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Publications by Prof. Mark Chaplain


Edited Books:



1) On Growth and Form: Spatio-temporal Pattern Formation in Biology , pp 1-439, eds. M.A.J. Chaplain, G.D. Singh, J. McLachlan, 1999, Wiley: Chichester.

2) Polymer and Cell Dynamics: Multiscale Modelling and Numerical Simulations , eds. W. Alt, M.A.J. Chaplain, M. Griebel, J. Lenz, 2003, Birkhauser Verlag, Basel.

3) Single-cell-based Models in Biology and Medicine , eds. A. Anderson, M.A.J. Chaplain, K. Rejniak, 2007, Birkhauser Verlag, Basel.



Contributed Chapters in Books:



1) "From mutation to metastasis: The mathematical modelling of the stages of tumour development'', chapter 5, pp187--236, in A Survey of Models for Tumor-Immune System Dynamics , eds. J.A. Adam, N. Bellomo, 1996, Birkhauser: Boston.

2) "Mathematical modeling of tumour-induced angiogenesis'', chapter 3.4, pp. 205--240 in Vascular Morphogenesis: In Vivo, In Vitro, In Mente , eds. C. Little, E.H. Sage, V. Mironov, 1998, Birkhauser: Boston.

3) "Modelling the growth and form of capillary networks'', chapter 13, pp225-250, in On Growth and Form: Spatio-temporal Pattern Formation in Biology , eds. M.A.J. Chaplain, G.D. Singh, J. McLachlan, 1999, Wiley: Chichester.

4) "Mathematical models in cancer research'', Chapter 60, pp937-951, in The Cancer Handbook , ed. M.R. Alison, Nature Publishing Group, 2002.

5) "Mathematical modelling of solid tumour growth: Applications of pre-pattern formation'', Chapter 24, pp283-293, in Morphogenesis and Pattern Formation in Biological Systems , eds. T. Sekimura, S. Noji, N. Ueno and P.K. Maini, Springer: Tokyo, 2003

6) "Mathematical modelling of tissue invasion'', Chapter 10, pp269-297, in Cancer Modelling and Simulation , ed. L. Preziosi, Chapman Hall/CRC, 2003

7) "Mathematical modelling of tumour-induced angiogenesis: Network growth and structure'', Chapter 3, pp51-75, in Angiogenesis in Brain Tumours , eds. Kirsch, M. and Black, P. McL., Kluwer Academic, Boston, 2004

8) "D'Arcy Thompson: nature and design through growth and form'', Chapter 5, pp85-93, in Nature and Design , eds. M.W. Collins, M.A. Atherton and J.A. Bryant, WIT Press, Southampton, Boston, 2005

9) "Mathematical modelling of spatio-temporal phenomena in tumour immunology'', Lect. Notes Math. 1872 , 131-183 (2006)

10) "Mathematical models of cancer growth and development'', Chapter 68, pp936-953, in The Cancer Handbook , 2nd Edition, ed. M.R. Alison, John Wiley and Sons, 2007

11) "Multiscale problems in the life sciences: From microscopic to macroscopic'', Lect. Notes Math. 1940 , 147-200 (2008)

12) "Multiscale Mathematical Modeling of Vascular Tumor Growth: An Exercise in Transatlantic Cooperation'', Chapter 13, in Multiscale Cancer Modeling , eds. T. Deisboeck and G. Stamatakos, CRC Press, Chapman and Hall/CRC Mathematical and Computational Biology (2010)

13) "A Hybrid Discrete-Continuum Model of Tumor-Induced Angiogenesis", Chapter 5, pp105 - 134, in Modeling Tumor Vasculature: Molecular, Cellular and Tissue Level Aspects and Implications , ed. T.L. Jackson, Springer: New York (2012)

14) "Blood Flow and Tumour-Induced Angiogenesis: Dynamically Adapting Vascular Networks", Chapter 8, pp167 - 212, in Modeling Tumor Vasculature: Molecular, Cellular and Tissue Level Aspects and Implications , ed. T.L. Jackson, Springer: New York (2012)

15) "Spatio-Temporal Modelling of Intracellular Signalling Pathways: Transcription Factors, Negative Feedback Systems and Oscillations", Chapter 4, pp55 - 82, in New Challenges for Cancer Systems Biomedicine , eds. A. D'Onofrio, P. Cerrai, A. Gandolfi, SIMAI Springer Series, DOI 10.1007/978-88-470-2571-4_4, Springer-Verlag Italia (2012)

16) "A Hybrid Multiscale Approach in Cancer Modelling and Treatment Prediction", pp 237 - 263, in Mathematical Oncology 2013 , eds. A. D'Onofrio, A. Gandolfi, Modeling and Simulation in Science, Engineering and Technology, DOI 10.1007/978-1-4939-0458-7_8, Springer Science+Business Media New York (2014)



Journal Articles:



1) M.A.J. Chaplain and B.D. Sleeman, "An application of membrane theory to the tip morphogenesis in Acetabularia" (1990) J. theor. Biol. 146, 177-200. Front cover of issue of journal

2) M.A.J. Chaplain and B.D. Sleeman, "A mathematical model for the production and secretion of tumour angiogenesis factor in tumours", (1990) IMA J. Math. Appl. Med. Biol. 7, 93-108 [PDF file]

3) M.A.J. Chaplain and A.M. Stuart, "A mathematical model for the diffusion of tumour angiogenesis factor into the surrounding host tissue." (1991) IMA J. Math. Appl. Med. Biol. 8, 191-220 [PDF file]

4) M.A.J. Chaplain and B.D. Sleeman, "A mathematical model for the growth and classification of a solid tumour: a new approach via nonlinear elasticity theory using strain-energy functions.", (1992) Math. Biosc. 111, 169-217.

