LAUSR

Abstract In this article, we aim to apply mathematical modelling by means of eight first-order ordinary differential equations to investigate the response of prostate cancer and the immune system to an allogenic whole-cell cancer vaccine and metronomic chemotherapy. Research to formulate our mathematical model was based on the clinical study developed by Kronik et al. In order to provide an accurate mathematical description of the global dynamics of our system, we apply the Localization of Compact Invariant Sets method to calculate upper bounds for all cell populations and define the so-called localizing domain. Further, by Lyapunov’s direct method and LaSalle’s invariance principle we study the asymptotic stability of the system and determine conditions for a global attractor existence. The latter allow us to establish sufficient conditions to ensure prostate cancer elimination by applying the metronomic chemotherapy treatment. In silico experiments were performed by setting six different initial tumor sizes and considering two cases: one with the sole administration of metronomic chemotherapy, and another with the combined application of chemoimmunotherapy. Numerical simulations are consistent with our analytical results as they successfully illustrate that the prostate cancer cells population is eliminated in both considered cases.