The NSW and ACT branches of the Australian and New Zealand Industrial and Applied Mathematics society will meet again on 25 November 2019. The meeting will be held at UNSW Sydney (Kensington Campus), at the Kirby Institute.
The talks will commence at 9.00 am and finish at 5.00 pm. Talks will be followed by dinner at the Cookhouse in Randwick (meal included in registration fee, details to follow).If you wish to join the meeting please register with the registration form.
Invited Speakers
Dr Justin Tzou (Macquarie University)
Dr Timothy Schlub (University of Sydney)
Dr Xiaoping Lu (University of Wollongong)
Abstract Submission
Delegates are invited to submit an abstract in order to present their research at the meeting. Abstract submission closes 11 November 2019.
Mercer Prize for best student presentation
A prize will be awarded for the best student presentation during the meeting. The prize is in honour of Professor Geoff Mercer.
ANZIAM NSW Branch AGM
ANZIAM Members from NSW should be aware that the AGM will be held during the meeting.
Conference Code of Conduct
Agreeing to the ANZIAM2019 Conference Code of Conduct is a condition of registration.
Organising Committee
David Khoury (UNSW), Deborah Cromer (UNSW), Christopher Lustri (MQ), Eva Stadler (UNSW) and Steffen Docken (UNSW)
A cure for HIV is prevented by the very small population of “latently” infected cells that persist despite treatment. Experimental and ethical challenges studying this cellular population result in few HIV infected recruits per study. Consequently, the analysis of such data presents several challenges including limited by statistical power, correlated errors and data with undefined error distributes. We use statistical modelling strategies to overcome these challenges and find that a limiting factor in many study designs is the high across participant variability; and limited number of cells available for collection per participant. We use power and sample size estimation to explore how these limiting factors need to be balanced to optimize future study designs in HIV latency.
The HIV epidemic remains a massive burden on global health, and as a result, a great deal of resources have been invested into developing an effective vaccine or cure that does not require life-long treatment. One of the fundamental questions that must be answered in order to evaluate potential vaccines is how effective must a vaccine be at blocking HIV replication in order to prevent infection following exposure? The ability of a virus such as HIV to grow and persist within an individual is dependent on the average number of subsequently infected cells resulting from viruses released from a single infected cell, also known as the Basic Reproductive Number or $R_0$ (similar to $R_0$ in epidemiology). A vaccine must lower $R_0$ to below 1 in order to prevent the infection from growing following exposure, and therefore the how effective a vaccine must be at blocking HIV replication is dependent on the underlying $R_0$ of HIV. As $R_0$ cannot be measured directly, $R_0$ has been estimated based on the observed growth of virus within people living with HIV or animals infected with the related simian immunodeficiency virus (SIV). However, such estimates of $R_0$ are heavily dependent on assumptions made about the replication cycle of HIV, such as the time interval from when a cell is infected to when the cell releases newly produced virus. In order to develop an effective, long-term cure for HIV, we need to better understand the dynamics of the infection.
To better understand the HIV replication cycle and therefore better determine what is needed of an effective vaccine, collaborators developed a barcoded SIV virus, which allows us to track the progress within an animal of multiple infections all initiated by a single virion. We observe a high degree of variability in the early stages of infection, with blood concentrations of different barcoded viruses varying by over four orders of magnitude. We demonstrate that this variability in fact arises from stochasticity in the processes of SIV replication, such as the time to viral production following infection. Finally, we examine how variability in time to viral production affects our estimate for $R_0$, thereby adjusting our expectation for the required efficacy of potential vaccines and curative therapies.
Antiretroviral Therapy (ART) provides effective control of human immunodeficiency virus (HIV) replication and maintains the viral loads of HIV at undetectable levels. Interruption of ART causes recrudescence of HIV plasma viremia due to the reactivation of latently HIV-infected cells, generally within weeks of discontinuation of ART. Here we characterize the timing of both the initial and subsequent successful viral reactivations following ART interruption in macaques infected with simian immunodeficiency virus (SIV). We compare these to previous results from human patients infected with HIV. We find that on average the time until the first successful viral reactivation event is longer than the time between subsequent successful reactivations. Based on this result, we hypothesise that the reactivation frequency of both HIV and SIV may fluctuate over time and that this may have implications for treatment of HIV. We develop a stochastic model to simulate the behaviour of viral reactivation following ART interruption that incorporates fluctuations in the frequency of reactivation. Our model is able to explain the difference in timing between the initial and subsequent successful reactivation events. Furthermore, we show that one of the impacts of a fluctuating reactivation frequency would be to significantly reduce the efficacy of “anti-latency” interventions for HIV that aim to reduce the frequency of reactivation. It is therefore essential to consider the possibility of a fluctuating reactivation frequency when assessing the impact of such intervention strategies.
