3 Presentations

• 
  11:15 AM - 11:40 AM

  A Stackelberg approach to cancer treatment

  • Monica Salvioli, presenter, Politecnico di Milano

  Standard cancer therapy conventionally applies chemotherapy at the maximum tolerated dose.
  The underlying idea is that killing the maximum number of cancer cells will result in the best outcome for the patient. However, though this approach is usually able to kill the majority of malignant cells, it often spares a small number of them, which evolve resistance to treatment leading to its failure.
  We develop a game theoretical model of cancer treatment to compare the standard treatment protocols with a dynamic therapy that takes into account the evolutionary dynamics of resistance.
  The players of this game are the cancer cells and the oncologist, where the former evolve resistance to maximize their proliferation rate and the latter applies therapy to maximize the patient's quality of life, expressed as a trade-off between the tumor size and therapy toxicity.
  Our model shows that the Nash solution of the game, which corresponds to the standard of care, is often disappointing from the oncologist's and patient's perspective. If the oncologist can play rationally and can anticipate the cancer response to the therapy, she can become the leader in a Stackelberg game, exploiting her significant advantages given by the nonrationality of her follower.
  Our results show that the Stackelberg approach can remarkably improve the outcome for the oncologist (and the patient), compared to the current standard of care and contribute to the on-going discussion on the importance of personalized therapies and on the need to change targets for cancer treatment.

• 
  11:40 AM - 12:05 PM

  Evolutionary vaccination dynamics in the reinfection SIRI model

  • José Martins, presenter, LIAAD-INESC TEC and Polytechnic Institute of Leiria
  • Alberto Pinto, University of Porto

  We use the reinfection SIRI epidemiological model to analyze the impact of education programs and vaccine scares on individuals decisions to vaccinate or not. The presence of the reinfection provokes the novelty of the existence of three Nash equilibria for the same level of the morbidity relative risk instead of a single Nash equilibrium as occurs in the SIR model. The existence of three Nash equilibria, with two of them being evolutionary stable, introduces two scenarios with relevant and opposite features for the same level of the morbidity relative risk: the low-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a low probability; and the high-vaccination scenario corresponding to the evolutionary stable vaccination strategy, where individuals will vaccinate with a high probability. We introduce the evolutionary vaccination dynamics for the SIRI model and we prove that it is bistable. The bistability of the evolutionary dynamics indicates that the damage provoked by false scares on the vaccination perceived morbidity risks can be much higher and much more persistent than in the SIR model. Furthermore, the vaccination education programs to be efficient need to implement a mechanism to suddenly increase the vaccination coverage level.

• 
  12:05 PM - 12:30 PM

  Evolutionary game of metastatic castrate-resistant prostate cancer and its treatment

  • Katerina Stankova, presenter, Networks and Strategic Optimization Group, Department of Data Science and Knowledge Engineering, Maastricht University

  We analyze an evolutionary game of metastatic castrate-resistant prostate cancer (mCRPC) that involves three distinct cancer cell types: 1) those dependent on exogenous testosterone (T+), 2) those with increased CYP17A expression that produce testosterone and provide it to the micro-environment as a public good (TP), and 3) those independent of testosterone (T-). The composition of the three distinct types within the tumor is crucial for applying mCRPC treatment: a tumor with primarily T+ and TP cells can be effectively treated with drugs such as abiraterone that target androgen receptors; a tumor with high frequencies of T- cells will be unresponsive to abiraterone and requires chemotherapy. Standard treatment aims to greatly reduce the tumor mass/PSA level by continuously giving abiraterone to the patients. Unfortunately, a complete recession of the tumor is rarely observed in the clinic; instead, the tumor progresses to the worst treatment scenario – being majorly composed of T- cells. In this talk, we will analyze a nonspatial game of mCRPC, its continuous-space extension, and treatment regimens that we found as optimal with respect to different treatment goals. We will discuss what our results imply for the clinic.