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Dengue is hyper-endemic in Singapore and Malaysia, and daily movement rates between the two countries are consistently high, allowing inference on the role of local transmission and imported dengue cases. This paper describes a custom built sparse space-time autoregressive (SSTAR) model to infer and forecast contemporaneous and future dengue transmission patterns in Singapore and 16 administrative regions within Malaysia, taking into account connectivity and geographical adjacency between regions as well as climatic factors. A modification to forecast impulse responses is developed for the case of the SSTAR and is used to simulate changes in dengue transmission in neighbouring regions following a disturbance. The results indicate that there are long-term responses of the neighbouring regions to shocks in a region. By computation of variable inclusion probabilities, we found that each region's own past counts were important to describe contemporaneous case counts. In 15 out of 16 regions, other regions case counts were important to describe contemporaneous case counts even after controlling for past local dengue transmissions and exogenous factors. Leave-one-region-out analysis using SSTAR showed that dengue transmission counts could be reconstructed for 13 of 16 regions' counts using external dengue transmissions compared to a climate only approach. Lastly, one to four week ahead forecasts from the SSTAR were more accurate than baseline univariate autoregressions.