Research Publications (Mathematical and Statistical Sciences)

2019-01-01

Fazly, Mostafa, Lewis, Mark A, Wang, Hao

We study a hybrid impulsive reaction-advection-diffusion model given by a reaction-advection-diffusion equation composed with a discrete-time map in space dimension $n\in\mathbb N$. The reaction-advection-diffusion equation takes the form \begin{equation}\label{} u^{(m)}_t = \text{div}(A\nabla...

2002-01-01

Hans F. Weinberger, Mark A. Lewis, Bingtuan Li

The discrete-time recursion system \un+1=Q[\un] with \un(x) a vector of population distributions of species and Q an operator which models the growth, interaction, and migration of the species is considered. Previously known results are extended so that one can treat the local invasion of an...

2012-01-01

Ashander, Jaime, Lewis, Mark A., Krkošek, Martin

Exchange of diseases between domesticated and wild animals is a rising concern for conservation. In the ocean, many species display life histories that separate juveniles from adults. For pink salmon (Oncorhynchus gorbuscha) and parasitic sea lice (Lepeophtheirus salmonis), infection of juvenile...

2004

McCrosky, Jesse, Kouritzin, Michael, Blount, Douglas

A hybrid weighted/interacting particle filter, the selectively resampling particle (SERP) filter, is used to detect and track an unknown number of independent targets on a one-dimensional \"racetrack\" domain. The targets evolve in a nonlinear manner. The observations model a sensor positioned...

1997

Kouritzin, Michael

Herein, an averaging theory for the solutions to Cauchy initial value problems of arbitrary order,ε-dependent parabolic partial differential equations is developed. Indeed, by directly developing bounds between the derivatives of the fundamental solution to such an equation and derivatives of the...

2014-01-01

Peacock, Stephanie J., Connors, Brendan M., Krkošek, Martin, Irvine, James R., Lewis, Mark A.

The impact of parasites on hosts is invariably negative when considered in isolation, but may be complex and unexpected in nature. For example, if parasites make hosts less desirable to predators then gains from reduced predation may offset direct costs of being parasitized. We explore these...

2013-01-01

Krkosek, Martin, Orr, Craig, Peacock, Stephanie J., Proboszcz, Stan, Lewis, Mark A.

The resilience of coastal social-ecological systems may depend on adaptive responses to aquaculture disease outbreaks that can threaten wild and farm fish. A nine-year study of parasitic sea lice (Lepeophtheirus salmonis) and pink salmon (Oncorhynchus gorbuscha) from Pacific Canada indicates that...

2013-01-01

Lewis, Mark A., Proboscsz, S., Orr, C., Krkošek, M., Peacock, S.J.

The resilience of coastal social–ecological systems may depend on adaptive responses to aquaculture disease outbreaks that can threaten wild and farm fish. A nine-year study of parasitic sea lice (Lepeophtheirus salmonis) and pink salmon (Oncorhynchus gorbuscha) from Pacific Canada indicates that...

2009-01-01

Bampfylde, Caroline J., Jerde, Christopher L., Lewis, Mark A.

We formalize the establishment process for a sexual, semelparous organism through the use of hierarchical probability modeling from parameters of survival, probability of being female, probability of being fertilized, and expected fecundity.We show how to calculate the expected per capita growth...

2013-01-01

Merrill, E., Lewis, Mark A., Pybus, M., Potapov, A., Coltman, D.

We develop a model for the spread of chronic wasting disease (CWD) in a mule deer (Odocoileus hemionus) population to assess possible mechanisms of disease transmission and parameterize it for the mule deer population in Alberta, Canada. We consider seven mechanisms of disease transmission...