[Mathematical Biosciences and Engineering, 24 March 2022]

Tick infestation and tick-borne disease spread in a region of multiple adjacent patches with different environmental conditions depend heavily on the host mobility and patch-specific suitability for tick growth. Here we introduce a two-patch model where environmental conditions differ in patches and yield different tick developmental delays, and where feeding adult ticks can be dispersed by the movement of larger mammal hosts. We obtain a coupled system of four delay differential equations with two delays, and we examine how the dynamical behaviours depend on patch-specific basic reproduction numbers and host mobility by using singular perturbation analyses and monotone dynamical systems theory. Our theoretical results and numerical simulations provide useful insights for tick population control strategies.

[BMJ Open, 2 November 2023]

Introduction: There are limited data on the longitudinal impact of Lyme disease. Predictors of recovery have not been fully established using validated data collection instruments. There are sparse data on the immunological response to infection over time.

Methods and analysis: This study is a longitudinal cohort study that will recruit 120 participants with Lyme disease in Ontario and Nova Scotia, Canada, with follow-up for up to 24 months. Data will be collected using the Short-Form 36 physical and mental component summaries, Depression and Anxiety Severity Scale Questionnaire, Fatigue Severity Scale and a battery of neuropsychological tests. Mononuclear cells, gene expression and cytokine profiling from blood samples will be used to assess immunological response. Analyses will include the use of non-linear mixed-effects modelling and proportional hazards models.

Ethics and dissemination: Ethics approval has been obtained from ethics boards at McMaster University (Hamilton Integrated Research Ethics Board) (7564), Queens University (EMD 315-20) and Nova Scotia Health Research Ethics Board (1027173), and the study is enrolling participants. Written informed consent is obtained from all participants. The results will be disseminated by publication in a peer-reviewed journal and presented at a relevant conference. A brief report will be provided to decision-makers and patient groups.