**28** Publications

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Mult Scler 2021 Jan 11:1352458520981300. Epub 2021 Jan 11.

CORe, Department of Medicine, University of Melbourne, Melbourne, VIC, Australia/Melbourne MS Centre, Department of Neurology, Royal Melbourne Hospital, Melbourne, VIC, Australia.

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http://dx.doi.org/10.1177/1352458520981300 | DOI Listing |

January 2021

Math Biosci 2020 Dec 5:108520. Epub 2020 Dec 5.

Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, VIC 3122, Australia.

A model capturing the dynamics between virus and tumour cells in the context of oncolytic virotherapy is presented and analysed. The ability of the virus to be internalised by uninfected cells is described by an infectivity parameter, which is inferred from available experimental data. The parameter is also able to describe the effects of changes in the tumour environment that affect viral uptake from tumour cells. Results show that when a virus is inoculated inside a growing tumour, strategies for enhancing infectivity do not lead to a complete eradication of the tumour. Within typical times of experiments and treatments, we observe the onset of oscillations, which always prevent a full destruction of the tumour mass. These findings are in good agreement with available laboratory results. Further analysis shows why a fully successful therapy cannot exist for the proposed model and that care must be taken when designing and engineering viral vectors with enhanced features. In particular, bifurcation analysis reveals that creating longer lasting virus particles or using strategies for reducing infected cell lifespan can cause unexpected and unwanted surges in the overall tumour load over time. Our findings suggest that virotherapy alone seems unlikely to be effective in clinical settings unless adjuvant strategies are included.

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http://dx.doi.org/10.1016/j.mbs.2020.108520 | DOI Listing |

December 2020

Brain 2020 09;143(9):2742-2756

CORe, Department of Medicine, University of Melbourne, Melbourne, 3050, Australia.

In multiple sclerosis, treatment start or switch is prompted by evidence of disease activity. Whilst immunomodulatory therapies reduce disease activity, the time required to attain maximal effect is unclear. In this study we aimed to develop a method that allows identification of the time to manifest fully and clinically the effect of multiple sclerosis treatments ('therapeutic lag') on clinical disease activity represented by relapses and progression-of-disability events. Data from two multiple sclerosis registries, MSBase (multinational) and OFSEP (French), were used. Patients diagnosed with multiple sclerosis, minimum 1-year exposure to treatment, minimum 3-year pretreatment follow-up and yearly review were included in the analysis. For analysis of disability progression, all events in the subsequent 5-year period were included. Density curves, representing incidence of relapses and 6-month confirmed progression events, were separately constructed for each sufficiently represented therapy. Monte Carlo simulations were performed to identify the first local minimum of the first derivative after treatment start; this point represented the point of stabilization of treatment effect, after the maximum treatment effect was observed. The method was developed in a discovery cohort (MSBase), and externally validated in a separate, non-overlapping cohort (OFSEP). A merged MSBase-OFSEP cohort was used for all subsequent analyses. Annualized relapse rates were compared in the time before treatment start and after the stabilization of treatment effect following commencement of each therapy. We identified 11 180 eligible treatment epochs for analysis of relapses and 4088 treatment epochs for disability progression. External validation was performed in four therapies, with no significant difference in the bootstrapped mean differences in therapeutic lag duration between registries. The duration of therapeutic lag for relapses was calculated for 10 therapies and ranged between 12 and 30 weeks. The duration of therapeutic lag for disability progression was calculated for seven therapies and ranged between 30 and 70 weeks. Significant differences in the pre- versus post-treatment annualized relapse rate were present for all therapies apart from intramuscular interferon beta-1a. In conclusion we have developed, and externally validated, a method to objectively quantify the duration of therapeutic lag on relapses and disability progression in different therapies in patients more than 3 years from multiple sclerosis onset. Objectively defined periods of expected therapeutic lag allows insights into the evaluation of treatment response in randomized clinical trials and may guide clinical decision-making in patients who experience early on-treatment disease activity. This method will subsequently be applied in studies that evaluate the effect of patient and disease characteristics on therapeutic lag.

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http://dx.doi.org/10.1093/brain/awaa231 | DOI Listing |

September 2020

Nano Lett 2020 05 21;20(5):3396-3402. Epub 2020 Apr 21.

