  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 advance existing research by developing a mechanistic model for the
mosquito life cycle that accurately accounts for the non-Markovian nature of
the process. 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.
Furthermore, we demonstrate how to reduce the model to the corresponding
differential equations, enabling us to utilize existing methods for analyzing
the system and fitting the model to observations. This approach can be further
applied to similar non-Markovian processes that are currently described with
less accurate Markovian models.
