Evolution dynamics of some population models in heterogeneous environments

Wu, Ruiwen (2019) Evolution dynamics of some population models in heterogeneous environments. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Spatial and/or temporal evolutions are very important topics in epidemiology and ecology. This thesis is devoted to the study of the global dynamics of some population models incorporating with environmental heterogeneities. Vector-borne diseases such as West Nile virus and malaria, pose a threat to public health worldwide. Both vector life cycle and parasite development are highly sensitive to climate factors. To understand the role of seasonality on disease spread, we start with a periodic West Nile virus transmission model with time-varying incubation periods. Apart from seasonal variations, another important feature of our environment is the spatial heterogeneity. Hence, we incorporate the movement of both vectors and hosts, temperature-dependent incubation periods, seasonal fluctuations and spatial heterogeneity into a general reaction-diffusion vector-borne disease model. By using the theory of basic reproduction number, R₀, and the theory of infinite dimensional dynamical systems, we derive R₀ and establish a threshold-type result for the global dynamics in terms of R₀ for each model. As biological invasions have significant impacts on ecology and human society, how the growth and spatial spread of invasive species interact with environment becomes an important and challenging problem. We first propose an impulsive integro-differential model to describe a single invading species with a birth pulse in the reproductive stage and a nonlocal dispersal stage. Next, we study the propagation dynamics for a class of integro-difference two-species competition models in a spatially periodic habitat.

Item Type: Thesis (Doctoral (PhD))
URI: http://research.library.mun.ca/id/eprint/13973
Item ID: 13973
Additional Information: Includes bibliographical references (pages 143-153).
Keywords: Vector-borne diseases, basic reproduction number, threshold dynamics, traveling waves, spreading speeds
Department(s): Science, Faculty of > Mathematics and Statistics
Date: August 2019
Date Type: Submission
Library of Congress Subject Heading: Communicable diseases--Transmission--Mathematical models; Animals as carriers of diseases--Mathematical models

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