Department of Mathematics, School of Science, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, Victoria 3122, Australia.

Electropumping has been shown to be an effective means of inducing a net positive flow in fluids confined within planar nanochannels and carbon nanotubes. In this Letter, we investigate the efficiency of electropumping relative to Couette and Poiseuille flows. We apply a spatially uniform rotating electric field to a fluid confined in a functionalized nanochannel that couples the water's permanent dipole moment resulting in a net positive flow. We then induce a net positive flow in nanochannels for Couette and Poiseuille flows, matching volume flow rates to allow a direct comparison of average power dissipation per unit volume between all flow types. We show that while electropumping is less efficient than Couette flow, it is 4 orders of magnitude more efficient than Poiseuille flow. This suggests that, rather than being a mere novelty, electropumping is a far more energetically efficient means of transporting water compared to conventional pressure driven pumping.

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http://dx.doi.org/10.1021/acs.nanolett.0c00308 | DOI Listing |

May 2020

J Chem Phys 2019 Oct;151(16):164102

Department of Mathematics, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia.

We have computed the two- and three-particle contribution to the entropy of a Weeks-Chandler-Andersen fluid via molecular dynamics simulations. The three-particle correlation function and entropy were computed with a new method which simplified the calculation. Results are qualitatively similar to Lennard-Jones systems. We observed a numerical instability in the three-particle contribution. This phenomenon has been previously detected when the traditional method is used; thus, it is likely to be intrinsic in the computation. While the effect of statistical fluctuations can be removed through an extrapolation procedure, the discretization error due to the finite bin size is more difficult to characterize. With a correct choice of the bin size, a good estimate of the three-particle entropy contribution can be achieved at any state, even close to the freezing point. We observed that, despite the fact that the magnitude of the three-particle contribution increases significantly compared to that of the two-particle contribution as freezing is approached, the error induced from overestimation of the excess entropy by the two- and three-body terms exceeds that induced by approximating the excess entropy with the two body term alone.

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http://dx.doi.org/10.1063/1.5124715 | DOI Listing |

October 2019

J Theor Biol 2020 01 15;485:110052. Epub 2019 Oct 15.

School of Mathematics and Statistics, University of Sydney, Sydney, NSW, Australia. Electronic address:

Oncolytic virotherapy is a promising cancer treatment using genetically modified viruses. Unfortunately, virus particles rapidly decay inside the body, significantly hindering their efficacy. In this article, treatment perturbations that could overcome obstacles to oncolytic virotherapy are investigated through the development of a Voronoi Cell-Based model (VCBM). The VCBM derived captures the interaction between an oncolytic virus and cancer cells in a 2-dimensional setting by using an agent-based model, where cell edges are designated by a Voronoi tessellation. Here, we investigate the sensitivity of treatment efficacy to the configuration of the treatment injections for different tumour shapes: circular, rectangular and irregular. The model predicts that multiple off-centre injections improve treatment efficacy irrespective of tumour shape. Additionally, we investigate delaying the infection of cancer cells by modifying viral particles with a substance such as alginate (a hydrogel polymer used in a range of cancer treatments). Simulations of the VCBM show that delaying the infection of cancer cells, and thus allowing more time for virus dissemination, can improve the efficacy of oncolytic virotherapy. The simulated treatment noticeably decreases the tumour size with no increase in toxicity. Improving oncolytic virotherapy in this way allows for a more effective treatment without changing its fundamental essence.

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http://dx.doi.org/10.1016/j.jtbi.2019.110052 | DOI Listing |

January 2020

Langmuir 2019 Nov 29;35(45):14742-14749. Epub 2019 Oct 29.

Department of Mathematics, School of Science, Faculty of Science, Engineering and Technology , Swinburne University of Technology , Melbourne , Victoria 3122 , Australia.

