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Publications

Mathematical Medicine and Biology


C. Dempsey and A. Korobeinikov, A continuous strain-space model of viral evolution within a host. CRM Preprint, 2012 (link)

A.V. Melnik and A. Korobeinikov, Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility.Math. Biosci. Eng.,10(2) (2013, to appear).

E.V.Grigorieva, N.V. Bondarenko, E.N. Khailov, A. Korobeinikov, Analysis of optimal control problems for the process of wastewater biological treatment.Revista de Matemática: Teoría y Aplicaciones(2013, to appear).

E.V. Grigorieva, N.V. Bondarenko, E.N. Khailov and A. Korobeinikov, Three-dimensional nonlinear optimal control model of wastewater biotreatment,Neural, Parallel, and Scientic Computations20(1), 23-36 (2012) (link)

G. Huang, Y. Takeuchi and A. Korobeinikov, HIV evolution and progression of the infection to AIDS.J. Theor. Biol.,307149-159 (2012).link

E. Grigorieva, N. Bondarenko, E. Khailov and A. Korobeinikov, Finite-Dimensional Methods for Optimal Control of Autothermal Thermophilic Aerobic Digestion, in``Industrial Waste'', Kuan-Yeow Show and Xinxin Guo (Editors), InTech, 2012, 91-120. (ISBN 978-953-51-0253-3)link

S.M. O'Regan, T.C. Kelly, A. Korobeinikov, M.J.A. O'Callaghan and A.V. Pokrovskii, Chaos in a seasonally perturbed SIR model: avian inuenza in a seabird colony as a paradigm,J. Math Biol., 35 p. (2012). doi: 10.1007/s00285-012-0550-9 (link)

A. Pimenov, T.C. Kelly, A. Korobeinikov, M.J.A. O'Callaghan, A.V. Pokrovskii and D. Rachinskii, Memory effects in population dynamics: spread of infectious disease as a case study,Math. Model. Nat. Phenom., 7(3), 204-226 (2012). doi: 10.1051/mmnp/20127313 (link)

C. Vargas-De-León and A. Korobeinikov, Global stability of a population dynamics model with inhibition and negative feedback,Math. Med. Biol., 8 p. (2011). doi: 10.1093/imammb/dqr027 (link)

A.V. Melnik and A. Korobeinikov, Global asymptotic properties of staged models with multiple progression pathways for infectious diseases.Mathematical Biosciences & Engineering,8(4), 1019-1034 (2011). doi:10.3934/mbe.2011.8.1019 (link)

A. Pimenov, T.C. Kelly, A. Korobeinikov, M.J.A. O'Callaghan and A.V. Pokrovskii, Systems with Hysteresis in Mathematical Biology via a Canonical Example, in``Clustering Algorithms and Mathematical Modeling'', Caroline L. Wilson (Editor), Nova Science Publishers, New York 2010, 247-279 (link)

A. Korobeinikov, Global properties of a general predator-prey model with non-symmetric attack and consumption rate,Discrete and Continuous Dynamical System B,14(3) 1095-1103 (2010). doi:10.3934/dcdsb.2010.14.1095 (link)

S.M. O'Regan, T.C. Kelly, A. Korobeinikov, M.J.A. O'Callaghan and A.V. Pokrovskii, Lyapunov functions forSIRandSIRSepidemic models,Appl. Math. Lett.,23(4), 446-448 (2010) (link)

S.M. O'Regan, T.C. Kelly, A. Korobeinikov, M.J.A. O'Callaghan and A.V. Pokrovskii, The impact of an emerging avian influenza virus (H5N1) in a seabird colony. In``Global View at Fight against Influenza'', Petar M. Mitrasinovic (Editor), Nova Science Publishers, New York, 2009, 315-360 (link)

S. Iwami, Y. Takeuchi, X. Liu, A. Korobeinikov, E. Jung and T.-C. Jo, Theoretical Aspect of Prevention Policies against Influenza Pandemic. In``Global View at Fight against Influenza'', Petar M. Mitrasinovic (Editor), Nova Science Publishers, New York, 2009, 285-314 (link)

A. Korobeinikov, Stability of ecosystem: Global properties of a general prey-predator model.Mathematical Medicine and Biology,26(4), 309-321 (2009) (link)

A. Korobeinikov, Global asymptotic properties of virus dynamics models with dose dependent parasite reproduction and virulence, and nonlinear incidence rate,Mathematical Medicine and Biology,26(3), 225-239 (2009) (link)

A. Korobeinikov and W.T. Lee, Global asymptotic properties for a Leslie-Gower food chain model,Mathematical Biosciences & Engineering6(3) 585-590 (2009) (link)

A. Korobeinikov, Global properties ofSIRandSEIRepidemic models with multiple parallel infectious stages.Bull. Math. Biology71(1) 75-83 (2009) (link)

A. Korobeinikov, J. Norbury and G.C. Wake, Long-term coexistence for a competitive system of spatially varying reaction-diffusion equations,Nonlinear Analysis B10, 93-103 (2009).

A. Korobeinikov, P.K. Maini and W.J. Walker, Non-linear transmission, mortality and stability of discrete-time infectious disease models. In``Mathematical Biology Research Trends'', Lachlan B. Wilson (Editor), Nova Science Publishers, New York, 2008, 237-259.

A. Korobeinikov and S.V. Petrovskii, Toward a general theory of ecosystem stability: plankton--nutrient interaction as a paradigm, in``Aspects of Mathematical Modelling'', Roger J. Hosking and Ezio Venturino (Editors), Birkhauser, Basel, 2008, 27-40.

