Mathematics & Statistics Department
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Selected publications and research from Mathematics and Statistics Faculty
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The impact of induced drug resistance in cancer chemotherapy
(201901)Resistance to chemotherapy is a major impediment to successful cancer treatment that has been extensively studied over the past three decades. Classically, resistance is thought to arise primarily through random genetic ... 
Robust optimization of cancer immunotherapy
(201901)Mathematical models of biological systems are often validated by fitting the model to the average of an often small experimental dataset. Here we ask the question of whether predictions made from a model fit to the average ... 
Developing a minimally structured mathematical model of cancer treatment with oncolytic viruses and dendritic cell injections
(Hindawi, 20181030)Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. ... 
Identifying robust optimal cancer treatment protocols from small experimental
(201807)Mathematical models of biological systems are often validated by fitting the model to the average of an (often small) experimental dataset. Here we ask the question of whether predictions made from a model fit to the average ... 
Limiting the development of anticancer drug resistance in a spatial model of micrometastases
(201607)Using a hybrid spatial model, we explore how chemoresistance in micrometastases depends on the drug dosing schedule. We separately consider weakly and strongly resistant populations that can acquire drug resistance, or can ... 
Studying the robustness of optimal protocols using oncolytic virotherapy with dendritic cell vaccines
(201604)Oncolytic viruses (OVs) are emerging as a promising cancer treatment, as they selectively replicate inside of and lyse tumor cells. The efficacy of these viruses is further enhanced by engineering the OVs to release molecules ... 
Choosing a solution strategy: distinguishing between analytic, qualitative and numerical approaches
(201601)In many undergraduate Ordinary Differential Equations courses that cover firstorder initial value problems, students learn analytic approaches for solving such equations, qualitative approaches to extract some solution ... 
Mathematical oncology: using mathematics to understand cancer progression and treatment
(20151114)Over the last several decades, much has been learned about cancer through experimental and clinical research. However, the more we learn about cancer, the more it is recognized that cancer is a multifaceted disease that ... 
A mathematical exploration of the development and therapeutic implications of anticancer drug resistance
(201406)Practically all chemotherapeutic agents, and many newer targeted cancer therapeutics, lead to drug resistance. Drug resistance can arise due to a number of different intracellular and microenvironmental causes. Further, ... 
Computational modeling of tumor response to vasculartargeting therapies
(201208)A mathematical model that examines tumorvasculature interactions is briefly presented in this work. I will discuss validation studies which demonstrate the model’s ability to qualitatively predict: 1) tumor growth under ... 
Using mathematical cancer models in an introductory differential equations course
(201201)Many incarnations of the Introductory Differential Equations course aim to teach students analytical, qualitative and numerical methods for gaining insight into the behavior of ODE solutions. Using mathematical models to ...