# Biological Modeling

In recent decades, an explosive synergy between biology and mathematics has greatly enriched and extended both fields. Indeed, given its ability to reveal otherwise invisible worlds in all kinds of biological systems, mathematics has been called the "new microscope in biology." In turn, biology has stimulated the creation of new realms of mathematics. Duke's Mathematics Department has a large group of mathematicians who work on specific biological and medical applications and as well as the development of new applied mathematical techniques and new mathematical theorems inspired by biological applications. The range of applications is large and the mathematical techniques diverse, including dynamical systems, partial differential equations, stochastic dynamics, fluid dynamics, geometry, topology, and algebra.

## Faculty

#### Ingrid Daubechies

###### James B. Duke Professor of Mathematics and Electrical and Computer Engineering

**Keywords in this area**

shape space

#### Rick Timothy Durrett

###### James B. Duke Professor of Mathematics

**Keywords in this area**

population genetics, selective sweeps, stepping stone models, interacting particle systems, contact processes, spatial ecological models, cancer modeling, tumor heterogeneity

#### John Harer

###### Professor of Mathematics

**Keywords in this area**

Gene Regulatory Networks, Network Inference

#### Gregory Joseph Herschlag

###### Assistant Research Professor of Mathematics

**Keywords in this area**

biological modeling

#### Alexander A. Kiselev

###### William T. Laprade Professor of Mathematics

**Keywords in this area**

Chemotaxis, enhancement of biological reactions

#### David P. Kraines

###### Associate Professor Emeritus of Mathematics

**Keywords in this area**

Prisoner's dilemma, sequestering CO2

#### Anita T. Layton

###### Bass Fellow

**Keywords in this area**

mathematical biology, mathematical physiology, mathematical modeling, kidney physiology, renal hemodynamics, diabetes, multiscale modeling, fluid-structure interactions, computational fluid dynamics, numerical partial differential equations, feedback control, systems biology

#### Jonathan Christopher Mattingly

###### Professor of Mathematics

**Keywords in this area**

Stochastic and Random PDEs, Stochastic Dynamical Systems, Mathematical Ecology and Evolution, Metabolic and Cellular modeling, Out of equilibrium statistical mechanics

#### Sayan Mukherjee

###### Professor of Statistical Science

**Keywords in this area**

quantitative genetics, statistical genetics

#### James H. Nolen

###### Associate Professor of Mathematics

**Keywords in this area**

asymptotic analysis

#### Amanda Randles

###### Alfred Winborne and Victoria Stover Mordecai Assistant Professor of Biomedical Sciences

#### Marc Daniel Ryser

###### Instructor in the Department of Population Health Sciences

**Keywords in this area**

cancer biology, cancer epidemiology, early carcinogenesis, Human papillomavirus, cancer evolution

#### Hau-Tieng Wu

###### Associate Professor of Mathematics

**Keywords in this area**

physiological time series, multimodal time series