Mathematical Model of the Interactions of a Neoantigen Cancer Vaccine and the Human Immune System: Evaluating the Safety and Efficacy of a Personalized Therapy Tumor-specific neoantigens, are derived from random somatic mutations expressed only in tumor cells and are highly individual- and tumor-specific. Due to these features, neoantigens provide targets for developing a personalized cancer immunotherapy. Cancer vaccines have recently attracted attention due to their success in clinical trials claiming increased potential for their specificity, efficacy, and safety. Neoantigen cancer vaccines are designed by mixing adjuvants and carefully selected neoantigens which could be effectively presented by antigen presenting cells (APCs) with the goal of training the immune system to recognize unique neoantigens associated with a person’s cancer. These vaccines have the potential to enhance the immune system to target and eliminate cancer by activating CD4+ and CD8+ T cells. Here, we present a system of ordinary differential equations to model the interactions of a personalized neoantigen cancer vaccine with the immune system of an individual by considering the vaccine concentration of neo-peptides and adjuvant, major histocompatibility complex (MHC) I and II copy numbers, tumor size, T cells, and APCs pre-vaccination. This model has been calibrated using melanoma patient-specific data from a clinical trial study (NCT01970358). To evaluate the safety and efficacy of a potential vaccine, we include a patient’s HLA profile which can display and specify the MHC I and II binding affinity with T cells, and therefore measure antigen-specific T cell response towards fighting tumor cells. Finally, our model can predict vaccine efficacy by measuring T cell response and tumor burden, as well as determining ideal therapy initiation time after surgery for optimal results.