Global dynamics of some vector-borne infectious disease models with seasonality

Wang, Xiunan (2017) Global dynamics of some vector-borne infectious disease models with seasonality. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

Vector-borne infectious diseases such as malaria, dengue, West Nile fever, Zika fever and Lyme disease remain a threat to public health and economics. Both vector life cycle and parasite development are greatly influenced by climatic factors. Understanding the role of seasonal climate in vector-borne infectious disease transmission is particularly important in light of global warming. This PhD thesis is devoted to the study of global dynamics of four vector-borne infectious disease models. We start with a periodic vector-bias malaria model with constant extrinsic incubation period (EIP). To explore the temperature sensitivity of the EIP of malaria parasites, we also formulate a functional differential equations model with a periodic time delay. Moreover, we incorporate the use of insecticide-treated bed nets (ITNs) into a climate-based mosquito-stage-structured malaria model. Lastly, we develop a time-delayed Lyme disease model with seasonality. By using the theory of basic reproduction ratio, R0, and the theory of dynamical systems, we derive R0 and establish a threshold type result for the global dynamics in terms of R0 for each model. By conducting numerical simulations of case studies, we propose some practical strategies for the control of the diseases.

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