Electropumping has shown great potential as an effective means of inducing a net positive flow of water in confined channels. In this paper we present the first nonequilibrium molecular dynamics study and continuum based numerical solutions that demonstrate an effective net positive flow between concentric carbon nanotubes (CNT) using electropumping. We apply a spatially uniform rotating electric field that couples to the water's permanent dipole moment. Taking advantage of the coupling between the spin angular momentum and the linear momentum we break the symmetry of the channel radius by functionalizing the inner CNT's outer surface with carboxyl groups to induce a net positive flow. We also show that our results for concentric nanotubes are consistent with our previous work where we demonstrated that an increase in functionalization beyond an optimal point in a single walled carbon nanotube resulted in a decrease in positive net flow. We then numerically solve the coupled hydrodynamic momentum equations to show that the nonequilibrium molecular dynamics results are consistent with the continuum theory.

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http://dx.doi.org/10.1021/acs.langmuir.9b02594 | DOI Listing |

November 2019

Math Biosci 2019 09 8;315:108238. Epub 2019 Aug 8.

Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Hawthorn, Victoria, Australia. Electronic address:

Cancer development is driven by mutations and selective forces, including the action of the immune system and interspecific competition. When administered to patients, anti-cancer therapies affect the development and dynamics of tumours, possibly with various degrees of resistance due to immunoediting and microenvironment. Tumours are able to express a variety of competing phenotypes with different attributes and thus respond differently to various anti-cancer therapies. In this paper, a mathematical framework incorporating a system of delay differential equations for the immune system activation cycle and an agent-based approach for tumour-immune interaction is presented. The focus is on those metastatic, secondary solid lesions that are still undetected and non-vascularised. By using available experimental data, we analyse the effects of combination therapies on these lesions and investigate the role of mutations on the rates of success of common treatments. Findings show that mutations, growth properties and immunoediting influence therapies' outcomes in nonlinear and complex ways, affecting cancer lesion morphologies, phenotypical compositions and overall proliferation patterns. Cascade effects on final outcomes for secondary lesions are also investigated, showing that actions on primary lesions could sometimes result in unexpected clearances of secondary tumours. This outcome is strongly dependent on the clonal composition of the primary and secondary masses and is shown to allow, in some cases, the control of the disease for years.

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http://dx.doi.org/10.1016/j.mbs.2019.108238 | DOI Listing |

September 2019

J Theor Biol 2019 11 7;480:129-140. Epub 2019 Aug 7.

Department of Mathematics, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, VIC, Australia.

Oncolytic viruses are genetically engineered to treat growing tumours and represent a very promising therapeutic strategy. Using a Gompertz growth law, we discuss a model that captures the in vivo dynamics of a cancer under treatment with an oncolytic virus. With the aid of local stability analysis and bifurcation plots, the typical interactions between virus and tumour are investigated. The system shows a singular equilibrium and a number of nonlinear behaviours that have interesting biological consequences, such as long-period oscillations and bistable states where two different outcomes can occur depending on the initial conditions. Complete tumour eradication appears to be possible only for parameter combinations where viral characteristics match well with the tumour growth rate. Interestingly, the model shows that therapies with a high initial injection or involving a highly effective virus do not universally result in successful strategies for eradication. Further, the use of additional, "boosting" injection schedules does not always lead to complete eradication. Our framework, instead, suggests that low viral loads can be in some cases more effective than high loads, and that a less resilient virus can help avoid high amplitude oscillations between tumours and virus. Finally, the model points to a number of interesting findings regarding the role of oscillations and bistable states between a tumour and an oncolytic virus. Strategies for the elimination of such fluctuations depend strongly on the initial viral load and the combination of parameters describing the features of the tumour and virus.

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http://dx.doi.org/10.1016/j.jtbi.2019.08.002 | DOI Listing |

November 2019

Math Biosci Eng 2019 03;16(4):1729-1749

Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC 3122, Australia.

In this paper, we construct a discrete time delay Lac operon model with nonlinear degradation rate for mRNA, resulting from the interaction among several identical mRNA pieces. By taking a discrete time delay as bifurcation parameter, we investigate the nonlinear dynamical behaviour arising from the model, using mathematical tools such as stability and bifurcation theory. Firstly, we discuss the existence and uniqueness of the equilibrium for this system and investigate the effect of discrete delay on its dynamical behaviour. Absence or limited delay causes the system to have a stable equilibrium, which changes into a Hopf point producing oscillations if time delay is increased. These sustained oscillation are shown to be present only if the nonlinear degradation rate for mRNA satisfies specific conditions. The direction of the Hopf bifurcation giving rise to such oscillations is also determined, via the use of the so-called multiple time scales technique. Finally, numerical simulations are shown to validate and expand the theoretical analysis. Overall, our findings suggest that the degree of nonlinearity of the model can be used as a control parameter for the stabilisation of the system.

