Reference number : GC-2017-Q1-01863, amendment number : , agreement type : G, recipient legal name : Yuan, Yuan (Memorial University of Newfoundland), recipient country : CA, recipient province : nan, recipient city : Newfoundland and Labrador|Terre-Neuve-et-Labrador, recipient postal code : nan, program name english : Discovery Grants Program - Individual, program name french : Programme de subventions à la découverte - individuelles, program purpose english : A distinguishing feature of the functional differential equations (FDEs) is that the evolution rate of the process described by such equations depends on the past history. During the past three decades, study on the theory and application of FDEs has been very active, the FDE related mathematical models are applicable to phenomena of different natures, such as, in biology, ecology, epidemiology, engineering and economy. 
 
The long-term goals of the research include, understanding in-depth the dynamical behavior and the reasons that govern such behavior in biological and epidemiological systems that can be illustrated by FDEs, especially how time delay and the system structure affect the evolution of the species, whether the infectious disease can spread and persist, or lead to an infectious disease outbreak. Mathematical techniques based on nonlinear analysis, FDEs and dynamical systems including existence, non-existence, stability of certain type of periodic/quasi-periodic solutions, persistence, bifurcations will be mainly approached. 
 
More realistic models may relate to the variation of environment which result in non-autonomous systems. In the literature, although some work has been done for autonomous and non-autonomous FDEs, there is a lack of theoretical analysis, especially for the stability and bifurcations. In the proposed research I will seek to extend and develop the stability and bifurcation theories to non-monotonic autonomous, non-autonomous, spatial and temporal involved FDEs with delays . And I will apply the theoretical results to tackle problems of qualitative analysis of dynamical behaviors arising in biological and epidemiological systems with stage/age-structures, or even disease transmission network models, with particular emphasis on establishing strong links on the effect of time delay, system construction and the dynamical behavior. I am also flexible enough to explore promising avenues of research as they emerge. 
 
This proposed research will increase our knowledge of the qualitative properties in applied FDEs, from mathematical and biological/epidemiological points of view. The theories and methodologies developed in the proposal will have very high impact on the development in the nonlinear dynamics community. They will not only strengthen the foundation for theoretical expansion in a large class of FDEs, but will also provide a practical view to support biological and epidemiological decision making. The interdisciplinary collaboration and the application to the fishery will have great potential to provide novel insights to strength marine population dynamics, optimize harvesting rates, and maintain ecosystem structure. The anticipated outcomes are likely to have impact by leading to advancements in the field of applied dynamics and will enhance HQP training and collaboration benefiting in Canada., program purpose french : A distinguishing feature of the functional differential equations (FDEs) is that the evolution rate of the process described by such equations depends on the past history. During the past three decades, study on the theory and application of FDEs has been very active, the FDE related mathematical models are applicable to phenomena of different natures, such as, in biology, ecology, epidemiology, engineering and economy. 
 
The long-term goals of the research include, understanding in-depth the dynamical behavior and the reasons that govern such behavior in biological and epidemiological systems that can be illustrated by FDEs, especially how time delay and the system structure affect the evolution of the species, whether the infectious disease can spread and persist, or lead to an infectious disease outbreak. Mathematical techniques based on nonlinear analysis, FDEs and dynamical systems including existence, non-existence, stability of certain type of periodic/quasi-periodic solutions, persistence, bifurcations will be mainly approached. 
 
More realistic models may relate to the variation of environment which result in non-autonomous systems. In the literature, although some work has been done for autonomous and non-autonomous FDEs, there is a lack of theoretical analysis, especially for the stability and bifurcations. In the proposed research I will seek to extend and develop the stability and bifurcation theories to non-monotonic autonomous, non-autonomous, spatial and temporal involved FDEs with delays . And I will apply the theoretical results to tackle problems of qualitative analysis of dynamical behaviors arising in biological and epidemiological systems with stage/age-structures, or even disease transmission network models, with particular emphasis on establishing strong links on the effect of time delay, system construction and the dynamical behavior. I am also flexible enough to explore promising avenues of research as they emerge. 
 
This proposed research will increase our knowledge of the qualitative properties in applied FDEs, from mathematical and biological/epidemiological points of view. The theories and methodologies developed in the proposal will have very high impact on the development in the nonlinear dynamics community. They will not only strengthen the foundation for theoretical expansion in a large class of FDEs, but will also provide a practical view to support biological and epidemiological decision making. The interdisciplinary collaboration and the application to the fishery will have great potential to provide novel insights to strength marine population dynamics, optimize harvesting rates, and maintain ecosystem structure. The anticipated outcomes are likely to have impact by leading to advancements in the field of applied dynamics and will enhance HQP training and collaboration benefiting in Canada., agreement title english : Functional Differential Equations in Biology and Epidemiology, agreement title french : Functional Differential Equations in Biology and Epidemiology, agreement number : RGPIN, agreement value : 100000.0, agreement start date : 2017-05-10, agreement end date : nan, description english : nan, description french : nan, expected results english : nan, expected results french : nan, additional information english : Grant or Award spanning more than one fiscal year. (2017-2018 to 2022-2023), additional information french : Subvention ou bourse octroyée s'appliquant à plus d'un exercice financier. (2017-2018 à 2022-2023), owner organization : nserc-crsng, owner organization title : Natural Sciences and Engineering Research Council of Canada | Conseil de recherches en sciences naturelles et en génie du Canada