Proefschrift

Mathematical modeling of biological processes has roots as far back as Malthus modeling population dynamics in 1798 (Malthus, 1798). In 1878, Mu¨ller published the earliest application of mathematical modeling to evolution (Mu¨ller, 1878). In the early 1900’s the Lotka-Volterra equations, which are used as a foundation for the modeling in this thesis, were developed to describe the dynamics of multiple species interacting (Lotka, 2002; Volterra, 1926). While these underlying mathematics that apply to the growth and evolution of cancer are quite old, it’s application to the understanding and treatment of cancer is relatively new. Only since the early 2000’s has the mathematical treatment of cancer as an evolutionary or ecological topic in a Darwinian framework been explored (Rockne et al., 2019). Metastatic cancer is an ecologically and evolutionarily dynamic system, and with few exceptions, remains incurable (Gatenby and Brown, 2018). This thesis is focused on metastatic prostate cancer, as it is one of the most common cancers among men. Additionally, the 5-year overall survival for patients with metastatic prostate cancer has actually shortened by 3.1% (from 31.8% to 28.7%) since 1975-1977 (Jemal et al., 2017). Despite the increasing numbers of effective agents for treating metastatic cancers, evolution of resistance remains the fundamental barrier to cure and long-term disease control (Dong et al., 2019). Anticipating the evolutionary responses of metastatic disease to treatment permits the development of “evolutionarily enlightened” cancer therapy, where the administration of therapy becomes as adaptive and dynamic as the system it is treating. The successful application of evolutionary principles to the clinical treatment of prostate cancer requires formal mathematical models that frame the complex, often nonlinear, interactions that define response and resistance to therapy in individual patients (Michor and Beal, 2015). This thesis presents a methodology for integrating evolutionary dynamics in the clinical treatment of metastatic prostate cancer using a variety of disciplines in order to design treatment schedule and dose that delay or completely prevent the evolution of resistance to treatment. From fundamental cell biology to translational clinical cancer research, from evolutionary ecology to pest management, and from evolutionary game theory to optimal control theory, knowledge from all of these fields comes together to inspire and design what is known as evolutionary therapy of cancer. In the simplest sense, the ultimate goal of treating cancer is for the patient to remain alive. This is not synonymous with eradicating all tumor cells in the body. This thesis proposes, at its core, to abandon the idea of curing metastatic disease. As H.G. Wells once stated, “If we don’t end war, war will end us.” In an attempt for a ceasefire, this thesis presents multiple alternative approaches to current standard of care, developed using mathematical oncology, to reimagine metastatic disease as a chronic illness that is managed in the long term. 1.1 Brief History of Prostate Cancer and Its Treatment Cancer has a history as long as the history of multicellularity, more than half a billion years, with the oldest cancer ever discovered being a 240 million year old osteosarcoma in a stem-turtle (Haridy et al., 2019; Michod and Roze, 2001; Nunney, 2013). No doubt, 3