Mathematics Applied to Biology

Research

Examples of current research projects

Biomechanics in tumour growth and angiogenesis

Mathematical modelling of bio-mechanical aspects in tumour growth and angiogenesis, cell deformation and movement.

  • Cell deformation and movement
  • Bio-mechanical aspects in tumour growth and angiogenesis

For details on this project and related research areas, contact Dr Anotida Madzvamuse.

Mathematics of epidemics on networks

Research in this area is at the interface between network science, stochastic processes, dynamical systems and PDEs. The starting point is to develop paradigm/theoretical models that capture complexities arising in real networks, such as heterogeneity in the characteristics, behaviour and interaction of individuals, as well as higher-order network structure. Special attention is given to the rigorous mathematical analysis of the resulting models. Typical research questions include:

  • Model coarse graining and network inference
  • Identifiying links between approximate models and their rigorous mathematical counterpart
  • Proving exactness or obtaining error bounds for certain epidemic models
  • Extending modelling to more realistic networks exhibiting higher-order structure
  • Control model, non-Markovian dynamics on networks

For details on this project and related research areas, contact Prof Istvan Kiss.

Pattern formation, reaction diffusion systems (RDES)

Novel applications of RDES in biological systems through numerical simulations on geometrically accurate fixed and growing domains.

  • RDES on fixed and growing/continously deforming domains
  • Moving grid finite elements for RDES
  • Adaptive moving grid finite elements for RDES
  • ALE formulations and finite differences for RDES
  • Bifurcation theory for RDES on continuously deforming domains

For details on this project and related research areas, contact Dr Anotida Madzvamuse.

Mathematical Immunology

Derivation and analysis of mathematical models of immune responses and autoimmunity, using techniques of nonlinear dynamics, delay equations and stochastic processes.

  • Pathogen-induced onset and development autoimmunity
  • Effects of virus life cycle on the dynamics of immune response
  • Stochastic resonance and sustained oscillations in immune dynamics 

For details on this project and related research areas, please contact Dr Konstantin Blyuss.

Plant immunity and crop protection

Mathematical modelling of plant immune response to parasites, and crop protection

  • RNA interference in plants and parasites
  • Dynamics of nutrient uptake by plants
  • Protection of crops against parasites: use of bioregulators, and effects of awareness

For details on this project and related research areas, please contact Dr Konstantin Blyuss.

Mathematical neuroscience

Analysis of dynamics of neural networks, with an emphasis on stability and emergence of cooperation.

  • neural networks with discrete and distributed delays
  • analysis and classification of different cooperative behaviours: synchronization, chimera states
  • numerical bifurcation analysis of time-delayed models

For details on this project and related research areas, please contact Dr Yuliya Kyrychko.

Gene regulatory networks

Fundamental properties of gene regulatory networks are explored using techniques of nonlinear dynamics.

  • effects of transcriptional and translational time delays on the dynamics of gene regulatory networks
  • gene regulatory networks in immunology: T- and B-cell differentiation

For details on this project and related research areas, please contact Dr Yuliya Kyrychko.

2023

Kiss, Istvan (2023) On parameter identifiability in network-based epidemic models. Bulletin of Mathematical Biology, 86 (18). pp. 1-17. ISSN 0092-8240

2019

Krause, Marina, Wei Yang, Feng, Lindert, Mariska te, Isermann, Philipp, Schepens, Jan, Maas, Ralph J A, Eid, Khouloud, Venkataraman, Chandrasekhar, Lammerding, Jan, Madzvamuse, Anotida, Hendriks, Wiljan, Riet, Joost te and Wolf, Katarina (2019) Cell migration through 3D confining pores: speed accelerations by deformation and recoil of the nucleus. Philosophical Transactions B: Biological Sciences, 374 (201802). pp. 1-12. ISSN 0962-8436

Fatehi, Farzad, Kyrychko, Yuliya N and Blyuss, Konstantin B (2019) Time-delayed model of autoimmune dynamics. Mathematical Biosciences and Engineering, 16 (5). pp. 5613-5639. ISSN 1547-1063