5) M.A.J. Chaplain and B.D. Sleeman, "Modelling the growth of solid tumours and incorporating a method for their classification using nonlinear elasticity theory.", (1993) J. Math. Biol. 31, 431-479 [PDF file]

6) M.A.J. Chaplain and N.F. Britton, "A qualitative analysis of some models of tissue growth", (1993) Math. Biosci. 113, 77-89 [PDF file]

7) M.A.J. Chaplain, "The development of a spatial pattern in a model for cancer growth'', in Experimental and Theoretical Advances in Biological Pattern Formation pp 45-60 (Othmer, H.G., Maini, P.K. & Murray, J.D.), Plenum Press (1993).

8) M.A.J. Chaplain and N.F. Britton "On the concentration profile of a growth inhibitory factor in multicell spheroids.", (1993) Math. Biosci., 115, 233-245 [PDF file]

9) M.A.J. Chaplain, "The strain energy function of an ideal plant cell wall ", (1993) J. theor. Biol., 163, 77-97.

10) M.A.J. Chaplain and A.M. Stuart "A model mechanism for the chemotactic response of endothelial cells to tumour angiogenesis factor.", (1993) IMA J. Math. Appl. Med. Biol., 10, 149-168 [PDF file]

11) T. Hoefer, P.K. Maini, J.A. Sherratt, M.A.J. Chaplain, P. Chauvet, D. Metevier, P.C. Montes, J.D. Murray "A resolution of the chemotactic wave paradox'' (1994) Appl. Math. Lett., 7, 1-5. [PDF file]

12) M.A.J. Chaplain, D.L. Benson, P.K. Maini "Nonlinear diffusion of a growth inhibitory factor in multicell spheroids'', (1994) Math. Biosci., 121, 1-13

13) M.A.J. Chaplain "Reaction-diffusion pre-patterning and its potential role in tumour invasion'' (1995) J. Bio. Systems 3, 929-936. [PDF file]

14) T. Hoefer, P.K. Maini, J.A. Sherratt, M.A.J. Chaplain, J.D. Murray "Resolving the chemotactic wave paradox: A mathematical model for chemotaxis of dictyostelium amoebae'' (1995) J. Bio. Systems 3, 967-973. [PDF file]

15) N.F.Britton, S.M. Skevington & M.A.J. Chaplain "Mathematical Modelling of Acute Pain'' (1995) J. Bio. Systems 3, 1119-1124. [PDF file]

16) M.A.J. Chaplain, H.M. Byrne "Mathematical models for tumour angiogenesis: numerical simulations and nonlinear wave solutions'' (1995) Bull. Math. Biol. 57, 461-486 [PDF file]

17) H.M. Byrne, M.A.J. Chaplain "Explicit solutions of a simplified model of capillary sprout growth during tumour angiogenesis'' (1995) Appl. Math. Letters 8, 71-76. [PDF file]

18) H.M. Byrne, M.A.J. Chaplain "Growth of non-necrotic tumours in the presence and absence of inhibitors'' (1995) Math. Biosci. 130, 151-181 [PDF file]

19) M.A.J. Chaplain "The mathematical modelling of tumour angiogenesis and invasion'' (1995) Acta Biotheor. 43, 387-402 [PDF file]

20) M.A.J. Chaplain, S.M. Giles, B.D. Sleeman, R.J. Jarvis "A mathematical analysis of a model for tumour angiogenesis'' (1995) J. Math. Biol. 33, 744-770 [PDF file]

21) M.A.J. Chaplain "Avascular growth, angiogenesis and vascular growth in solid tumours: The mathematical modelling of the stages of tumour development'' (1996) Math. Comp. Modell. 23 (6), 47-87 [PDF file]

22) M.A.J. Chaplain & M.E. Orme "Travelling Waves Arising in Mathematical Models of Tumour Angiogenesis and Tumour Invasion'' (1996) FORMA 10, 147-170.

23) M.A.J. Chaplain & H.M. Byrne "The mathematical modelling of wound healing and tumour growth: Two sides of the same coin'' (1996) WOUNDS 8, 42-48.

24) M.E. Orme & M.A.J. Chaplain "A Mathematical Model of Vascular Tumour Growth and Invasion'' (1996) Math. Comp. Modelling 23 (10), 43-60 [PDF file]

25) M.E. Orme & M.A.J. Chaplain "A mathematical model of the first steps of tumour-related angiogenesis: capillary sprout formation and secondary branching'' (1996) IMA J. Math. Appl. Med. Biol. 13, 73-98 [PDF file]

26) N.F.Britton, M.A.J. Chaplain & S.M. Skevington "The role of N-methyl-D-aspartate (NMDA) receptors in wind-up - a mathematical model'' (1996) IMA J. Math. Appl. Med. Biol. 13, 193-205 [PDF file]

27) H.M. Byrne & M.A.J. Chaplain "Growth of Necrotic Tumours in the Presence and Absence of Inhibitors'' (1996) Math. Biosci. 135, 187-216 [PDF file]

28) S. A. Gourley, N.F. Britton, M.A.J. Chaplain & H.M Byrne "Mechanisms for stabilisation and destabilisation of systems of reaction-diffusion equations'' (1996) J. Math. Biol. 34, 857 - 877 [PDF file]

29) G. Pettet, M.A.J. Chaplain, D.L.S. McElwain, H.M. Byrne "On the role of angiogenesis in wound healing'' (1996) Proc. Roy. Soc. Lond. B 263, 1487-1493.

