June 24-28, 2012
The 2012 Annual Meeting of the Canadian Applied and Industrial Mathematics Society


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Mini Symposium Ecology and Dynamics of Vector-borne Diseases

Huaiping Zhu, York University

It is expected that climate change would have a great impact on the ecology of emerging and reemerging vector-borne diseases. The transmission and spreading of vector-borne diseases are highly sensitive to the effects of climatic change on vectors and parasites, which are highly sensitive to changes in temperature and precipitation. It is important to study the whole environmental context in which vector-borne diseases are transmitted. This mini-symposium, with speakers from public health and academic, aims to understand the effects of a changing environment on the ecological dynamics of vector-borne diseases.
4 invited speakers:

Chris Cosner, University of Miami
Modeling the spatial spread of Rift Valley Fever in Egypt

Rift Valley fever (RVF) is a severe vector-borne viral zoonosis present in Africa and the Middle East that harms both human health and livestock production. It is believed that RVF in Egypt may be introduced by the importation of infected animals from Sudan. We propose a three-patch model for the process of animals entering Egypt from Sudan, being moved up the Nile, and then consumed at population centres in Egypt. The basic reproduction number for each patch is computed and then the threshold dynamics of the model are established. We consider a scenario showing a possible explanation of outbreak patterns of RVF in Egypt. Outbreaks appear to be related to the level of the Nile and to the number of animals being imported.

Abba Gumel, University of Manitoba
Bifurcations in mosquito-borne Diseases

Mosquito-borne diseases, such as malaria, continue to pose significant public health problems in many parts of the world. I will discuss the bifurcations associated with the population dynamics (ecology) and spread of some vector-borne diseases, and their consequences vis-a-vis the persistence or effective control of the disease.

Rongsong Liu, University of Wyoming
Spatiotemporal Mutualistic Model of Mistletoes and Birds

A mathematical model which incorporates the spatial dispersal and interaction dynamics of mistletoes and birds is derived and studied to gain insights of the spatial heterogeneity in abundance of mistletoes. Fickian diffusion and chemotaxis are used to model the random movement of birds and the aggregation of birds due to the attraction of mistletoes, respectively. The spread of mistletoes by birds is expressed by a convolution integral with a dispersal kernel. Two different types of kernel functions are used to study the model, one is {\color{green} a} Dirac delta function which reflects the extreme case that the spread behavior is local, and the other one is a general non-negative symmetric function which describes the nonlocal spread of mistletoes. When the kernel function is taken as the Dirac delta function, the threshold condition for the existence of mistletoes is given and explored in term of parameters. For the general non-negative symmetric kernel case, we prove the existence and stability of non-constant equilibrium solutions. Numerical simulations are conducted by taking specific forms of kernel functions. Our study shows that the spatial heterogeneous patterns of mistletoes are related to the specific dispersal pattern of birds which carry mistletoe seeds.

Huaiping Zhu York University
Forecasting practice of mosquito abundance using weather and environmental conditions in Peel region of Canada

It has been witnessed for the last decades that climate change has great impact on the emerging and reemerging of vector-borne diseases, yet it must be admitted thatthe actual impact of climate change on vector population and diseases transmission are still far from clear. In this talk, I will present a modeling study and practice of forecasting of mosquito abundance and the West Nile virus in the Peel region of Ontario, Canada. By using surveillance data, weather data and land use information, we develop both statistical and dynamical models incorporating weather conditions and land use information for the vector-mosquitoes abundance and risk assessment of West Nile virus. I will discuss the statistical properties of the dynamical models and present a collaborative effort with Peel region and Public Health Agency of Canada in developing tools for forecasting the mosquito-abundance and the virus risk.

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Nicholas Ogden, Public Health Agency of Canada and University of Montreal;

Shigui Ruan, University of Miami;