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http://dx.doi.org/10.3934/mbe.2019083 | DOI Listing |

March 2019

Infect Dis Model 2018 15;3:118-135. Epub 2018 Jun 15.

School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia.

In some disease systems, the process of waning immunity can be subtle, involving a complex relationship between the duration of immunity-acquired either through natural infection or vaccination-and subsequent boosting of immunity through asymptomatic re-exposure. We present and analyse a model of infectious disease transmission where primary and secondary infections are distinguished to examine the interplay between infection and immunity. Additionally we allow the duration of infection-acquired immunity to differ from that of vaccine-acquired immunity to explore the impact on long-term disease patterns and prevalence of infection in the presence of immune boosting. Our model demonstrates that vaccination may induce cyclic behaviour, and the ability of vaccinations to reduce primary infections may not lead to decreased transmission. Where the boosting of vaccine-acquired immunity delays a primary infection, the driver of transmission largely remains primary infections. In contrast, if the immune boosting bypasses a primary infection, secondary infections become the main driver of transmission under a sufficiently long duration of immunity. Our results show that the epidemiological patterns of an infectious disease may change considerably when the duration of vaccine-acquired immunity differs from that of infection-acquired immunity. Our study highlights that for any particular disease and associated vaccine, a detailed understanding of the waning and boosting of immunity and how the duration of protection is influenced by infection prevalence are important as we seek to optimise vaccination strategies.

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http://dx.doi.org/10.1016/j.idm.2018.06.002 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6326260 | PMC |

June 2018

Bull Math Biol 2019 11 12;81(11):4313-4342. Epub 2018 Apr 12.

Centre for Disease Modelling, Department of Mathematics and Statistics, York University, Toronto, Canada.

Human papillomavirus (HPV), a sexually transmitted infection, is the necessary cause of cervical cancer, the third most common cancer affecting women worldwide. Prevention and control strategies include vaccination, screening, and treatment. While HPV prevention and control efforts are important worldwide, they are especially important in low-income areas with a high infection rate or high rate of cervical cancer. This study uses mathematical modeling to explore various vaccination and treatment strategies to control for HPV and cervical cancer while using Nepal as a case study. Two sets of deterministic models were created with the goal of understanding the impact of various prevention and control strategies. The first set of models examines the relative importance of screening and vaccination in an unscreened population, while the second set examines various screening scenarios. Partial rank correlation coefficients confirm the importance of screening and treatment in the reduction of HPV infections and cancer cases even when vaccination uptake is high. Results also indicate that less expensive screening technologies can achieve the same overall goal as more expensive screening technologies.

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http://dx.doi.org/10.1007/s11538-018-0425-3 | DOI Listing |

November 2019

J Theor Biol 2016 12 27;410:55-64. Epub 2016 Aug 27.

School of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia; Melbourne School of Population and Global Health, University of Melbourne, Victoria 3010, Australia; Modelling and Simulation, Infection and Immunity Theme, Murdoch Childrens Research Institute, Royal Children's Hospital, Parkville, Victoria 3052, Australia. Electronic address:

Incidence of whooping cough, an infection caused by Bordetella pertussis and Bordetella parapertussis, has been on the rise since the 1980s in many countries. Immunological interactions, such as immune boosting and cross-immunity between pathogens, have been hypothesised to be important drivers of epidemiological dynamics. We present a two-pathogen model of transmission which examines how immune boosting and cross-immunity can influence the timing and severity of epidemics. We use a combination of numerical simulations and bifurcation techniques to study the dynamical properties of the system, particularly the conditions under which stable periodic solutions are present. We derive analytic expressions for the steady state of the single-pathogen model, and give a condition for the presence of periodic solutions. A key result from our two-pathogen model is that, while studies have shown that immune boosting at relatively strong levels can independently generate periodic solutions, cross-immunity allows for the presence of periodic solutions even when the level of immune boosting is weak. Asymmetric cross-immunity can produce striking increases in the incidence and period. Our study underscores the importance of developing a better understanding of the immunological interactions between pathogens in order to improve model-based interpretations of epidemiological data.

