Asymptotic dynamics of some t-periodic one-dimensional model with application to prostate cancer immunotherapy

Mathematical model of hormone sensitive prostate cancer treatment using leuprolide: A small step towards personalization

In this paper we present a new version of a mathematical model of Elishmereni et al. describing androgen deprivation therapy (ADT) for hormone sensitive prostate cancer patients (HSPC). We first focus on the detail description of the model, and then we present mathematical analysis of the proposed model, starting from the simplified model without resistance and ending on the full model with two resistance mechanisms present. We make a step towards personalization proposing an underlying tumor growth law base on a cohort of patients from Mayo hospital. We conclude that the model is able to reflect reality, that is in clinical scenarios the level of testosterone in HSPC patients inevitably rises leading to the failure of ADT.

Accelerating the Development of Personalized Cancer Immunotherapy by Integrating Molecular Patients' Profiles with Dynamic Mathematical Models

We review the evolution, achievements, and limitations of the current paradigm shift in medicine, from the "one-size-fits-all" model to "Precision Medicine." Precision, or personalized, medicine-tailoring the medical treatment to the personal characteristics of each patient-engages advanced statistical methods to evaluate the relationships between static patient profiling (e.g., genomic and proteomic), and a simple clinically motivated output (e.g., yes/no responder). Today, precision medicine technologies that have facilitated groundbreaking advances in oncology, notably in cancer immunotherapy, are approaching the limits of their potential, mainly due to the scarcity of methods for integrating genomic, proteomic and clinical patient information. A different approach to treatment personalization involves methodologies focusing on the dynamic interactions in the patient-disease-drug system, as portrayed in mathematical modeling. Achievements of this scientific approach, in the form of algorithms for predicting personal disease dynamics in individual patients under immunotherapeutic drugs, are reviewed as well. The contribution of the dynamic approaches to precision medicine is limited, at present, due to insufficient applicability and validation. Yet, the time is ripe for amalgamating together these two approaches, for maximizing their joint potential to personalize and improve cancer immunotherapy. We suggest the roadmap toward achieving this goal, technologically, and urge clinicians, pharmacologists, and computational biologists to join forces along the pharmaco-clinical track of this development.

Mathematical Prostate Cancer Evolution: Effect of Immunotherapy Based on Controlled Vaccination Strategy

Basic immunology research over several decades has led to an improved understanding of tumour recognition by components of the immune system and mechanism of tumour evasion from immune detection. These findings have ultimately led to creating antitumour immunotherapies in patients with different kind of cancer including prostate cancer. The increasing number of reports confirms that immune-based therapies have clinical benefit in patients with prostate cancer with potentially less toxicity in comparison with traditional systemic treatments including surgical resection, chemotherapy, or radiotherapy in various forms. This review focuses on the possibility of modulation of the optimal immunotherapy based on vaccination strategy adopted to individual patients in order to increase quality and quantity of their life.