Research Projects

Cancer is a major cause of human deaths, accounting for over 2.5 lakhs of potential years lost each year. It is responsible for 29% of male and 25% of female deaths, with a 40% chance of developing cancer in one's lifetime. Despite treatment efforts, cancer rates decrease by only 1.8% annually for males but remain nearly constant for females. Understanding tumor growth and its interaction in the tumor micro-environment is crucial for developing effective treatments. Mathematical models have proven to be an effective tool for studying disease spread dynamics, as they are the only systematic way to study control and mitigation strategies. Applied mathematics can prevent time-consuming experiments and provide valuable insight into the tumor micro-environment by developing mathematical models and their solutions. The tumor microenvironment was previously assumed to consist of monomorphic populations of tumor cells, but recent theories suggest that it consists of a polymorphic state of tumor cells. This polymorphic state leads to different competitive abilities to access nutrients and oxygen for different cancer/tumor cell phenotypes in the same tumor micro-environment. This results in difficulties in understanding tumor spread and diagnosis. The goal is to develop game-theoretic models that describe different payoffs when they interact with monomorphic and polymorphic cells inside the tumor micro environment. This may help understand cancer progression more accurately and develop heterogeneity in treatment strategies, as recent research predicts that heterogeneity in treatment offers more favorable outcomes than fixed treatments for cancer patients.