Skip to main content
"By creating we think, by living we learn" Patrick Geddes
Main University menu

Templates Top-Level Menu

Dr Raluca Eftimie

picture of Raluca Eftimie

Raluca Eftimie
Department of Mathematics
University of Dundee
Dundee DD1 4HN
Fulton G10
+44 (0)1382 384488
+44 (0)1382 385516

Research Interests:

  • Mathematical Biology, Applied Mathematics:
    • pattern formation in ODEs and PDEs; bifurcation theory; numerical investigation of ODEs and PDEs
    • modelling in population ecology & cell biology:
      1. modelling animal communication in ecological aggregations;
      2. modelling signalling pathways in cell aggregations;
    • investigation of mathematical & biological mechanisms underpinning the formation of self-organised biological aggregations:
      1. in ecology: swarming and schooling/shoaling phenomena;
      2. in cell biology: collective cell movement in developmental cell biology, cancer biology (cancer growth, metastasis, invasion)
    • cancer immuno-therapies, cancer viral therapies;
    • immunology;
    • metabolic regulation of immune responses and cancer;
  • Collaboration projects

Group News

  • Congratulations to Haneen for passing her Viva with flying colours!
  • Congratulations to Vasiliki for having her paper accepted for publication in Mathematical Medicine and Biology.
  • Congratulations to Vasiliki for passing her Viva with flying colours!
  • Congratulations to Vasiliki for having her paper accepted for publication in Mathematical Models and Methods in Applied Sciences (M3AS).
  • Congratulations to Haneen for having her paper accepted for publication in J. Theor. Biol.
  • Congratulations to Vasiliki for being invited to present some of her research work at the STEM for BRITAIN 2017 event (Mathematics Section) in the House of Commons.

Current & Former Group Members:

  • PhD students:
    • Miss Arnina Goodlad (October 2016 - current)
    • Mr. Raed Qahiti (October 2017 - current)
    • Ms. Nada Almuallem (January 2018 - current)
    • Mr. Szabolcs Suveges (October 2018 - current); Joint supervision with Dr. D. Trucu
    • Mr. Abdulhamed Alsisi (September 2018 - current); Joint supervision with Dr. D. Trucu
    • Former PhD Students

    • * Self-funded PhD students are welcome to contact me for possible research projects in applied mathematics
  • MSc students:
  • Post-Doctoral Fellows:
    • Dr. Miguel Pineda (November 2013 - December 2014)
  • Visitors:
    • Dr. Cicely Macnamara (November 2014 - March 2015)
    • Dr. Nicoline den Breems (August 2016 - December 2016)


    • 2016-2019: EPSRC DTP (to fund Miss Arnina Goodlad)
    • 2015-2016: MOD Dstl (PI)
    • 2014-2017: EPSRC DTP (to fund Miss Vasiliki Bitsouni)
    • 2013-2015: EPSRC First Grant Scheme (PI)
    • 2014-2015: Northern Research Partnership ECR Engagement and Exchanges with Business & Industry (PI)
    • 2013-2014: Northern Research Partnership Early Career Researcher (ECR) Exchanges (PI)

    Current Admin:

    • PGR Programme Leader for Mathematics
    • ERASMUS & Global Exchange Advisor for Mathematics
    • University of Dundee Research Governance & Policy Sub-Committee
    • LMS Representative for Dundee
    • Main academic organiser of Edinburgh Mathematical Society (EMS) Postgraduate Students Meeting at The Burn (2016 Poster) (2015 Poster) (2014 Poster)
    • Help with Outreach & Visit Days
      • Organised a maths event part of the "Saturday Science Live" (on 28 March 2015, during the 2015 `Women in Science Festival')
      • built a level-1 MegaMenger cube (see photo) during the 2015 University of Dundee `Women in Science Festival'

    Teaching (2019/2020):

    • MA21001 Mathematics 2A
    • MA52002 Mathematical Ecology and Epidemiology
    • MA52001 Mathematical Oncology
    • Supervision of 5 Honours Projects part of MA40001 module