30) H.M. Byrne, M.A.J. Chaplain "On the role of cell-cell adhesion in models for solid tumour growth'' (1996) Math. Comp. Modelling 24, 1-17 [PDF file]

31) M.A.J. Chaplain "The mathematical modelling of angiogenesis and vascular tumour growth'' (1996) ZAMM 76 (S4), 24-27

32) H.M. Byrne, M.A.J. Chaplain "On the importance of constitutive equations in mechanochemical models of pattern formation'' (1996) Appl. Math. Letters 9, 85-90 [PDF file]

33) M.E. Orme and M.A.J. Chaplain "Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies'' (1997) IMA J. Math. Appl. Med. Biol. 14, 189-205 [PDF file]

34) M.A.J. Chaplain, A.R.A. Anderson "The mathematical modelling, simulation and prediction of tumour-induced angiogenesis'' (1997) Invas. Metast. 16, 222-234

35) A.R.A. Anderson, M.A.J. Chaplain "A mathematical model for capillary network formation in the absence of endothelial cell proliferation'' (1998) Appl. Math. Letters 11, 109-114 [PDF file]

36) H.M. Byrne, M.A.J. Chaplain "Free boundary problems arising in models of tumour growth and development'' (1998) Euro. Jnl. of Applied Mathematics 8, 639-658 [PDF file]

37) H.M. Byrne, M.A.J Chaplain "Apoptosis and necrosis as distinct cell loss mechanisms in avascular tumour growth'' (1998) J. theor. Med. 1, 223-235 [PDF file]

38) S.A. Gourley, H.M. Byrne, M.A.J. Chaplain "Asymptotic behaviour of solutions of a scalar differential equation with piecewise constant argument'' (1998) Differential and Integral Equations (to appear)

39) A.R.A. Anderson, M.A.J. Chaplain "Continuous and discrete mathematical models of tumour-induced angiogenesis'' (1998) Bull. Math. Biol. 60, 857-899 [PDF file]

40) M.A.J. Chaplain, V.A. Kuznetsov, Z.H. James, L.A. Stepanova "Spatio-Temporal Dynamics of the Immune System Response to Cancer'' (1998) (Refereed) Proceedings of the Mathematical Methods and Modelling in Health Sciences Conference (eds. M.A. Horn, G. Simonett, G. Webb), Vanderbilt University Press, ISBN 0-8265-1310-7.

41) J.C. Panetta, M.A.J. Chaplain, J. Adam "The mathematical modelling of cancer: A review'' (1998) (Refereed) Proceedings of the MMMHS Conference (eds. M.A. Horn, G. Simonett, G. Webb), Vanderbilt University Press, ISBN 0-8265-1310-7.

42) H.M. Byrne, M.A.J. Chaplain, G.J. Pettet, D.L.S. McElwain "A mathematical model of trophoblast invasion'' (1999) J. theor. Med. 1, 275-286

43) B.D. Sleeman, A.R.A. Anderson and M.A.J. Chaplain "A mathematical analysis of a model for capillary network formation in the absence of endothelial cell proliferation'' (1999) Appl. Math. Lett. 12, 121-127 [PDF file]

44) F.A. Davidson, A.R.A. Anderson and M.A.J. Chaplain "Steady State Solutions of a Generic Model for the Formation of Capillary Networks'' (1999) Appl. Math. Lett. 13, 127-132 [PDF file]

45) M. Baum, M.A.J. Chaplain, A.R.A. Anderson, M. Douek, J.S. Vaidya "Does breast cancer exist in a state of chaos?'' (1999) Euro. Jnl. Cancer 35, 886-891 [PDF file]

46) A.R.A. Anderson, M.A.J. Chaplain, E.L. Newman, R.J.C. Steele, A.M. Thompson "Mathematical modelling of tumour invasion and metastasis'' (2000) J. theor. Med. 2, 129-154 [PDF file]

47) D.L. Feltham and M.A.J. Chaplain "Analytical solutions of a minimal model of species migration in a bounded domain'' (2000) J. Math. Biol. 40, 321-342 [PDF file]

48) D.L. Feltham and M.A.J. Chaplain "Travelling waves in a model of species migration'' (2000) Appl. Math. Lett. 13, 67-73 [PDF file]

49) H.M. Byrne, M.A.J. Chaplain, I. Hopkinson and D. Evans "Mathematical modelling of angiogenesis in wound healing: Comparison of theory and experiment'' (2000) J. theor. Med. 2, 175-197

50) Panetta, J.C., Chaplain, M.A.J. and Cameron, D. "Modelling the effects of Paclitaxel and Cisplatin on breast and ovarian cancer'' (2000) J. theor. Med. 3, 11-23

51) Anderson, A.R.A., Chaplain, M.A.J., Garcia-Reimbert, C. and Vargas, C.A. "A gradient-driven mathematical model of anti-angiogenesis'' (2000) Math. Comput. Modell. 32, 1141-1152 [PDF file]

52) P.G. Schofield, M.A.J. Chaplain and S.F. Hubbard "Mathematical modelling of the spatio-temporal dynamics of host-parasitoid systems'' (2000) Euro. Comm. Math. Theor. Biol. 2, 12-16

53) A.W. Pitcairn, M.A.J. Chaplain, C.J. Weijer and A.R.A. Anderson "Continuum-discrete mathematical models of Dictyostelium aggregation'' (2000) Euro. Comm. Math. Theor. Biol. 2, 6-11.