Church, Jon Matteo, Guo, Zhenlin, Jimack, Peter K, Madzvamuse, Anotida, Promislow, Keith, Wetton, Brian, Wise, Stephen M and Yang, Fengwei (2019) High accuracy benchmark problems for Allen-Cahn and Cahn-Hilliard dynamics. Communications in Computational Physics, 26 (4). pp. 947-972. ISSN 1815-2406

Barnard, Rosanna C, Berthouze, Luc, Simon, Péter and Kiss, István (2019) Epidemic threshold in pairwise models for clustered networks: closures and fast correlations. Journal of Mathematical Biology. ISSN 0303-6812

Blyuss, Konstantin B, Fatehi Chenar, Farzad, Tsygankova, Victoria A, Biliavska, Liudmyla O, Iutynska, Galyna O, Yemets, Alla I and Blume, Yaroslav B (2019) RNAi-based biocontrol of wheat nematodes using natural poly-component biostimulants. Frontiers in Plant Science, 10 (483). pp. 1-12. ISSN 1664-462X

Fatehi, Farzad, Kyrychko, Yuliya N, Molchanov, Robert and Blyuss, Konstantin B (2019) Bifurcations and multistability in a model of cytokine-mediated autoimmunity. International Journal of Bifurcation and Chaos, 29 (3). 1950034 1. ISSN 0218-1274

Vizi, Zsolt, Kiss, István Z, Miller, Joel and Röst, Gergely (2019) A monotonic relationship between the variability of the infectious period and final size in pairwise epidemic modelling. Journal of Mathematics in Industry, 9 (1). pp. 1-15. ISSN 2190-5983

Bishop, A, Kiss, I Z and House, T (2019) Consistent approximation of epidemic dynamics on degree-heterogeneous clustered networks. COMPLEX NETWORKS 2018 The 7th International Conference on Complex Networks and Their Applications, Cambridge, United Kingdom, December 11-13, 2018. Published in: Complex Networks and Their Applications VII. 812 376-391. Springer ISSN 1860-949X ISBN 9783030054106

Chaplain, Mark A J, Lorenzi, Tommaso, Lorz, Alexander and Venkataraman, Chandrasekhar (2019) Mathematical modelling of phenotypic selection with solid tumours. ENUMATH 2017, Voss, Norway, 25-29 September 2017. Published in: Radu, Florin Adrian, Kumar, Kundan, Berre, Inga, Nordbotten, Jan Martin and Pop, Iuliu Sorin, (eds.) Numerical Mathematics and Advanced Applications: Proceedings of ENUMATH 2017. 126 237-245. Springer ISSN 1439-7358 ISBN 9783319964140

2018

Al Basir, Fahad, Blyuss, Konstantin B and Ray, Santanu (2018) Modelling the effects of awareness-based interventions to control the mosaic disease of Jatropha curcas. Ecological Complexity, 36. pp. 92-100. ISSN 1476-945X

Kiss, István Z, Miller, Joel C and Simon, Péter L (2018) Fast variables determine the epidemic threshold in the pairwise model with an improved closure. Complex Networks 2018: The 7th International Conference on Complex Networks and Their Applications, Cambridge, United Kingdom, December 11-13, 2018. Published in: Proceedings of Complex Networks 2018 (The Seventh International Conference on Complex Networks and their Applications. 365-675. Springer Verlag ISBN 9783030054106

Barnard, Rosanna C, Kiss, Istvan Z, Berthouze, Luc and Miller, Joel C (2018) Edge-based compartmental modelling of an SIR epidemic on a dual-layer static-dynamic multiplex network with tunable clustering. Bulletin of Mathematical Biology, 80 (10). pp. 2698-2733. ISSN 0092-8240

Cusseddu, D, Edelstein-Keshet, L, Mackenzie, J A, Portet, S and Madzvamuse, A (2018) A coupled bulk-surface model for cell polarisation. Journal of Theoretical Biology, 481. pp. 119-135. ISSN 0022-5193

Lorenzi, Tommaso, Venkataraman, Chandrasekhar, Lorz, Alexander and Chaplain, Mark (2018) The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity. Journal of Theoretical Biology, 451. pp. 101-110. ISSN 0022-5193