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http://dx.doi.org/10.1016/j.jtbi.2016.08.034 | DOI Listing |

December 2016

J Chem Phys 2016 Sep;145(10):104501

Centre for Molecular Simulation, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia.

The thermodynamic, structural, and vapor-liquid equilibrium properties of neon are comprehensively studied using ab initio, empirical, and semi-classical intermolecular potentials and classical Monte Carlo simulations. Path integral Monte Carlo simulations for isochoric heat capacity and structural properties are also reported for two empirical potentials and one ab initio potential. The isobaric and isochoric heat capacities, thermal expansion coefficient, thermal pressure coefficient, isothermal and adiabatic compressibilities, Joule-Thomson coefficient, and the speed of sound are reported and compared with experimental data for the entire range of liquid densities from the triple point to the critical point. Lustig's thermodynamic approach is formally extended for temperature-dependent intermolecular potentials. Quantum effects are incorporated using the Feynman-Hibbs quantum correction, which results in significant improvement in the accuracy of predicted thermodynamic properties. The new Feynman-Hibbs version of the Hellmann-Bich-Vogel potential predicts the isochoric heat capacity to an accuracy of 1.4% over the entire range of liquid densities. It also predicts other thermodynamic properties more accurately than alternative intermolecular potentials.

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http://dx.doi.org/10.1063/1.4961682 | DOI Listing |

September 2016

Langmuir 2016 05 3;32(19):4765-73. Epub 2016 May 3.

School of Applied Sciences, RMIT University , Melbourne, Victoria 3001, Australia.

The extent of confinement effects on water is not clear in the literature. While some properties are affected only within a few nanometers from the wall surface, others are affected over long length scales, but the range is not clear. In this work, we have examined the dielectric response of confined water under the influence of external electric fields along with the dipolar fluctuations at equilibrium. The confinement induces a strong anisotropic effect which is evident up to 100 nm channel width, and may extend to macroscopic dimensions. The root-mean-square fluctuations of the total orientational dipole moment in the direction perpendicular to the surfaces is 1 order of magnitude smaller than the value attained in the parallel direction and is independent of the channel width. Consequently, the isotropic condition is unlikely to be recovered until the channel width reaches macroscopic dimensions. Consistent with dipole moment fluctuations, the effect of confinement on the dielectric response also persists up to channel widths considerably beyond 100 nm. When an electric field is applied in the perpendicular direction, the orientational relaxation is 3 orders of magnitude faster than the dipolar relaxation in the parallel direction and independent of temperature.

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http://dx.doi.org/10.1021/acs.langmuir.6b00791 | DOI Listing |

May 2016

Math Med Biol 2017 06;34(2):215-240

School of Mathematics and Statistics, University of Sydney, New South Wales, Australia.

We present a three-dimensional model simulating the dynamics of an anti-cancer T-cell response against a small, avascular, early-stage tumour. Interactions at the tumour site are accounted for using an agent-based model (ABM), while immune cell dynamics in the lymph node are modelled as a system of delay differential equations (DDEs). We combine these separate approaches into a two-compartment hybrid ABM-DDE system to capture the T-cell response against the tumour. In the ABM at the tumour site, movement of tumour cells is modelled using effective physical forces with a specific focus on cell-to-cell adhesion properties and varying levels of tumour cell motility, thus taking into account the ability of cancer cells to spread and form clusters. We consider the effectiveness of the immune response over a range of parameters pertaining to tumour cell motility, cell-to-cell adhesion strength and growth rate. We also investigate the dependence of outcomes on the distribution of tumour cells. Low tumour cell motility is generally a good indicator for successful tumour eradication before relapse, while high motility leads, almost invariably, to relapse and tumour escape. In general, the effect of cell-to-cell adhesion on prognosis is dependent on the level of tumour cell motility, with an often unpredictable cross influence between adhesion and motility, which can lead to counterintuitive effects. In terms of overall tumour shape and structure, the spatial distribution of cancer cells in clusters of various sizes has shown to be strongly related to the likelihood of extinction.