54) M.A.J. Chaplain " Mathematical modelling of angiogenesis'' (2000) Journal of Neuro-Oncology 50, 37-51 [PDF file]

55) Byrne, H.M., Chaplain, M.A.J., Pettet, G., and McElwain, D.L.S. "An analysis of a mathematical model of trophoblast invasion'' (2001) Appl. Math. Letters 14, 1005-1010 [PDF file]

56) A. Gerisch, D.F. Griffiths, R. Weiner and M.A.J. Chaplain "Splitting methods for mixed hyperbolic-parabolic systems'' (2001) Numer. Meth. Part. Diff. Eq. 17, 152-168 [PDF file]

57) M.A.J. Chaplain, M. Ganesh and I.G. Graham "Spatio-temporal pattern formation on spherical surfaces: Numerical simulation and application to solid tumour growth'' (2001) J. Math. Biol. 42, 387-423 [PDF file]

58) S.A. Gourley, M.A.J. Chaplain and F. Davidson "Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation'' (2001) Dyn. Syst. 16, 173-192 [PDF file]

59) J.A. Sherratt, M.A.J. Chaplain "A new mathematical model for avascular tumour growth'' J. Math. Biol. (2001) 43 , 291-312 [PDF file]

60) R. Xu, M.A.J. Chaplain and L. Chen "Global stability for a delayed ratio-dependent predator-prey system without dominating instantaneous negative feedbacks'' Comm. Appl. Nonlinear Anal. (2001) 8, 17-27

61) Rui Xu, M.A.J. Chaplain and F.A. Davidson (2001) "Global asymptotic stability in a nonautonomous n-species Lotka-Volterra predator-prey system with infinite delays'' Applicable Analysis 80, 107-126 [PDF file]

62) S.A. Gourley, M.A.J. Chaplain "Travelling fronts in a food-limited population model with time delay'' Proc. Roy. Soc. Edin. A (2002) 132A, 75-89 [PDF file]

63) Rui Xu, Chaplain M.A.J. "Persistence and global stability in a delayed Gause-type predator-prey system without dominating instantaneous negative feedbacks'' J. Math. Anal. Appl. (2002) 265, 148-162 [PDF file]

64) P.G. Schofield, M.A.J. Chaplain and S.F. Hubbard "Mathematical modelling of host-parasitoid systems: effects of chemically mediated parasitoid foraging strategies on within- and between-generation spatio-temporal dynamics'' J. Theor. Biol. (2002) 214, 31-47 [PDF file]

65) S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain and J.A. Sherratt "Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies'' Bull. Math. Biol. (2002) 64, 673-702 [PDF file]

66) R. Xu, F.A. Davidson, and M.A.J. Chaplain "Persistence and stability for a two species ratio-dependent predator-prey system with distributed time delay'' J. Math. Anal. Appl. (2002) 269, 256-277 [PDF file]

67) Rui Xu, M.A.J. Chaplain and Lansun Chen "Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with infinite delays'' Appl. Math. Comp. (2002) 130, 295-309 [PDF file]

68) Rui Xu and M.A.J. Chaplain "Persistence and global stability in a delayed predator-prey system with Michaelis-Menten type functional response'' Appl. Math. Comp. (2002) 130, 441-455 [PDF file]

69) Rui Xu and M.A.J. Chaplain "Persistence and stability in an N-species ratio-dependent predator-prey system with distributed time delays'' Appl. Math. Comp. (2002) 131 , 59-80 [PDF file]

70) D.L. Feltham, M.A.J. Chaplain, I.M. Young and J. Crawford "A mathematical analysis of a minimal model of nematode migration in soil'' (2002) J. Biol. Sys. 10, 15-32 [PDF file]

71) J. Valenciano and M.A.J. Chaplain (2003) "Computing highly accurate solutions of a tumour angiogenesis model'' Math. Modell. Meth. Appl. Sci. 13, 747-766

72) Xu, R., Chen, L., Chaplain, M.A.J. (2003) "Attractivity in a delayed three-species ratio-dependent predator-prey system without dominating instantaneous negative feedback'' Acta Math. Appl. Sinica 19, 317-332 [PDF file]

73) Xu R, Chen LS, Chaplain MAJ (2003) "Global asymptotic stability in n-species nonautonomous Lotka-Volterra competitive systems with delays'' Acta Math. Sci. 23, 208-218.

74) J. Valenciano and M.A.J. Chaplain (2004) "An explicit subparametric spectral element method of lines applied to a tumour angiogenesis system of partial differential equations'' Math. Modell. Meth. Appl. Sci. 14, 1-23

75) Matzavinos, A., Chaplain, M., Kuznetsov, V. (2004) "Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour'' Math. Med. Biol. 21 , 1-34 [PDF file]

76) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Periodic solution of a Lotka-Volterra predator-prey model with dispersion and time delays'' Appl. Math. Comp. 148, 537-560 [PDF file]

77) Valenciano, J., Chaplain, M.A.J. (2004) "Mathematical modelling of the growth of a solid tumour using a moving spectral element method'' Math. Modell. Meth. Appl. Sci. (to appear)

78) Stephanou, A., Chaplain, M.A.J., Tracqui, P. (2004) "A mathematical model for the dynamics of large membrane deformations of isolated fibroblasts'' Bull. Math. Biol. 66, 1119-1154 [PDF file]

79) Samoletov, A. , Chaplain, M.A.J. and Levi, V. (2004) "Global spatiotemporal order and induced stochastic resonance due to a locally applied signal'' Phys. Rev. E 69 045102(R)

80) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays'' Discr. Cont. Dyn. Syst. B 4, 823-831

81) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Persistence and periodicity of a delayed ratio-dependent predator-prey model with stage structure and prey dispersal'' Appl. Math. Comput. 159, 823-846 [PDF file]

82) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Global stability of a Lotka-Volterra type predator-prey model with stage structure and time delay'' Appl. Math. Comput. 159, 863-880 [PDF file]

83) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Global asymptotic stability of periodic solution for a cooperative system with time delays'' Indian J. pure appl. Math. 35, 915-936

84) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments'' Nonlin. Anal. Real World Appl. 5, 183-206 [PDF file]

85) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Persistence and stability of a stage-structured predator-prey model with time delays'' Appl. Math. Comp. 150, 259-277 [PDF file]

86) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Periodic solutions of a predator-prey model with stage structure for predator'' Appl. Math. Comp. 154, 847-870 [PDF file]

87) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Persistence and global stability of a ratio-dependent predator-prey model with stage structure'' Appl. Math. Comp. 158, 729-744 [PDF file]

