Dengue is a vector-borne disease transmitted by the mosquito Aedes aegypti. The incidence of dengue disease shows a clear dependence on seasonal variation. How does the temperature affect the incidence? We addressed this question indirectly by estimating the size of the A. aegypti population for different temperatures applying population dynamics theory. In order to achieve this objective we designed temperature-controlled experiments to assess the entomological parameters regarding the mosquito's life-cycle at different temperatures. By obtaining the mortality, transition and oviposition rates for different stages of the life-cycle of the mosquito we were able to calculate the basic offspring number Q(0), which is the capacity of vector reproduction and ultimately gives the size of the vector population.

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Biological invasion is an important area of research in mathematical biology and more so if it concerns species which are vectors for diseases threatening the public health of large populations. That is certainly the case for Aedes aegypti and the dengue epidemics in South America. Without the prospect of an effective and cheap vaccine in the near future, any feasible public policy for controlling the dengue epidemics in tropical climates must necessarily include appropriate strategies for minimizing the mosquito population factor. The present paper discusses some mathematical models designed to describe A. aegypti's vital and dispersal dynamics, aiming to highlight practical procedures for the minimization of its impact as a dengue vector. A continuous model including diffusion and advection shows the existence of a stable travelling wave in many situations and a numerical study relates the wavefront speed to a few crucial parameters. Strategies for invasion containment and its prediction based on measurable parameters are analysed.

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The incidence of dengue infection, a vector-borne disease transmitted by the mosquito Aedes aegypti, shows clear dependence on seasonal variation. Based on the quantification method that furnishes the size of the A. aegypti population in terms of the estimated entomological parameters for different temperatures, we assessed the risk of dengue outbreaks. The persistence and severity of epidemics can be assessed by the basic reproduction number R(0), which varies with temperature. The expression for R(0) obtained from 'true' and 'pseudo' mass action laws for dengue infection is discussed.

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The dengue virus is a vector-borne disease transmitted by mosquito Aedes aegypti and the incidence is strongly influenced by temperature and humidity which vary seasonally. To assess the effects of temperature on dengue transmission, mathematical models are developed based on the population dynamics theory. However, depending on the hypotheses of the modelling, different outcomes regarding to the risk of epidemics are obtained. We address this question comparing two simple models supplied with model's parameters estimated from temperature-controlled experiments, especially the entomological parameters regarded to the mosquito's life cycle in different temperatures. Once obtained the mortality and transition rates of different stages comprising the life cycle of mosquito and the oviposition rate, we compare the capacity of vector reproduction (the basic offspring number) and the risk of infection (basic reproduction number) provided by two models. The extended model, which is more realistic, showed that both mosquito population and dengue risk are situated at higher values than the simplified model, even that the basic offspring number is lower.