# MS-9 Linear Algebra and Mathematical Biology (Mathematical Biology)

### Organizers: Julien Arino (University of Manitoba, Canada) and Natalia Komarova (University of California Irvine)

Mathematical biology and linear algebra have a rich history of interactions. Early on, the relationship was somewhat one-sided, with mathematical biology using linear algebra mostly as a tool. For instance, population biology models involving more than one population or stage were naturally formulated using systems of difference equations, leading, for example, to the Leslie matrix. Nonlinear systems of differential equations are often studied using a technique called linearisation, which requires to understand the localisation of the spectrum of the associated Jacobian matrix. With the introduction of more complex models, the interactions among individuals or molecules on networks in diverse contexts required more complex mathematics, utilizing the intricate connections between graph theory and matrix theory. As a consequence, more recently, the relationship between biology and linear algebra has become more symbiotic: mathematical biology produces problems that are interesting in their own right to linear algebraists. This minisymposium brings together researchers interested in a wide variety of applications of linear algebra in the context of mathematical biology. Presentations will more than cover the span of topics mentioned earlier and will provide a glimpse into an area that offers interesting theoretical challenges.

### Speakers

**Lee Altenberg**,* "Error Catastrophes" and the Information Content of the Perron vector in Quasispecies Models of Evolution*

**Julien Arino**, *The population dynamics of a fish species subject to environmental stochasticity*

**Mark Artzrouni**, *A Leslie matrix model for Sicyopterus lagocephalus in La RĂ©union: sensitivity, uncertainty and research prioritization*

**Bruce Ayati**, *Mathematics for Musculoskeletal Diseases*

**Jim Cushing**, *Some Matrix Population Models with Imprimitive Projection Matrices*

**Patrick De Leenheer**, *The effects of different types of density dependence in the evolution of partial migration*

**Marc Feldman**, *Reduction Principle for recombination, mutation and migration*

**Natalia Komarova**, *Stability of control networks in stem cell lineages*

**Evan Milliken**, *A technique to approximate the probability of partial extinction events in metapopulations.*

**Gleb Pogudin**, *Elimination for nonlinear ODEs arising in biology*

**Vladimir Protasov**, *How to find the closest stable nonnegative matrix?*

**Jonathan Smith**, *Virtual species and matrix solution of Eigen's equations*

**Joe Tien**, *Disease spread on networks: integrating structure and dynamics through a generalized inverse*

**Pauline van den Driessche**,* Inequalities on Spectral Bounds for Matrices in a Stage-Structured Population Model*

**Zhijun Wu**, *Computing Dense versus Sparse Equilibrium States for Evolutionary Games*