88) Xu, R., Chaplain, M.A.J., Davidson, F.A. (2004) "Periodic solutions of a discrete time three-species Lotka-Volterra food-chain system'' Nonlinear Funct. Anal. & Appl. 9, 429-440

89) Matzavinos, A., Chaplain, M. (2004) "Travelling wave analysis of a model of the immune response to cancer'' C. R. Biologies 327, 995-1008 [PDF file]

90) Xu R, Chen LS, Chaplain MAJ (2004) "Persistence and global stability in a delayed predator-prey system with Holling-type functional response'' Anziam J. 46, 121-141 [PDF file]

91) Xu R, Chaplain MAJ, Davidson FA (2004) "Periodic solution for a three-species Lotka-Volterra food-chain model with time delays'' Math. Comp. Modell. 40, 823-837 [PDF file]

92) Xu R, Chaplain MAJ, Davidson FA (2005) "Global stability of a stage-structured predator-prey model with prey dispersal'' Appl. Math. Comp. 171, 293-314 [PDF file]

93) Xu R, Chaplain MAJ, Davidson FA (2005) "Modelling and analysis of a competitive model with stage structure'' Math. Comp. Modell. 41, 159-175 [PDF file]

94) Xu R, Chaplain MAJ, Davidson FA (2005) "Permanence and periodicity of a delayed ratio-deplendent predator-prey model with stage structure'' J. Math. Anal. Appl. 303, 602-621 [PDF file]

95) Xu R, Chaplain MAJ, Davidson FA (2005) "Periodic solutions for a predator-prey model with Holling-type functional response and time delays'' Appl. Math. Comp. 161, 637-654 [PDF file]

96) Valenciano, J., Chaplain, M.A.J. (2005) "A Laguerre-Legendre spectral element method for the solution of partial differential equations on infinite domains: Application to the diffusion of tumour angiogenesis factors'' Math. Comp. Modell. 41, 1171-1192 [PDF file]

97) Stephanou, A., McDougall, S.R., Anderson, A.R.A. and Chaplain, M.A.J. (2005) "Mathematical Modelling of Flow in 2D and 3D Vascular Networks: Applications to Anti-angiogenic and Chemotherapeutic Drug Strategies" Math. Comput. Modell. 41, 1137-1156 [PDF file]

98) Schofield, P.G., Chaplain, M.A.J., Hubbard, S.F. (2005) "Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations'' J. Math. Biol. 50, 559-583 [PDF file]

99) Schofield, P.G., Chaplain, M.A.J., Hubbard, S.F. (2005) "Evolution of searching and life history characteristics in individual-based models of host-parasitoid-microbe associations'' J. theor. Biol. 237, 1-16 [PDF file]

100) Chaplain, M.A.J., Lolas, G. (2005) "Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system'' Math. Modell. Methods. Appl. Sci. 15, 1685-1734 [PDF file]

101) Gerisch, A., Chaplain, M.A.J. (2006) "Robust Numerical Methods for Taxis--Diffusion--Reaction Systems: Applications to Biomedical Problems'' Math. Comput. Modell. 43, 49-75 [PDF file]

102) Xu R, Chaplain MAJ, Davidson FA (2006) "Periodic solutions of a Lotka-Volterra type multi-species population model with time delays'' Math. Nachrichten 279, 911-927 [PDF file]

103) Xu R, Chaplain MAJ, Davidson FA (2006) "Global convergence of a reaction-diffusion predator-prey model with stage structure for the predator'' Appl. Math. Comp. 176, 388-401 [PDF file]

104) Xu R, Chaplain MAJ, Davidson FA (2006) "A Lotka-Volterra type food chain model with stage structure and time delays'' J. Math. Anal. Appl. 315, 90-105 [PDF file]

105) Enderling, H., Anderson, A.R.A., Chaplain, M.A.J., Munro, A.J., Vaidya, J. (2006) "Mathematical modelling of radiotherapy strategies for early breast cancer treatment'' J. theor. Biol. 241, 158-171 [PDF file]

106) McDougall, S., Anderson, A.R.A., Chaplain, M.A.J. (2006) "Mathematical Modelling of Dynamic Adaptive Tumour-Induced Angiogenesis: Clinical Implications and Therapeutic Targeting Strategies'' J. theor. Biol. 241, 564-589 [PDF file]

107) Pearce, I.G., Chaplain, M.A.J., Schofield, P.G., Anderson, A.R.A., Hubbard, S.F. (2006) "Modelling the spatio-temporal dynamics of multi-species host-parasitoid interactions: heterogeneous patterns and ecological implications'' J. theor. Biol. 241, 876-886 [PDF file]

108) Schor, S.L., Ellis, I.R., Harada, K., Motegi, K. Anderson, A.R.A., Chaplain, M.A.J., Keatch, R.P., Schor, A.M. (2006) "A novel sandwich assay for quantifying chemo-regulated cell migration within 3-dimensional matrices: Wound healing cytokines exhibit distinct motogenic activities compared to the transmembrane assay'' Cell Motil. Cytoskel. 63, 287-300 [PDF file]

109) Stephanou, A., McDougall, S., Anderson, A., Chaplain, M.A.J. (2006) "Mathematical modelling of the influence of blood rheological properties upon adaptive tumour-induced angiogenesis'' Math. Comput. Modell. 44, 96-123 [PDF file]

110) Chaplain, M.A.J., Graziano, L. Preziosi, L. (2006) "Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development'' Math. Med. Biol. 23, 197-229 [PDF file]

111) Chaplain, M.A.J., McDougall, S.R., Anderson, A.R.A. (2006) "Mathematical modelling of tumor-induced angiogenesis'' Annu. Rev. Biomed. Eng. 8, 233-257 [PDF file]

