000 n trailer <<4611254AC1D30E4884CFE0ADBEBDD3DB>]/Prev 756133>> startxref 777161 %%EOF