Sarfaraz, Wakil and Madzvamuse, Anotida (2018) Domain-dependent stability analysis of a reaction-diffusion model on compact circular geometries. International Journal of Bifurcation and Chaos, 28 (8). p. 1830024. ISSN 0218-1274

Fatehi Chenar, F, Kyrychko, Y N and Blyuss, K B (2018) Mathematical model of immune response to hepatitis B. Journal of Theoretical Biology, 447. pp. 98-110. ISSN 0022-5193

Kyrychko, Y N and Schwartz, I B (2018) Enhancing noise-induced switching times in systems with distributed delays. Chaos, 28 (6). ISSN 1054-1500

Fatehi Chenar, Farzad, Kyrychko, Yuliya and Blyuss, Konstantin (2018) Effects of Viral and cytokine delays on dynamics of autoimmunity. Mathematics, 6. p. 66. ISSN 2227-7390

Sherborne, Neil, Blyuss, Konstantin and Kiss, Istvan (2018) Bursting endemic bubbles in an adaptive network. Physical Review E (PRE), 97 (4). 042306. ISSN 2470-0045

Madzvamuse, Anotida, Gerisch, Alf and Barreira, Raquel (2018) Cross-diffusion in reaction-diffusion models: analysis, numerics and applications. Published in: ECMI 2016: Progress in Industrial Mathematics at ECMI 2016. 26 385-392. Springer ISBN 9783319630816

Fatehi Chenar, Farzad, Kyrychko, Sergey, Ross, Aleksandra, Kyrychko, Yuliya and Blyuss, Konstantin (2018) Stochastic effects in autoimmune dynamics. Frontiers in Physiology, 9. p. 45. ISSN 1664-042X

2017

Bauer, Larissa, Bassett, Jason, Hoevel, Philipp, Kyrychko, Yuliya and Blyuss, Konstantin (2017) Chimera states in multi-strain epidemic models with temporary immunity. Chaos, 27 (11). p. 114317. ISSN 1054-1500

Sarfaraz, Wakil and Madzvamuse, Anotida (2017) Classification of parameter spaces for a reaction-diffusion model on stationary domains. Chaos, Solitons & Fractals, 103. pp. 33-51. ISSN 0960-0779

Agaba, G O, Kyrychko, Y N and Blyuss, K B (2017) Dynamics of vaccination in a time-delayed epidemic model with awareness. Mathematical Biosciences, 294. pp. 92-99. ISSN 0025-5564

Rahman, Bootan, Blyuss, Konstantin and Kyrychko, Yuliya (2017) Aging transition in systems of oscillators with global distributed-delay coupling. Physical Review E, 96 (3). ISSN 2470-0045

Kiss, István, Miller, Joel C and Simon, Péter L (2017) Mathematics of epidemics on networks: from exact to approximate models. Interdisciplinary applied Mathematics, 46 . Springer International Publishing. ISBN 9783319508047

Tuncer, Necibe and Madzvamuse, Anotida (2017) Projected finite elements for systems of reaction-diffusion equations on closed evolving spheroidal surfaces. Communications in Computational Physics, 21 (3). pp. 718-747. ISSN 1815-2406

Elliott, Charles M, Ranner, Thomas and Venkataraman, Chandrasekhar (2017) Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics. SIAM Journal on Mathematical Analysis, 49 (1). pp. 360-397. ISSN 0036-1410

Neofytou, G, Kyrychko, Y N and Blyuss, K B (2017) Time-delayed model of RNA interference. Ecological Complexity, 30. pp. 11-25. ISSN 1476-945X

2016

Upadhyay, Ranjit Kumar, Roy, Parimita, Venkataraman, C and Madzvamuse, A (2016) Wave of chaos in a spatial eco-epidemiological system: generating realistic patterns of patchiness in rabbit-lynx dynamics. Mathematical Biosciences, 281. pp. 98-119. ISSN 0025-5564

2015

Madzvamuse, Anotida, Leube, Rudolf E, Othmer, Hans and Merkel, Rudolf (2015) Coupling geometric PDEs with physics, cell morphology, motility and pattern formation. In: Coupling geometric PDEs with physics, cell morphology, motility and pattern formation, 13th July 2015 to 18th December 2015.