Various mosquito control methods use factory raised males to suppress vector densities. But the efficiency of these methods is currently insufficient to prevent epidemics of arbovirus diseases such as dengue, chikungunya or Zika. Suggestions that the sterile insect technique (SIT) could be "boosted" by applying biopesticides to sterile males remain unquantified. Here, we assess mathematically the gains to SIT for Aedes control of either: boosting with the pupicide pyriproxifen (BSIT); or, contaminating mosquitoes at auto-dissemination stations. Thresholds in sterile male release rate and competitiveness are identified, above which mosquitoes are eliminated asymptotically. Boosting reduces these thresholds and aids population destabilisation, even at sub-threshold release rates. No equivalent bifurcation exists in the auto-dissemination sub-model. Analysis suggests that BSIT can reduce by over 95% the total release required to circumvent dengue epidemics compared to SIT. We conclude , BSIT provides a powerful new tool for the integrated management of mosquito borne diseases.