S.M. O'Regan, T.C. Kelly, A. Korobeinikov, M.J.A. O'Callaghan, and A.V. Pokrovskii, Qualitative and numerical investigations of the impact of a novel pathogen on a seabird colony.Journal of Physics: Conference Series138(2008), 012018 (link)

S. Iwami, Y. Takeuchi, A. Korobeinikov and Xianning Liu, Prevention of avian influenza epidemic: What policy should we choose?Journal of Theoretical Biology252(4) 732-741 (2008).

D. Okuonghae and A. Korobeinikov, Dynamics of Tuberculosis: The effect of Direct Observation Therapy Strategy (DOTS) in Nigeria,Mathematical Modelling of Natural Phenomena: Epidemiology2(1) 99-111 (2007).

A. Korobeinikov, Global properties of infectious disease models with non-linear incidence,Bulletin of Mathematical Biology69(6) 1871-1886 (2007).

A. Korobeinikov, Lyapunov functions and global stability for SIR and SIRS epidemiological models with non-linear transmission,Bulletin of Mathematical Biology68(3) 615-626 (2006).

A. Korobeinikov and P.K. Maini, Nonlinear incidence and stability of infectious disease models,Mathematical Medicine and Biology22, 113-128 (2005).

V. Calvez, A. Korobeinikov and P.K. Maini, Cluster formation for multi-strain infections with cross-immunity,J. Theor. Biol.233(1), 75-83 (2005).A. Korobeinikov, Global properties of basic virus dynamics models,Bulletin of Mathematical Biology66(4) 879-883 (2004).

A. Korobeinikov, Lyapunov functions and global properties for SEIR and SEIS epidemic models,Mathematical Medicine and Biology21(2) 75-83 (2004).

A. Korobeinikov and P.K. Maini, A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence,Mathematical Biosciences & Engineering1(1) 57-60 (2004).

A. Korobeinikov, P.K. Maini and W.J. Walker, Estimation of effective vaccination rate: pertussis in New Zealand as a case study,J. Theor. Biol.224(2) 269-275 (2003).

R.M. Cullen, A. Korobeinikov, W.J. Walker, Seasonality and critical community size for infectious diseases,ANZIAM Journal44, 501-512 (2003).

A. Korobeinikov and G.C. Wake, Lyapunov functions and global stability forSIR,SIRSandSISepidemiological models,Appl. Math. Lett.15(8) 955-961 (2002).

A. Korobeinikov, A Lyapunov function for Leslie-Gower predator prey models,Appl. Math. Lett.14(6) 697-699 (2001).

A. Korobeinikov, R.M. Cullen, W.J. Walker, Disease-induced mortality and stability of infectious disease models,Complexity International,8(2001) (link)

A. Korobeinikov, R.M. Cullen, W.J. Walker, Disease-induced mortality and stability of infectious disease models, In“Applied Complexity: From Neural Nets to Managed Landscapes”, S. Halloy and T. Williams (Editors), New Zealand Institute for Crop and Food Research, Christchurch (2000) 291-307.

A. Korobeinikov and G.C. Wake, Global properties of the three-dimensional prey-predator Lotka-Volterra systems,J. Appl. Math. Decision Sciences3(2) 155-162 (1999).


Mathematical economics


A. Korobeinikov, P. Read, A. Parshotam and J. Lermit, Modelling regional markets for co-produced timber and biofuel,Ecological Economics,69(3), 553-561 (2010) (link)

A. Korobeinikov, Financial crisis: an attempt of mathematical modelling,Appl. Math. Lett.,22(12), 1882-1886 (2009) (link)

A. Korobeinikov, P. Read, J. Lermit and A. Parshotam, Modeling key market impacts and land allocation for biofuel production and forestry,J. Appl. Math. Decision Sciences(2006) (link)

A. Korobeinikov, P. Read, J. Lermit, A. Parshotam and P. Kathirgamanathan, Market dynamics of allocating land to biofuel and forest sinks, in Proc. International Congress of Modelling and Simulation (MODSIM 2001), Volume 3: Socioeconomic Systems, Canberra (2001) 1079-1084.


Industrial Mathematics and Other Areas


T. Zhelev, K. Semkov, E. Mooney, T. Majozi and A. Korobeinikov, Industrial heat utilisation through water management,Heat Transfer Engineering(to appear).

A. Korobeinikov, A. Kovacec, M. McGuinness, M. Pascoal, A. Pereira and S. Vilela, Optimizing the profit from a complex cascade of hydroelectric stations with recirculating water,Mathematics-in-Industry Case Studies Journal,2, 111-133 (2010) (link)

J. Rojas, M. Burke, M. Chapwanya, K. Doherty, I. Hewitt, A. Korobeinikov, M. Meere, S. McCarthy, M. O'Brien, Vo Thi Ngoc Tuoi, H. Winstanley and T. Zhelev, Modeling of Autothermal Thermophylic Aerobic Digestion,Mathematics-in-Industry Case Studies Journal,2, 34-63 (2010) (link)

A. Korobeinikov and A. McNabb, Long-term global climate dynamics: A Hopf bifurcation causing recurrent Ice Ages,J. Appl. Math. Decision Sciences5(4), 201-214 (2001).

A. Korobeinikov, Numerical simulation of the oscillations of non-Newtonian viscous fluids with a free surface,J. Appl. Math. Decision Sciences4(2), 111-123 (2000).