Dengue is the most prominent arboviral infection known to humans, especially in tropical regions of the world like Bangladesh. This is often a tricky outbreak to deal with, given its nature of seasonality, and due to the impact of climate change, variations in the length of its on‐season have been observed. This article models the dengue scenario in Bangladesh using a periodic, nonautonomous SIS vector–host model, proposes some development over the existing algorithm to determine the basic reproduction number, R0, for nonautonomous models, namely the “linear operator method,” and hence patriots the behavior of R0 with respect to the length of the on‐season. Our experimentation shows that the infection transmission will be at its peak when the length of the on‐season is around 10 months. Based on the data of 2022, the current dynamic of the disease scenario in Bangladesh shows that the disease will not persist in the long run but occasional outbreaks may occur, given the right set of conditions. Finally, we conduct a sensitivity analysis of the model parameters, which shows that improving the recovery rate of the infected patient class and impeding the birth rate of the vector can effectively subdue the disease outbreak.