    Teaching (2018/2019):

    • MA21001 Mathematics 2A
    • MA52002 Mathematical Ecology and Epidemiology
    • MA52001 Mathematical Oncology
    • Supervision of 5 Honours Projects part of MA40001 module

    Teaching (2017/2018):

    • MA52002 Mathematical Ecology and Epidemiology
    • MA52001 Mathematical Oncology
    • Supervision of MSci/MMATH Projects part of MA50001 courses

    Teaching (2016/2017):

    • MA21001 Mathematics 2A
    • MA52002 Mathematical Ecology and Epidemiology
    • MA52001 Mathematical Oncology
    • Supervision of 4 Honours/MSci/MMATH Projects part of MA40001 & MA50001 courses

    Teaching (2015/2016):

    • MA32003 Operation Research
    • MA52002 Mathematical Ecology and Epidemiology
    • MA52001 Mathematical Oncology
    • Supervision of 4 Honours Projects part of MA42001 course, and MSci/MSc Projects


    • H. Hamam, R. Eftimie, 2018. The effect of chemotherapeutic drug Docetaxel on tumour-immune interactions during combined anti-cancer therapies. In Preparation.
    • A. Goodlad, R. Eftimie, 2018. Collective behaviours in schools of fish: the impact of large noise on inter-individual social interactions and overall group dynamics. In Preparation.
    • R. Eftimie, G. Eftimie, 2018. Investigating the role of glucocorticoid hormones and circadian rhythms on cancer-immune interactions. To be submitted.
    • M. Baister, R. Eftimie, 2019. Metabolic competition in tumour-macrophages interactions: a mathematical modelling and investigation approach. In Preparation
    • T. Alzahrani, R. Eftimie, D. Trucu, 2019. Multiscale moving boundary modelling of cancer interactions with a fusogenic enclitic virus: the impact of syncytial dynamics. Published.
    • S.H. Ho, D. He, R. Eftimie, 2018. Mathematical models of transmission dynamics and vaccine strategies in Hong Kong during the 2017-2018 winter influenza season. Published.
    • R. Eftimie, G. Eftimie 2018. Complex innate and adaptive immune responses during oncolytic viral therapies can support both immunocentric and virocentric points of view. Published.
    • T. Alzahrani, R. Eftimie, D. Trucu, 2019. Multi scale modelling of cancer response to oncolytic viral therapy. Mathematical Biosciences, 310, 76-95. (link to journal)
    • P.-L. Buono, R. Eftimie, M. Kovacic, L. van Veen, 2019. Kinetic models for pattern formation in animal aggregations: a symmetry and bifurcation approach. To appear in Active Particles, Vol. 2 (Ed. N. Bellomo, P. Degond, E. Tadmor)
    • V. Bitsouni, R. Eftimie, 2018. Non-local parabolic and hyperbolic models for cell polarisation in heterogeneous cancer cell populations. Bull. Math. Biol. (DOI: 10.1007/s11538-018-0477-4) (link to journal)
    • R. Eftimie, E. Hassanein, 2018. Improving cancer detection through combinations of cancer and immune biomarkers. Journal of Translational Medicine. DOI: 10.1186/s12967-018-1432-8 (link to journal)
    • R. Eftimie, G. Eftimie 2018. Tumour-associated macrophages and oncolytic virotherapies: a mathematical investigation into a complex dynamics. Letters in Biomathematics, 5(1), 70-99. DOI: 10.1080/23737867.2018.1430518 (link to journal)
    • V. Bitsouni, D. Trucu, M.A.J. Chaplain, R. Eftimie, 2018. Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasion. Mathematical Medicine & Biology. Accepted. DOI:10.1093/imammb/dqx019 (pdf) (link to journal)
    • M. Pineda, R. Eftimie, 2017. Modelling the collective response of heterogeneous cell populations to stationary linear gradients and chemical signal relay. Physical Biology, 14(6), 066003.