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http://dx.doi.org/10.1093/imammb/dqw004 | DOI Listing |

June 2017

J Math Neurosci 2015 Dec 12;5(1):28. Epub 2015 Aug 12.

Department of Biomedical and Health Sciences, School of Health Sciences, Faculty of Health, Arts and Design, Swinburne University of Technology, PO BOX 218, Hawthorn, 3122, Australia.

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http://dx.doi.org/10.1186/s13408-015-0028-3 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4532695 | PMC |

December 2015

Theor Biol Med Model 2014 Oct 4;11:43. Epub 2014 Oct 4.

Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, The University of Melbourne, Melbourne VIC, Australia.

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http://dx.doi.org/10.1186/1742-4682-11-43 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4200138 | PMC |

October 2014

J Theor Biol 2014 Nov 5;361:124-32. Epub 2014 Aug 5.

Melbourne School of Population and Global Health, The University of Melbourne, VIC, Australia; Murdoch Childrens Research Institute, VIC, Australia. Electronic address:

The impact of seasonal effects on the time course of an infectious disease can be dramatic. Seasonal fluctuations in the transmission rate for an infectious disease are known mathematically to induce cyclical behaviour and drive the onset of multistable and chaotic dynamics. These properties of forced dynamical systems have previously been used to explain observed changes in the period of outbreaks of infections such as measles, varicella (chickenpox), rubella and pertussis (whooping cough). Here, we examine in detail the dynamical properties of a seasonally forced extension of a model of infection previously used to study pertussis. The model is novel in that it includes a non-linear feedback term capturing the interaction between exposure and the duration of protection against re-infection. We show that the presence of limit cycles and multistability in the unforced system give rise to complex and intricate behaviour as seasonal forcing is introduced. Through a mixture of numerical simulation and bifurcation analysis, we identify and explain the origins of chaotic regions of parameter space. Furthermore, we identify regions where saddle node lines and period-doubling cascades of different orbital periods overlap, suggesting that the system is particularly sensitive to small perturbations in its parameters and prone to multistable behaviour. From a public health point of view - framed through the 'demographic transition' whereby a population׳s birth rate drops over time (and life-expectancy commensurately increases) - we argue that even weak levels of seasonal-forcing and immune boosting may contribute to the myriad of complex and unexpected epidemiological behaviours observed for diseases such as pertussis. Our approach helps to contextualise these epidemiological observations and provides guidance on how to consider the potential impact of vaccination programs.

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http://dx.doi.org/10.1016/j.jtbi.2014.07.028 | DOI Listing |

November 2014

Math Biosci 2014 Jul 20;253:50-62. Epub 2014 Apr 20.

Department of Mathematics and Statistics, The University of Melbourne, VIC, Australia.

A coupled ordinary differential equation model of tumour-immune dynamics is presented and analysed. The model accounts for biological and clinical factors which regulate the interaction rates of cytotoxic T lymphocytes on the surface of the tumour mass. A phase plane analysis demonstrates that competition between tumour cells and lymphocytes can result in tumour eradication, perpetual oscillations, or unbounded solutions. To investigate the dependence of the dynamic behaviour on model parameters, the equations are solved analytically and conditions for unbounded versus bounded solutions are discussed. An analytic characterisation of the basin of attraction for oscillatory orbits is given. It is also shown that the tumour shape, characterised by a surface area to volume scaling factor, influences the size of the basin, with significant consequences for therapy design. The findings reveal that the tumour volume must surpass a threshold size that depends on lymphocyte parameters for the cancer to be completely eliminated. A semi-analytic procedure to calculate oscillation periods and determine their sensitivity to model parameters is also presented. Numerical results show that the period of oscillations exhibits notable nonlinear dependence on biologically relevant conditions.

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http://dx.doi.org/10.1016/j.mbs.2014.04.003 | DOI Listing |

July 2014

Chaos 2013 Jun;23(2):023111

Vaccine and Immunisation Research Group, Murdoch Childrens' Research Institute and Melbourne School of Population Health, The University of Melbourne, Carlton VIC 3010, Australia.

The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.

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http://dx.doi.org/10.1063/1.4804176 | DOI Listing |

June 2013

PLoS One 2013 19;8(3):e59249. Epub 2013 Mar 19.

