Mathematics of dengue transmission dynamics: Roles of vector vertical transmission and temperature fluctuations

A new deterministic model is designed and used to gain insight into the effect of seasonal variations in temperature and vector vertical transmission on the transmission dynamics of dengue disease. The model, which incorporates (among many other features) the dynamics of the immature dengue-competent mosquitoes, vertical transmission in the vector population, density-dependent larval mortality and temperature effects, is rigorously analysed and simulated using data relevant to the disease dynamics in Chiang Mai province of Thailand. The non-trivial disease-free equilibrium of the model is shown to be globally-asymptotically stable when the associated basic reproduction number of the model is less than unity. Numerical simulations of the model, using data relevant to the disease dynamics in the Chiang Mai province of Thailand, show that vertical transmission in the vector population has only marginal impact on the disease dynamics, and that the effect of vertical transmission is temperature-dependent (in particular, the effect of vertical transmission on the disease dynamics increases for values of the mean monthly temperature in the range [16−28]^∘C, and decreases with increasing mean monthly temperature thereafter). It is further shown that dengue burden (as measured in terms of disease incidence) is maximized when the mean monthly temperature is in the range [26−28]^∘C (and dengue burden decreases for mean monthly temperature values above 28^∘C). Thus, this study suggests that anti-dengue control efforts should be intensified during the period when this temperature range is recorded in the Chiang Mai province (this occurs between June and August).