112) Enderling, H., Anderson, A., Chaplain, M.A.J., Rowe, G.W. (2006) "Visualisation of the Numerical Solution of Partial Differential Equation Systems in Three Space Dimensions and its Importance for Mathematical Models in Biology'' Math. Biosci. Eng., 3, 571-582 [PDF file]

113) Chaplain MAJ, Lolas G (2006) "Mathematical modelling of cancer invasion of tissue: Dynamic heterogeneity'' Net. Hetero. Med. 1, 399-439 [PDF file]

114) Xu R, Chaplain MAJ, Davidson FA, (2006) "Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays'' Chaos Sol. Fract. 30, 974-992 [PDF file]

115) Preedy, K., Schofield, P.G., Chaplain, M.A.J., Hubbard, S.F. (2006) "Disease induced dynamics in host-parasitoid systems: Chaos and coexistence'' Roy. Soc. Interface 4, 463-471 [PDF file]

116) Enderling, H., Chaplain, M.A.J., Anderson, A.R.A., Vaidya, J. (2007) "A mathematical model of breast cancer development, local treatment and recurrence'' J. theor. Biol. 246, 245-259 [PDF file]

117) Pearce I.G., Chaplain, M.A.J., Schofield, P.G., Anderson A.R.A., Hubbard S.F. (2007) "Chemotaxis-induced spatio-temporal heterogeneity in multi-species host-parasitoid systems'' J. Math. Biol. 55, 365-388 [PDF file]

118) Samoletov, A.A., Dettmann, C.P., Chaplain M.A.J. (2007) "Thermostats for "Slow" Configurational Modes'' J. Stat. Phys. 128, 1321-1336 [PDF file]

119) Gerisch, A., Chaplain, M.A.J. (2008) " Mathematical modelling of cancer cell invasion of tissue: Local and non-local models and the effect of adhesion'' J. Theor. Biol. 250, 684-704 [PDF file]

120) Lejeune O., Chaplain M.A.J., El Akili I., (2008) "Oscillations and bistability in the dynamics of cytotoxic reactions mediated by the response of immune cells to solid tumours'' Math. Comput. Modell. 47, 649-662 [PDF file]

121) Ramis-Conde I., Chaplain M.A.J., Anderson A.R.A., (2008) "Mathematical modelling of cancer cell invasion of tissue'' Math. Comput. Modell. 47, 533-545 [PDF file]

122) Ramis Conde, I., Drasdo, D., Chaplain, M.A.J., Anderson, A.R.A. (2008) "Modelling the influence of the E-Cadherin - beta-Catenin pathway in cancer cell invasion and tissue architecture: A multi-scale approach'' Biophys. J. 95, 155-165 [PDF file]

123) Stephanou, A., Mylona, E., Chaplain, M.A.J., Tracqui, P. (2008) "A computational model of cell migration coupling the growth of focal adhesions with oscillatory cell protrusions'' J. Theor. Biol. 253, 701-716 [PDF file]

124) Mistry, H.B., MacCallum, D.E., Jackson, R.C., Chaplain, M.A.J., Davidson F.A. (2008) "Modeling the temporal evolution of the spindle assembly checkpoint and role of Aurora B kinase'' PNAS 105, 20215-20220 [PDF file]

125) Szymanska, Z., Morales Rodrigo, C., Lachowicz, M., Chaplain, M.A.J. (2009) "Mathematical modelling of cancer invasion of tissue: The role and effect of nonlocal interactions'' Math. Mod. Meth. Appl. Sci. 19, 257-281 [PDF file]

126) Chaplain, M.A.J. (2009) Preface to Special Edition of Journal of Mathematical Biology on Computational Oncology, J. Math. Biol. 58, 481-483 [PDF file]

127) Macklin, P., McDougall, S., Anderson, A.R.A., Chaplain, M.A.J., Cristini, V., Lowengrub, J. (2009) "Multiscale modelling and nonlinear simulation of vascular tumour growth" J. Math. Biol. 58, 765-798 [PDF file]

128) Ramis-Conde, I., Chaplain, M.A.J., Anderson, A.R.A., Drasdo, D. (2009) "Multi-scale modelling of cancer cell intravasation: the role of cadherins in metastasis" Phys. Biol. 6 (2009) 016008 (12pp) [PDF file]

129) Gordon, K., Leuwen, I.M.M., Lain, S., Chaplain, M.A.J. (2009) "Spatio-temporal modelling of the p53--mdm2 oscillatory system" Math. Model. Nat. Phenom. 4, 97-116 [PDF file]

130) Joshi, B., Wang, X., Banerjee, S., Tian, H., Matzavinos, A., Chaplain, M.A.J. (2009) "On immunotherapies and cancer vaccination protocols: A mathematical modelling approach" J. Theor. Biol. 259, 820-827 [PDF file]

131) Enderling, H., Anderson, A.R.A., Chaplain, M.A.J., Beheshti, A., Hlatky, L., Hahnfeldt, P. (2009) "Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics" Cancer Res. 69, 8814-8821 [PDF file]

132) Mistry, H.B., MacCallum, D.E., Jackson, R.C., Chaplain, M.A.J., Davidson F.A. (2010) "A pharmacodynamic model of Aurora kinase inhibitors in the spindle assembly checkpoint" Frontiers in Bioscience 15, 249-258 [PDF file]

133) Preedy, K.F., Schofield, P.G., Liu, S., Matzavinos, A., Chaplain, M.A.J., Hubbard, S.F. (2010) "Modelling contact spread of infection in host-parasitoid systems: Vertical transmission of pathogens can cause chaos" J. Theor. Biol. 262, 441-451 [PDF file]

134) McDougall, S.R., Chaplain, M.A.J., Stephanou, A. and Anderson, A.R.A. (2010) "Modelling the Impact of Pericyte Migration and Coverage of Vessels on the Efficacy of Vascular Disrupting Agents" Math. Model. Nat. Phenom. 5, 163-202 [PDF file]

