## Description

Mathematical biology (or biomathematics) uses mathematical techniques to study biological systems.

## Faculty members involved

**Julien Arino** (link) is interested in mathematical population dynamics, i.e., the evolution of the number of individuals in a population over time. His recent research deals with the spatio-temporal spread of infectious pathogens, which he describes using metapopulations. He has also done some work about the use of antivirals and vaccination during an influenza pandemic. The models considered take the form of (potentially large) systems of ordinary or delay differential equations, as well as continuous-time Markov chains.

**Felicia Magpantay** (link) is interested in childhood disease, focusing on the mathematics of imperfect vaccines and understanding the distinct epidemiological signatures of different modes of vaccine failure. Infectious disease modelling involves a combination of theoretical analysis of both deterministic and stochastic systems, numerical experimentation and modern statistical inference techniques.

**Stéphanie Portet** (link) works in the area of cellular biology, and more specifically, cytoskeletal networks. The organization of a cytoskeletal network is the main determinant of its cellular function. Her work involves a multidisciplinary approach encompassing different domains such as biophysics and mathematical biology. She is interested in models of the organization of networks and assembly of filaments composing those networks to characterize the determinants of their structures and mechanical properties. Deterministic and stochastic dynamical models are used; mathematical and computational analyses are conducted to characterize the transient and asymptotic behaviour of models.

## Current students and postdoctoral fellows

- Agnes Adefisan (M.Sc.) - J. Arino
- Nazila Akhavan Kharazian (M.Sc.) - F. Magpantay
- Clifford Allotey (M.Sc.) - F. Magpantay
- Charlotte Giraud-Carrier (Ph.D. - Biological Sciences) - J. Arino & D. Gillis
- Negin Pasban (M.Sc.) - J. Arino & S. Kirkland

## Representative recent publications

- C. Bowman, J. Arino, S.M. Moghadas. Evaluation of vaccination strategies during pandemic outbreaks.
*Mathematical Biosciences and Engineering*, 8(1):113-122, 2011.
- J. Arino and C.C. McCluskey. Effect of a sharp change of the incidence function on the dynamics of a simple disease.
*Journal of Biological Dynamics*, 4(5):490-505, 2010.
- J. Arino. Diseases in metapopulations. In
*Modeling and Dynamics of Infectious Diseases*, Z. Ma, Y. Zhou and J. Wu (Eds), Volume 11 in Series in Contemporary Applied Mathematics, World Scientific, pages 65-123, 2009.
- M. Beil, S. Lueck, F. Fleischer, S. Portet, W. Arendt, V. Schmidt. Simulating the formation of keratin filament networks by a piecewise-deterministic Markov process.
*Journal of Theoretical Biology*, 256:518-532, 2009.
- K. Khan, J. Arino, W. Hu, P. Raposo, J. Sears, F. Calderon, C. Heidebrecht, M. Macdonald, J. Liauw, A. Chan, M. Gardam. Spread of a novel influenza A (H1N1) virus via global airline transportation.
*New England Journal of Medicine*, 361(2):212-214, 2009.
- F.M.G. Magpantay, M.A. Riolo, M. Domenech de Celles, A.A. King and P. Rohani (2014) Epidemiological consequences of imperfect accines for immunizing infections. SIAM J. Appl. Math, 74(6): 1810-1830.
- S. Portet, N. Muecke, R. Kirmse, J. Langowski, M. Beil, H. Herrmann. Vimentin intermediate filament formation: In vitro measurement and mathematical modeling of the filament length distribution during assembly.
*Langmuir* 25:8817-8823, 2009.
- S. Portet, J. Arino. An in vivo intermediate filament assembly model.
*Mathematical Biosciences and Engineering* 6:117-134, 2009.
- J. Arino, C.S. Bowman, A. Gumel and S. Portet. Effect of pathogen-resistant vectors on the transmission dynamicso f a vector-borne disease.
*Journal of Biological Dynamics*, 1(4):320-346, 2007.
- R. Kirmse, S. Portet, N. Muecke, U. Aebi, H. Herrmann, J. Langowski. A quantitative kinetic model for the in vitro assembly of intermediate filaments from tetrameric vimentin.
*Journal of Biological Chemistry*, 282:18563-18572, 2007.
- S. Portet, J.A. Tuszynski, J.M. Dixon, M.V. Sataric. Models of spatial and orientational self-organization of microtubules under the influence of gravitational fields.
*Physical Review E*, 68:021903, 2003.