Human primary glioblastomas (GBM) often harbor mutations within the epidermal growth factor receptor (EGFR). Treatment of EGFR-mutant GBM cell lines with the EGFR/HER2 tyrosine kinase inhibitor lapatinib can induce cell death in these models. However, EGFR inhibitors have shown little efficacy in the clinic, partly because of inappropriate dosing. We developed a computational approach to model in vitro cellular dynamics of the EGFR-mutant cell line SF268 in response to different lapatinib dosing schedules. We used this approach to identify an effective treatment strategy within the clinical toxicity limits of lapatinib, and developed a partial differential equation model to study in vivo GBM treatment response by taking into account its heterogeneous and diffusive nature. Despite the inability of lapatinib to induce tumor regressions with a continuous daily schedule, our modeling approach consistently predicts that continuous dosing remains the best clinically feasible strategy for lowering tumor burden, compared to pulsatile schedules. Our modeling platform provides a rational method for comparing treatment schedules in search for optimal dosing strategies for glioblastoma.