The transmission, progression and treatment of human immunodeficiency virus (HIV) can have unexpected effects on the acquisition and progression of human papillomavirus (HPV) in co-infected patients. HPV is the causative agent of cervical cancer, which is a leading cause of cancer death among women in the developing world. We have developed a dynamic model of HIV and HPV co-infection, accounting for a range of demographic and behavioural factors with the aim of assessing the impact of the HIV epidemic on HPV and cervical cancer in Tanzania. The model has been calibrated using epidemic data local to Tanzania and has been subjected to extensive validation and sensitivity analysis. Findings from this analysis suggest that in the near-term, effective HIV treatment and prevention will increase rates of cervical cancer in Tanzanian women due to the removal of HIV-death as a competing risk. However, in the long-term HIV treatment is predicted to reduce rates of cervical cancer, due to reconstitution of the immune system delaying progression from HPV infection to cervical cancer. These findings are useful for predicting epidemic trends and assessing the unexpected impacts of interventions, which can be used to guide future healthcare policy and investment decisions.
For the Schnakenberg activator-inhibitor model, in the singularly perturbed regime of small activator to inhibitor diffusivity ratio $\varepsilon^2 \ll 1$, we demonstrate the analytic-numerical computation of the dynamics and stability thresholds of localized spot patterns on a curved torus. By way of a hybrid asymptotic-numerical analysis, we obtain the results in terms of certain quantities associated with the Green's function for both the Laplace-Beltrami ($\Delta_g$) and Helmholtz ($\Delta_g - V$) operators on the torus. To this end, we introduce a new analytic-numerical method for computing Green's functions on surfaces that requires only the numerical solution of a problem that is as regular as is desired. This allows properties of Green's functions at the location of the singularity to be determined to a high degree of accuracy. We will then describe how the solution of this problem also leads directly to a framework for analysing the narrow escape problem on curved surfaces.
Neuronal polarity is critical for proper functioning of neurons. There is a lot of experimental evidence suggesting that the early establishment of this polarity is a dynamical event. One potential mechanism for achieving this polarity is via Turing patterns, where non-linear molecular interactions spontaneously produce spatiotemporal concentration gradients. Linear instability analysis of reaction-diffusion systems shows that the pattern formed should generally correspond to eigenfunctions of the Laplace-Beltrami operator. In this work, we develop a numerical method to efficiently approximate Laplace-Beltrami operator over the geometry of a neuron. We then compare the Laplacian eigenfunctions with the concentration profile of fluorophore labels extracted from the fluorescence micrographs of early developing hippocampal neurons (< 5 days in vitro). We also found that the position of axon initial segments (AIS), which dictates the boundary between axonal and somatodendritic domains, is also correlated with the nodal plane of the eigenfunctions in some mature neurons. This suggests that neurons may be able to self-detect an optimal region for AIS such that mixing between the two distinct domains is minimized.
The effect of ambient temperature oscillations on the critical ignition criteria for large stockpiles undergoing self-heating is investigated.
A two dimension reaction-diffusion model is examined on a rectangular domain subject to sinusoidal variation of ambient temperature. The parameters for the temperature variation is on data obtained for the Port Kembla region. The oscillatory behaviour approximates yearly fluctuations around the mean temperature, diurnal fluctuations are not included. The control parameter for bifurcation analysis is the ratio of the length of the stockpile to its height.
This work is motivated by the self-sintering of steel by-products in stockpiles. In this application high temperatures due to self-heating are desirable as the resulting product has improved physical properties which make it easier to recycle on site.
