Global Dynamics of Some Vector-Borne Infectious Disease Models with Seasonality

Xiunan Wang

Memorial University of Newfoundland

Vector-borne infectious diseases such as malaria, dengue, West Nile virus disease, Zika 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. In this talk, I will introduce our recent research on the global dynamics of some 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. At last, we develop a time-delayed Lyme disease model with seasonality. By using the theory of basic reproduction ratio R0 and the theory of infinite dimensional dynamical systems, we derive R0 and establish a threshold type result on the global dynamics in terms of R0 for each model. By conducting case studies, we propose some practical strategies for the control of the diseases. This talk is based on joint works with Prof. Xiaoqiang Zhao.

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