I will introduce three problems in mathematical oncology which involve dynamics, forecasting, longitudinal data, and control theory. In the first problem, I will describe our work using Markov chain models to forecast metastatic progression in 12 different soft tissue cancers. The models treat progression as a (weighted) random walk on a directed graph whose nodes are metastatic tumor locations. We estimate transition probabilities from site-to-site using historical autopsy data (untreated progression) and longitudinal patient data (treated progression) from Memorial Sloan Kettering and MD Anderson Cancer Centers. We characterize the inherent predictability of each cancer type using entropy methods. In the second problem, I will describe models (both deterministic and stochastic) that use evolutionary game theory (replicator dynamical systems with frequency dependent selection) to design novel adaptive chemotherapy schedules that mitigate chemoresistance by suppressing the ‘competitive release’ of resistant cells. The models make use of finding closed evolutionary cycles in the frequency distribution of competing subpopulations of cells so that neither the resistant population nor the sensitive population ever reach fixation. The third problem will describe our model of Covid-19 vaccine uptake as a reinforcement learning dynamic between two populations: the vaccine adopters, and the vaccine hesitant. We use uptake data from the Center for Disease Control (CDC) to estimate the payoff matrix governing the interaction between these two groups over time and show they are playing a Hawk-Dove evolutionary game with an internal evolutionarily stable Nash equilibrium. We then use the model, along with optimal control theory, to test several hypotheses associated with the size and timing of incentive programs to improve vaccine uptake (shift the Nash equilibrium upward) as much as possible. The model shows diminishing returns for larger incentive sizes.
Note:
Recording is available at https://umass-amherst.zoom.us/rec/share/b9E06EWXKRrV-4BM5h_BNJ-l88jQ4zAq...