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2009-12-22

Frédéric M. Hamelin, Mark A. Lewis

In this paper, elements of differential game theory are used to analyze a spatially explicit home range model for interactingwolf packs when movement behavior is uncertain. The model consists of a system of partial differential equations whose parameters reflect the movement behavior of...

2020-11-05

Chunxi Feng, Mark A. Lewis, Chuncheng Wang, Hao Wang

In this paper, we propose a novel free boundary problem to model the movement of single species with a range boundary. The spatial movement and birth/death processes of the species found within the range boundary are assumed to be governed by the classic Fisher–KPP reaction–diffusion equation,...

2019-01-01

Mark A. Lewis, Zhisheng Shuai, P. van den Driessche

A general framework for threshold parameters in population dynamics is developed using the concept of target reproduction numbers. This framework identies reproduction numbers and other threshold parameters in the literature in terms of their roles in population control. The framework is applied...

2014-10-01

Potts, Jonathan R, Marie Auger-M´eth´e, Karl Mokross, Mark A. Lewis

Complex systems of moving and interacting objects are ubiquitous in the natural and social sciences. Predicting their behaviour often requires models that mimic these systems with sufficient accuracy, while accounting for their inherent stochasticity. Although tools exist to determine which of a...

2021-01-01

Ammar Hassanzadeh Keshteli, Dana Allen, Afia Anjum, Yashvi Patel, Aadhavya Sivakumaran, Siyang Tian, Fei Wang, Hao Wang, Mark A. Lewis, Russell Greiner, David S. Wishart

One year after identifying the first case of the 2019 coronavirus disease (COVID-19) in Canada, federal and provincial governments are still struggling to manage the pandemic. Provincial governments across Canada have experimented with widely varying policies in order to limit the burden of...

2014-01-01

Jonathan R. Potts, Mark A. Lewis

Territorial behaviour is widespread in the animal kingdom, with creatures seeking to gain parts of space for their exclusive use. It arises through a complicated interplay of many different behavioural features. Extracting and quantifying the processes that give rise to territorial patterns...

2013-01-01

Qihua Huang, Laura Parshotam, Hao Wang, Caroline Bampfylde, Mark A. Lewis

Mathematical models have been widely applied to perform chemical risk assessments on biological populations for a variety of ecotoxicological pro- cesses. In this paper, by introducing a dose-dependent mortality rate function, we formulate a toxin-dependent aquatic population model that...

2020-01-14

Peter D. Harrington, Mark A. Lewis

In marine systems, adult populations confined to isolated habitat patches can be connected by larval dispersal. Source–sink theory provides effective tools to quantify the effect of specific habitat patches on the dynamics of connected populations. In this paper, we construct the next-generation...

2006-01-01

Chad M. Topaz, Andrea L. Bertozzi, Mark A. Lewis

We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and numerically. There exist strongly nonlinear states with compact...

2020-03-31

Samuel M. Fischer, Mark A. Lewis

Profile likelihood confidence intervals are a robust alternative toWald’s method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood confidence intervals can be difficult to solve in these...