    • R. Eftimie, M. Perez, P.-L. Buono, 2017. Pattern formation in a nonlocal mathematical model for the multiple roles of the TGFb pathway in tumour dynamics. Mathematical Biosciences, 289, 96-115. (link to journal)
    • V. Bitsouni, M.A.J. Chaplain, R. Eftimie, 2017. Mathematical modelling of cancer invasion: the multiple roles of TGF-β pathway on tumour proliferation and cell adhesion. Math. Models Methods Appl. Sci., 27(10), 1929.
    • R. Eftimie, H. Hamam 2016. Modelling and investigation of the CD4+ T cells - macrophages paradox in melanoma immunotherapies. J. Theor. Biol., 420: 82-104. DOI: 10.1016/j.jtbi.2017.02.022 (link to journal)
    • R. Eftimie, J.J. Gillard, D.A. Cantrell, 2016. Mathematical models for immunology: current state of the art and future research directions. Bull. Math. Biol, 78(10), 2091-2134. DOI: 10.1007/s11538-016-0214-9 (pdf)
    • R. Eftimie, C.K. Macnamara, J. Dushoff, J.L. Bramson, D.J.D. Earn, 2016. Bifurcations and chaotic dynamics in a tumour-immune-virus system. Math. Model. Nat. Phenom., 11(5), 135-155. doi: 10.1051/mmnp/201611510 (pdf)
    • R. Eftimie, 2016. Validation of multi-scale models for fibrosis. Comment on ``Towards a unified approach in the modelling of fibrosis: A review with research perspectives" by M. Ben Amar and C. Bianca. Physics of Life Reviews, 17, 90-91. doi:10.1016/j.plrev.2016.05.003 (link to journal)
    • N. den Breems, R. Eftimie, 2016. The re-polarisation of M2 and M1 macrophages and its role on cancer outcomes. Journal of Theoretical Biology. 390, 23-39. DOI:10.1016/j.jtbi.2015.10.034 (pdf)
    • P-L. Buono and R. Eftimie, 2016. Lyapunov-Schmidt and Centre Manifold Reduction Methods for Nonlocal PDEs Modelling Animal Aggregations. Accepted in "Mathematical Sciences with Multidisciplinary Applications", Eds. B. Toni. STEAM-H, Springer, New-York. (pdf)
    • C.K Macnamara, R. Eftimie, 2015. Memory versus effector immune responses in oncolytic virotherapies. Journal of Theoretical Biology, 377, 1-9. (doi:10.1016/j.jtbi.2015.04.004) (link to journal) (pdf)
    • J.A. Carrillo, R. Eftimie, F.K.O. Hoffmann, 2015, Non-local kinetic and macroscopic models for self-organised animal aggregations. Kinetic and Related Models (KRM), 8(3), 413-441 (link to journal)(.pdf)
    • M. Pineda, C.J. Weijer, R. Eftimie, 2015. Modelling cell movement, cell differentiation, cell sorting and proportion regulation in Dictyostelium discoideum aggregations. Journal of Theoretical Biology, 370, 135-150. (doi:10.1016/j.jtbi.2015.01.042) (link to journal) (pdf)
    • R. Eftimie, 2015. The quest for a new modelling framework in mathematical biology. Comment on "On the interplay between mathematics and biology: hallmarks towards a new systems biology" by N. Bellomo et al. Physics of Life Reviews, 12, 72-73. (DOI: 10.1016/j.plrev.2015.01.012) (link to journal) (pdf)
    • R. Eftimie, 2015. Modelling communication and movement: from cells to animals and humans. Snapshots of modern mathematics from Oberwolfach. No. 21. (link)
    • R. Eftimie, A. Coulier, 2015. The role of avoidance and learning behaviours on the formation and movement of biological aggregations. Mathematical Modelling of Natural Phenomena, 10(2), 27-44.(pdf) (link to journal)
    • P.-L. Buono, R. Eftimie, 2014, Symmetries and pattern formation in hyperbolic versus parabolic models of aggregation. Journal of Mathematical Biology. (link to journal) (DOI: 10.1007/s00285-014-0842-3)(pdf)
