Mathematical and Statistical Models of Culex Mosquito Abundance and Transmission Dynamics of West Nile Virus with Weather Impact
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West Nile virus (WNV) is a serious public health concern worldwide. Mosquitoes are the key factor in the transmission of the disease. Forecasting mosquito abundance and modeling WNV transmission dynamics with weather conditions are challenging scientific tasks due to the significant weather impact and the magnitude of uncertainty associated with incomplete information. In this dissertation, we employ mathematical and statistical methods to model and forecast the mosquito abundance, the WNV transmission and WNV risk with the weather impact. Compartmental models for WNV transmission usually assume that mosquito population grows with a constant recruiting rate. However in reality, the mosquito abundance is closely related to weather conditions. In the first part, we improve a generalized linear model (GLM) for Culex mosquito abundance with the weather effect. Then we integrate the GLM with a compartmental model for WNV transmission to build a hybrid model. The hybrid model can better capture the reported WNV human infection case pattern in Peel Region, Ontario. As far as we know, this hybrid model is novel and has never been proposed in the literature of modeling WNV transmission. In order to better describe the Culex mosquito behaviors of the whole year, in the second part, we first separate the year into two periods. Then we build a matrix population model for each period respectively. Our simulation results show that our model captures the trends of available mosquito data very well. It is important to model the spatial variation of mosquito population for each region. The classical statistical models are not suitable when some important explanatory factors for each trap are either missing or unobservable. Therefore, in the third part, we study the spatio-temporal distribution of Culex mosquito population by estimating the collective impact of all the unobservable information for each trap. The results demonstrate that the model has a high level of accuracy in comparison with the classical GLM. In the last part, we show our work in forecasting weekly Culex mosquito abundance since 2011 in Peel Region, Ontario. Then we forecast WNV risk using the hybrid model.