Department of Mathematics and Statistics, University of Melbourne, Victoria, Australia.

Cell migration in healthy and diseased systems is a combination of single and collective cell motion. While single cell motion has received considerable attention, our understanding of collective cell motion remains elusive. A new computational framework for the migration of groups of cells in three dimensions is presented, which focuses on the forces acting at the microscopic scale and the interactions between cells and their extracellular matrix (ECM) environment. Cell-cell adhesion, resistance due to the ECM and the factors regulating the propulsion of each cell through the matrix are considered. In particular, our approach emphasizes the role of receptors that mediate cell-cell and cell-matrix interactions, and examines how variation in their properties induces changes in cellular motion. As an important case study, we analyze two interacting cells. Our results show that the dynamics of cell pairs depends on the magnitude and the stochastic nature of the forces. Stronger intercellular stability is generally promoted by surface receptors that move. We also demonstrate that matrix resistance, cellular stiffness and intensity of adhesion contribute to migration behaviors in different ways, with memory effects present that can alter pair motility. If adhesion weakens with time, our findings show that cell pair break-up depends strongly on the way cells interact with the matrix. Finally, the motility for cells in a larger cluster (size 50 cells) is examined to illustrate the full capabilities of the model and to stress the role of cellular pairs in complex cellular structures. Overall, our framework shows how properties of cells and their environment influence the stability and motility of cellular assemblies. This is an important step in the advancement of the understanding of collective motility, and can contribute to knowledge of complex biological processes involving migration, aggregation and detachment of cells in healthy and diseased systems.

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http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0059249 | PLOS |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3602115 | PMC |

September 2013

J Chem Phys 2011 Mar;134(11):114112

Centre for Molecular Simulation, Swinburne University of Technology Hawthorn, Victoria 3122, Australia.

In this work we characterize the chaotic properties of atomic fluids subjected to planar mixed flow, which is a linear combination of planar shear and elongational flows, in a constant temperature thermodynamic ensemble. With the use of a recently developed nonequilibrium molecular dynamics algorithm, compatible and reproducible periodic boundary conditions are realized so that Lyapunov spectra analysis can be carried out for the first time. Previous studies on planar shear and elongational flows have shown that Lyapunov spectra organize in different ways, depending on the character of the defining equations of the system. Interestingly, planar mixed flow gives rise to chaotic spectra that, on one hand, contain elements common to those of shear and elongational flows but also show peculiar, unique traits. In particular, the influence of the constituent flows in regards to the conjugate-pairing rule (CPR) is analyzed. CPR is observed in homogeneously thermostated systems whose adiabatic (or unthermostated) equations of motion are symplectic. We show that the component associated with the shear tends to selectively excite some of those degrees, and is responsible for violations in the rule.

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http://dx.doi.org/10.1063/1.3567095 | DOI Listing |

March 2011

J Chem Phys 2010 Jun;132(24):244508

Centre for Molecular Simulation, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia.

In this work we present nonequilibrium molecular dynamics simulation results for the Lyapunov spectra of atomic fluids confined in narrow channels of the order of a few atomic diameters. We show the effect that realistic walls have on the Lyapunov spectra. All the degrees of freedom of the confined system have been considered. Two different types of flow have been simulated: planar Couette flow and planar Poiseuille flow. Several studies exist on the former for homogeneous flows, so a direct comparison with previous results is performed. An important outcome of this work is the demonstration of how the spectrum reflects the presence of two different dynamics in the system: one for the unthermostatted fluid atoms and the other one for the thermostatted and tethered wall atoms. In particular the Lyapunov spectrum of the whole system does not satisfy the conjugate-pairing rule. Two regions are instead distinguishable, one with negative pairs' sum and one with a sum close to zero. To locate the different contributions to the spectrum of the system, we computed "approximate" Lyapunov exponents belonging to the phase space generated by the thermostatted area and the unthermostatted area alone. To achieve this, we evolved Lyapunov vectors projected into a reduced dimensional phase space. We finally observe that the phase-space compression due to the thermostat remains confined into the wall region and does not significantly affect the purely Newtonian fluid region.