    • P.-L. Buono, R. Eftimie, 2014, Codimension-2 bifurcations in animal aggregation models with symmetry. SIAM Journal on Applied Dynamical Systems. 13(4), 1542-1582 (DOI: 10.1137/130932272) (pdf)
    • P.-L. Buono, R. Eftimie, 2014, Analysis of Hopf/Hopf bifurcations in nonlocal hyperbolic models for self-organised aggregations. Mathematical Models and Methods in Applied Sciences, 24(2), 327-357. (DOI: 10.1142/S0218202513400101) (link to journal) (pdf)
    • D. He, J. Dushoff, R. Eftimie, D.J.D. Earn, 2013, Patterns of spread of influenza A in Canada. Proceedings of the Royal Society B. 280(1770), 20131174. (DOI: 10/1098/rspb.2013.1174) (link to journal)
    • R. Eftimie, 2013, The effect of different communication mechanisms on the movement and structure of self-organised aggregations. Mathematical Modelling of Natural Phenomena, 7(2), 32-51. (pdf)
    • R. Eftimie, 2013, Simultaneous use of different communication mechanisms leads to spatial sorting and unexpected collective behaviours in animal groups. J. Theor. Biol., 337, 42-53 (DOI: 10.1016/j.jtbi.2013.08.001) (link to .pdf)
    • R. Eftimie, 2012, Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review. J. Math. Biol., 65(1), 35-75. (link to .pdf)
    • R. Eftimie, J. Dushoff, B.W. Bridle, J.L. Bramson, D.J.D. Earn, 2011, Multi-stability and multi-instability phenomena in a mathematical model of tumor-immune-virus interactions, Bull. Math. Biol., 73(12), 2932-2961. (link to .pdf)
    • R. Eftimie, J.L. Bramson, D.J.D. Earn, 2010, Modeling anti-tumor Th1 and Th2 immunity in the rejection of melanoma, J. Theor. Biol., 265(3), 467-480. (link to .pdf)
    • R. Eftimie, J.L. Bramson, D.J.D. Earn, 2010, Interactions between the immune system and cancer: a brief review of non-spatial mathematical models, Bull. Math. Biol., 73(1), 2-32. (link to .pdf)*
    • * selected by Thomson Reuters Essential Science Indicators as one of the most cited papers in its research area
    • R. Fetecau, R. Eftimie, 2010, An investigation of a nonlocal hyperbolic model for self-organization of biological groups, J. Math. Biol.,61(4), 545-579. (link to .pdf)
    • C.O. Stan, E. Panaitescu, R. Eftimie, 2009. Hydrogeochemical aspects linked to the shallow groundwater quality at Cristesti (Iasi County), Scientific Annals of the "Al. I. Cuza" University Iasi, LV, no. 1, 113-126.
    • R. Eftimie, G. de Vries, M.A. Lewis, 2009, Weakly nonlinear analysis of a hyperbolic model for animal group formation, J. Math. Biol., 59(1), 37-74. (link to .pdf)
    • R. Eftimie, G. de Vries, M.A. Lewis, 2007, Complex spatial group patterns result from different animal communication mechanisms, PNAS, 104(17), 6974-6979. (link to .pdf)
    • R. Eftimie, G. de Vries, M.A. Lewis, F. Lutscher, 2007, Modeling group formation and activity patterns in self-organizing collectives of individuals, Bull. Math. Biol., 69(5), 1537-1565. (link to .pdf)
    • Gh. Eftimie, R. Eftimie, 2000. Mathematics. Chapter in "Examene 2001. Teste pentru capacitate. Limba si literatura romana. Istorie. Matematica. Geografie."(in Romanian) (link)
    • R. Eftimie, 2018. Hyperbolic and Kinetic Models for Self-organised Biological Aggregations: A modelling and pattern formation approach. Springer, 280 p. (Springer link)
      PhD Thesis:
    • R. Eftimie, 2008. Modelling group formation and activity patterns in self-organising communities of organisms. University of Alberta, Canada. (info)