Dengue is one of the most damaging vector-borne diseases in the world and about 2.5 billion individuals are vulnerable in the tropical regions across the world. Sri Lanka is also one country affected by the disease and every year severe outbreaks of dengue causes significant impact to the economy and social well-being. The complex and uncertain transmission dynamic of the disease has made it very difficult to irradiate. The form of the virus and mosquito behavior is ever-changing due to multiple factors such as climate variation, entomology of mosquitoes, demography of humans and their behavior. The only solution to this public health problem is controlling the transmission after an scientific and analytical investigation of the dynamic. This study develops a mathematical model which describes the transmission of dengue, and critical parameters of the model equations are determined by the climate variation. Techniques to model these parameters considering their uncertainty are also developed. The stability analysis of the model with deterministic parameter space is carried out. The model equations are numerically solved using time-invariant parameters, and the simulated dengue infections are validated with the actual cases in Colombo.