Comparative Analysis Of Various Continuous-time Deterministic Models Of Tumor-immune Interactions

Abstract

Cancer is historically a leading cause of death in the United States. In 2013,cancer was the second leading cause of death with 584,881 deaths \cite{CDC}.Having solely been responsible for 22.5\% of all deaths in 2013 alone \cite{CDC},obtaining as complete an understanding as possible of cancer is obviously necessitated.I investigate deterministic ordinary differential equation models of increasingcomplexity simulating avascular tumor growth and interactions with the innate immuneresponse. After first establishing a baseline of tumor growth limited only by theavailability of local nutrients, I compare the effects on said growth of the nativeimmune system response, chemotherapy, immunotherapy, and various combinations ofthe aforementioned treatment options and responses. These efforts focus onincreasing the understanding of tumor-immune interactions under various conditionsand scenarios in hopes of identifying the most effective approach in combatingsimilar cancerous tumors.