135) Vasiev, B., Balter, A., Chaplain, M.A.J., Glazier, J.A. and Weijer C.J. (2010) "Modeling Gastrulation in the Chick Embryo: Formation of the Primitive Streak" PLoS ONE 5(5): e10571. doi:10.1371/journal.pone.0010571 [PDF file]

136) Samoletov, A.A., Dettmann, C.P., Chaplain, M.A.J. (2010) "Notes on configurational thermostat schemes'' J. Chem. Phys. 132, Article Number 246101

137) Enderling, H., Chaplain, M.A.J., Hahnfeldt, P. (2010) "Quantitative modeling of tumor dynamics and radiotherapy" Acta Biotheor. 58, 341-353 [PDF file]

138) Chaplain, M.A.J., Lachowicz, M., Szymanska, Z., Wrzosek, D. (2011) "Mathematical modelling of cancer invasion: The importance of cell-cell adhesion and cell-matrix adhesion" Math. Mod. Meth. Appl. Sci. 21, 719-743 [PDF file]

139) Machado, M.J.C., Watson, M.G., Devlin, A.H., Chaplain, M.A.J., McDougall, S.R., Mitchell, C.A. (2011) "Dynamics of angiogenesis during wound healing: a coupled in vivo and in silico study" Microcirculation 18, 183-197 [PDF file]

140) Sturrock, M., Terry, A.J., Xirodimas, D.P., Thompson, A.M., Chaplain, M.A.J. (2011) "Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways" J. Theor. Biol. 21, 15-31 [PDF file]

141) Aubert, M., Chaplain, M.A.J., McDougall, S.R., Devlin, A., Mitchell, C.A. (2011) "A continuum mathematical model of the developing murine retinal vasculature" Bull. Math. Biol. 73, 2430-2451 [PDF file]

142) Andasari, V., Gerisch, A., Lolas, G., South, A.P., Chaplain, M.A.J. (2011) "Mathematical modeling of cancer cell invasion of tissue: biological insight from mathematical analysis and computational simulation" J. Math. Biol. 63, 141-171 [PDF file]

143) Frieboes, H.B., Chaplain, M.A.J., Thompson, A.M., Bearer, E.L., Lowengrub, J.S., Cristini, V. (2011) "Physical oncology: A bench-to-bedside quantitative and predictive approach" Cancer Res. 71, 298-302 [PDF file]

144) Terry, A.J., Sturrock, M., Dale, J.K., Maroto, M., Chaplain, M.A.J. (2011) "A spatio-temporal model of Notch signalling in the zebrafish segmentation clock: conditions for synchronised oscillatory dynamics" PLoS ONE 6(2): e16980. doi:10.1371/journal.pone.0016980 [PDF file]

145) Trucu, D., Chaplain, M.A.J., Marciniak-Czochra, A. (2011) "Three-scale convergence for processes in heterogeneous media" Applic. Analysis 91, 1351-1373 [PDF file]

146) Chaplain, M.A.J. (2011) "Multiscale mathematical modelling in biology and medicine" IMA J. Appl. Math. 76, 371-388 [PDF file]

147) Terry, A.J., Chaplain, M.A.J. (2011) "Spatio-temporal modelling of the NF-kB intracellular signalling pathway: the roles of diffusion, active transport, and cell geometry" J. Theor. Biol. 290, 7-26. [PDF file] [Movie 1] [Movie 2] [Movie 3] [Movie 4]

148) Swanson, K.R., Rockne, R.C., Claridge, J., Chaplain, M.A.J., Alvord Jr, E.C., Anderson, A.R.A. (2011) "Quantifying the role of angiogenesis in malignant progression of gliomas: in silico modeling integrates imaging and histology" Cancer Res. 71, 7366-7375 [PDF file]

149) Chaplain, M.A.J. (2012) Preface to Special Edition of Mathematical Modelling of Natural Phenomena on Cancer Modelling, Math. Model. Nat. Phenom. 7, 1-2 [PDF file]

150) Andasari, V., Chaplain, M.A.J. (2012) "Intracellular modelling of cell-matrix adhesion during cancer cell invasion" Math. Model. Nat. Phenom. 7, 29-48 [PDF file]

151) Watson, M.G., McDougall, S.R., Chaplain, M.A.J., Devlin, A.H., Mitchell, C.A. (2012) "Dynamics of angiogenesis during murine retinal development: a coupled in vivo and in silico study" J.R. Soc. Interface 9, 2351-2364 [PDF file]

152) Andasari, V., Roper, R., Swat, M.H., Chaplain, M.A.J. (2012) "Integrating intracellular dynamics using CompuCell3D and Bionetsolver: Applications to multiscale modelling of cancer cell growth and invasion" PLoS ONE 7(3): e33726. doi:10.1371/journal.pone.0033726 [PDF file]

153) van de Ven, A.L., Wu, M., Lowengrub, J., McDougall, S.R., Chaplain, M.A.J., Cristini, V., Ferrari, M., Frieboes, H.B. (2012) "Integrated intravital microscopy and mathematical modeling to optimize nanotherapeutics delivery to tumors" AIP Advances 2, 011208 (2012) [PDF file]

154) Sturrock, M., Terry, A.J., Xirodimas, D.P., Thompson, A.M., Chaplain, M.A.J. (2012) "Influence of the nuclear membrane, active transport, and cell shape on the Hes1 and p53–Mdm2 pathways: Insights from spatio-temporal modelling" Bull. Math. Biol. 74, 1531–1579 [PDF file] [Movie 1] [Movie 2]

155) Powathil, G.G., Gordon, K.E., Hill, L.A., Chaplain, M.A.J. (2012) "Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: Biological insights from a hybrid multiscale cellular automaton model" J. Theor. Biol. 308 , 1-19
[PDF file]