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http://dx.doi.org/10.1063/1.3446809 | DOI Listing |

June 2010

Phys Rev E Stat Nonlin Soft Matter Phys 2008 May 30;77(5 Pt 2):056217. Epub 2008 May 30.

Centre for Molecular Simulation, Swinburne University of Technology, P. O. Box 218, Hawthorn, Victoria 3122, Australia.

An investigation of the chaotic properties of nonequilibrium atomic systems under planar shear and planar elongational flows is carried out for a constant pressure and temperature ensemble, with the combined use of a Gaussian thermostat and a Nosé-Hoover integral feedback mechanism for pressure conservation. A comparison with Lyapunov spectra of atomic systems under the same flows and at constant volume and temperature shows that, regardless of whether the underlying algorithm describing the flow is symplectic, the degrees of freedom associated with the barostat have no overall influence on chaoticity and the general conjugate pairing properties are independent of the ensemble. Finally, the dimension of the strange attractor onto which the phase space collapses is found not to be significantly altered by the presence of the Nosé-Hoover barostatting mechanism.

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http://dx.doi.org/10.1103/PhysRevE.77.056217 | DOI Listing |

May 2008

Phys Rev E Stat Nonlin Soft Matter Phys 2007 Jun 7;75(6 Pt 2):066702. Epub 2007 Jun 7.

Centre for Molecular Simulation, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia.

The simulation of liquid systems in a nonequilibrium steady state under planar elongational flow (PEF) for indefinite time is possible only with the use of the so-called Kraynik-Reinelt (KR) periodic boundary conditions (PBCs) on the simulation cell. These conditions admit a vast range of implementation parameters, which regulate how the unit lattice is deformed under elongation and periodically remapped onto itself. Clearly, nonequilibrium properties of homogeneous systems in a steady state have to be independent of the boundary conditions imposed on the unit cell. In order to confirm the independence of measurable properties of a system under PEF from the particular set of periodic boundary conditions, we compute the Lyapunov spectra, apply the conjugate pairing rule, and carefully analyze the so-called unpaired exponents for an atomic fluid of various sizes and state points. We further compute the elongational viscosity for various implementations of boundary conditions. All our results confirm the independence from KR PBCs for the dynamics of phase-space trajectories and for the transport coefficients.

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http://dx.doi.org/10.1103/PhysRevE.75.066702 | DOI Listing |

June 2007

J Chem Phys 2007 Jan;126(4):044506

Centre for Molecular Simulation, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia.

Molecular dynamics simulations of liquid systems under planar elongational flow have mainly been performed in the NVT ensemble. However, in most material processing techniques and common experimental settings, at least one surface of the fluid is kept in contact with the atmosphere, thus maintaining the sample in the NpT ensemble. For this reason, an implementation of the Nose-Hoover integral-feedback mechanism for constant pressure is presented, implemented via the SLLOD algorithm for elongational flow. The authors test their procedure for an atomic liquid and compare the viscosity obtained with that in the NVT ensemble. The scheme is easy to implement, self-starting and reliable, and can be a useful tool for the simulation of more complex liquid systems, such as polymer melts and solutions.

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http://dx.doi.org/10.1063/1.2431359 | DOI Listing |

January 2007

Phys Rev E Stat Nonlin Soft Matter Phys 2006 Apr 18;73(4 Pt 2):046206. Epub 2006 Apr 18.

The simulation of planar elongational flow in a nonequilibrium steady state for arbitrarily long times has recently been made possible, combining the SLLOD algorithm with periodic boundary conditions for the simulation box. We address the fundamental questions regarding the chaotic behavior of this type of flow, comparing its chaotic properties with those of the well-established SLLOD algorithm for planar shear flow. The spectra of Lyapunov exponents are analyzed for a number of state points where the energy dissipation is the same for both flows, simulating a nonequilibrium steady state for isoenergetic and isokinetic constrained dynamics. We test the conjugate-pairing rule and confirm its validity for planar elongation flow, as is expected from the Hamiltonian nature of the adiabatic equations of motion. Remarks about the chaoticity of the convective part of the flows, the link between Lyapunov exponents and viscosity, and phase space contraction for both flows complete the study.

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http://dx.doi.org/10.1103/PhysRevE.73.046206 | DOI Listing |

April 2006