Although endocrine therapies and Cdk4/6 inhibitors have produced significantly improved outcomes for patients with estrogen receptor positive (ER+) breast cancer, continuous application of these drugs often results in resistance. We hypothesized that cancer cells acquiring drug resistance might increase their dependency on negative regulators of the cell cycle. Therefore, we investigated the effect of inhibiting WEE1 on delaying the development of resistance to palbociclib and fulvestrant. We treated ER+ MCF7 breast cancer cells with palbociclib alternating with a combination of fulvestrant and a WEE1 inhibitor AZD1775 for 12 months. We found that the alternating treatment prevented the development of drug resistance to palbociclib and fulvestrant compared to monotherapies. Furthermore, we developed a mathematical model that can simulate cell proliferation under monotherapy, combination or alternating drug treatments. Finally, we showed that the mathematical model can be used to minimize the number of fulvestrant plus AZD1775 treatment periods while maintaining its efficacy.