Range expansion of  Ixodes scapularis ticks and of  Borrelia burgdorferi by migratory birds

Jane M. Heffernan; Yijun Lou; Jianhong Wu

doi:10.3934/dcdsb.2014.19.3147

Article Contents

2014, Volume 19, Issue 10: 3147-3167. Doi: 10.3934/dcdsb.2014.19.3147

This issue Previous Article A periodic Ross-Macdonald model in a patchy environment Next Article Further studies of a reaction-diffusion system for an unstirred chemostat with internal storage

Range expansion of Ixodes scapularis ticks and of Borrelia burgdorferi by migratory birds

1.
Mprime Centre for Disease Modelling, York Institute of Health Research, Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3
2.
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

Received: March 31, 2014

Revised: April 30, 2014

Published: November 2014

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Abstract

Recent studies have suggested that the risk of exposure to Lyme disease is emerging in Canada because of the expanding range of I. scapularis ticks. The wide geographic breeding range of I. scapularis-carrying migratory birds is consistent with the widespread geographical occurrence of I. scapularis in Canada. However, how important migratory birds from the United States are for the establishment and the stable endemic transmission cycle of Lyme disease in Canada remains an issue of theoretical challenge and practical significance. In this paper, we design and analyze a periodic model of differential equations with a forcing term modeling the annual bird migration to address the aforementioned issue. Our results show that ticks can establish in any migratory bird stopovers and breeding sites. Moreover, bird-transported ticks may increase the probability of B. burgdorferi establishment in a tick-endemic habitat.

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Mathematics Subject Classification: Primary: 34C25; Secondary: 37N25.

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