156) McDougall, S.R., Watson, M.G., Devlin, A.H., Mitchell, C.A., Chaplain, M.A.J. (2012) "A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature" Bull. Math. Biol. 74, 2272-2314 [PDF file]
Winner of the 2014 Lee Segel Prize for Best Paper in the Bulletin of Mathematical Biology [Prize Details]

157) Schlueter, D.K., Ramis-Conde-I., Chaplain, M.A.J. (2012) "Computational modeling of single-cell migration: The leading role of extracellular matrix fibers" Biophys. J. 103, 1141-1151 [PDF file] [Supplementary Material file]
Open Access

158) Al-Tameemi, M.M., Chaplain, M.A.J., D'Onofrio, A. (2012) "Evasion of tumours from the control of the immune system: consequences of brief encounters" Biology Direct 7:31, doi:10.1186/1745-6150-7-31. [PDF file]
Open Access

159) Sturrock, M., Hellander, A., Matzavinos, A., Chaplain, M.A.J. (2013) "Spatial stochastic modelling of the Hes1 gene regulatory network: intrinsic noise can explain heterogeneity in embryonic stem cell differentiation" J. R. Soc. Interface 10, 20120988. http://dx.doi.org/10.1098/rsif.2012.0988 [PDF file] [Supplementary Material file]
Open Access

160) Trucu, D., Lin, P., Chaplain, M.A.J., Wang, Y. (2013) "A multiscale moving boundary model arising in cancer invasion" Multiscale Model. Simul. 11, 309-335. [PDF file]

161) Wu, M., Frieboes, H.B., McDougall, S.R., Chaplain, M.A.J., Cristini, V., Lowengrub, J. (2013) "The effect of interstitial pressure on tumor growth: Coupling with the blood and lymphatic vascular systems" J. Theor. Biol. 320, 131-151 [PDF file]

162) Deakin, N.E., Chaplain, M.A.J. (2013) "Mathematical modeling of cancer invasion: the role of membrane-bound matrix metalloproteinases" Front. Oncol. 3, 70 [PDF file] [Supplementary Material file]
Open Access

163) Powathil, G.G., Adamson, D.J.A., Chaplain, M.A.J. (2013) "Towards Predicting the Response of a Solid Tumour to Chemotherapy and Radiotherapy Treatments: Clinical Insights from a Computational Model" PLoS Comput. Biol. 9(7): e1003120. doi:10.1371/journal.pcbi.1003120 [PDF file]
Open Access

164) Sturrock, M., Hellander, A., Aldakheel, S., Petzold, L., Chaplain, M.A.J. (2014) "The role of dimerisation and nuclear transport in the Hes1 gene regulatory network" Bull. Math. Biol. 76, 766-798. [PDF file]

165) Wu, M., Frieboes, H.B., Chaplain, M.A.J., McDougall, S.R., Cristini, V., Lowengrub, J.S. (2014) "The effect of interstitial pressure on therapeutic agent transport: Coupling with the tumor blood and lymphatic vascular systems" J. Theor. Biol. 355, 194-207. [PDF file]

166) Enderling, H., Chaplain, M.A.J. (2014) "Mathematical Modeling of Tumor Growth and Treatment" Curr. Pharm. Des. 20 4934-4940. [PDF file]

167) Domschke, P., Trucu, D., Gerisch, A., Chaplain, M.A.J. (2014) "Mathematical modelling of cancer invasion: Implications of cell adhesion variability for tumour infiltrative growth patterns" J. Theor. Biol. 361, 41-60. [PDF file]

168) Matzavinos, A., Shtylla, B., Voller, Z., Liu, S., Chaplain, M.A.J. (2014) "Stochastic Modelling of Chromosomal Segregation: Errors Can Introduce Correction" Bull. Math. Biol. 76 , 1590-1606. [PDF file]

169) Sturrock, M., Murray, P.J., Matzavinos, A., Chaplain, M.A.J. (2014) "Mean field analysis of a spatial stochastic model of a gene regulatory network" J. Math. Biol. DOI 10.1007/s00285-014-0837-0 [PDF file]

170) Schlueter, D.K., Ramis-Conde, I., Chaplain, M.A.J. (2015) "Multi-scale modelling of the dynamics of cell colonies: insights into cell adhesion forces and cancer invasion from in silico simulations" J. R. Soc. Interface 12: 20141080. http://dx.doi.org/10.1098/rsif.2014.1080 [PDF file] [Supplementary Material file]
Open Access

171) Powathil, G.G., Swat, M, Chaplain, M.A.J. (2015) "Systems Oncology: Towards patient-specific treatment regimes informed by multiscale mathematical modelling" Sem. Cancer Biol. 30, 13-20. [PDF file]

172) Chaplain, M.A.J., Ptashnyk, M., Sturrock, M. (2015) "Hopf Bifurcation in a Gene Regulatory Network Model: Molecular Movement Causes Oscillations" Math. Mod. Meth. Appl. Sci. 25, 1179-1215. [PDF file]
Open Access

173) Chaplain, M.A.J., Powathil, G.G. (2015) "Multiscale Modelling of Cancer Progression and Treatment Control: The Role of Intracellular Heterogeneities in Chemotherapy Treatment" Biophys. Rev. Lett. (to appear) DOI: 10.1142/S1793048015300029

174) Kim, Y., Powathil, G.G., Kang, H., Trucu, D., Kim, H., Lawler, S., Chaplain, M.A.J. (2015) "Strategies of eradicating glioma cells: A multi-scale mathematical model with miR-451-AMPK-mTOR control" PLoS ONE 10(1): e0114370. doi:10.1371/journal.pone.0114370
[PDF file]
Open Access

Updated 21.IV.15