Dengue is a vector-borne disease transmitted by Aedes mosquitoes. The worldwide spread of these mosquitoes and the increasing disease burden have emphasized the need for a spatio-temporal risk map capable of assessing dengue outbreak conditions and quantifying the outbreak risk. Given that the life cycle of Aedes mosquitoes is strongly influenced by habitat temperature, numerous studies have utilized temperature-dependent development rates of these mosquitoes to construct virus transmission and outbreak risk models. In this study, we contribute to existing research by developing a mechanistic model for the mosquito life cycle that accurately captures its non-Markovian nature. Beginning with integral equations to track the mosquito population across different life cycle stages, we demonstrate how to derive the corresponding differential equations using phase-type distributions. This approach can be further applied to similar non-Markovian processes that are currently described with less accurate Markovian models. By fitting the model to data on human dengue cases, we estimate several model parameters, allowing the development of a global spatiotemporal dengue risk map. This risk model employs temperature and precipitation data to assess the environmental suitability for dengue outbreaks in a given area.
Keywords: Aedes mosquitoes; Dengue; Non-Markovian models.
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