Mathematical Models in the Biosciences I

This book introduces mathematical modeling to bioscience students, with first semester calculus as the only prerequisite. It is the first of a two-part series exploring essential concepts of calculus in the context of biological systems. Michael Frame covers the essential ideas and theories of basic calculus while providing examples of how they relate and are applicable to subjects such as chemotherapy and tumor growth, chemical diffusion, allometric scaling, predator-prey relations, nerve impulses, and more. He presents Pearl’s causality calculus to resolve Simpson’s paradox, simple cardiac dynamics models, basic epidemiological models including Ronald Ross’s study of malaria and its epidemic curves, and limit cycles for the glycolysis model. Based on the author’s calculus class at Yale, the book makes concepts of calculus less abstract and more relatable for science majors and premedical students.