The production of one-dimensional carbon structures has recently been made easier by using carbon nanotubes. Here, we consider encapsulated coronene molecules inside carbon nanotubes. Coronene is a flat, circular-shaped polycyclic aromatic hydrocarbon. Depending on the radius of the nanotube, specific configuration of the coronene molecules can be achieved, giving rise to the formation of stacked columns or aid in forming nanoribbons. Due to its symmetrical structure, we assume that a coronene molecule comprises three inner circular rings of carbon atoms and one outer circular ring of hydrogen atoms. Using a continuum approach and the Lennard-Jones potential, we obtain the interaction energy between the nanotube and the coronene molecule. Minimising this energy, we obtain a range of nanotube radii that give rise to particular configurations of a coronene molecule, including tilted, perpendicular to the nanotube’s axis and lying flat on the nanotube’s axis. We also extend this model to consider a stack of coronene molecules inside a nanotube. Finally, we compare our analytical results with molecular dynamics simulations as well as briefly discuss an alternative approach to model coronene using a flat disk instead of a combination of rings.
The results come from work done in 2002; Pinheiro's thesis for an MSci in Mathematics from 2003 done in exchange for a Vice Chancellor's grant. It was the first description of the Bubble Problem, which deals with plastic film formation, that involved exclusively Mathematics. The work was a development from the work of Tam, a Master's thesis from 2002, RMIT. Refinements on scaling, and description, thanks to how practical the problem is, allowed for much simpler calculations, and simulations in the computer using Maple led to confirmation of the results. This talk also brings some initial theory on how to avoid mistakes when modelling real-life situations.
A stock loan is a financial derivative that allows the holder of stocks use them as collaterals for borrowing fund. Mathematically, stock loans can be treated as a special type of American call options. In this talk, we will first discuss the “American” connection between stock loans and options. Then, we shall discuss the valuation of stock loans as American options in the following cases: non-recourse stock loans as American call options, margin call stock loans as American down-and-out barrier options with rebate, stocks loans under regime switching economy as American calls under regime switching economy and capped stock loans as American capped calls.
The clonal expansion of T cells during an infection is a tightly regulated event to ensure an appropriate immune response is mounted against invading pathogens. Although experiments have mapped the dynamics of the response from expansion to contraction, the mechanisms which control this response are not well defined. Here, we propose a model in which the dynamics of T cell expansion is ultimately controlled through continuous interactions between T cells and antigen presenting cells. T cell clonal expansion is proportional to antigen availability and antigen availability is regulated through downregulation of antigen by T cells. We show that our model can predict overall T cell expansion, recruitment into division and burst size per cell. Importantly, the findings demonstrates how an intimate relationship between T cells and APCs can explain the ability of the immune system to tailor its response to dose of antigen, regardless of initial T cell precursor frequencies.
Malaria is killing one child every two minutes in some of the most vulnerable parts of the word. The development of new antimalarial drug therapies has led to an essential reduction of malaria incidence and mortality rates for the past 15 years. But malaria also has a track record for developing resistance against its treatment, and it is now once more developing resistance against artemisinin, its most effective treatment in south-east Asia. Therefore, we need to continue developing better drug therapies. A standard method to assess drug efficacy is to look at how quickly parasites are removed from patients blood after the treatment. This method assumes that parasites remaining in the blood after the drug treatment are only alive parasites, and the drug killing rate is them thought to be equal to the parasites number decline rate. This standard method is imprecise because recently, we could estimate that dead parasites represent an important portion of circulating parasites after a treatment. Therefore, it is crucial to develop a new method of drug efficacy assessment that takes into account these dead circulating parasites.
To do so, we used data from ex-vivo cultures to measure parasite viability after treatment. Then, we used these parasite viability measurements to extend an existing within-host model of parasites growth and drugs killing. This extended model allowed us to separately measure the drug killing rate and the host removal rate of the dead parasites. Hence, our new model revealed artesunate killed parasite with a 0.3-hour half-life (95% CI: 0.2-h, 0.5-h), which is tenfold faster than the 3-hours estimate from the old measure. We then applied these approaches to understanding artemisinin resistance. The modelling demonstrated that parasites are much more resistant than is indicated by the standard method of assessing drug killing. In conclusion, more accurate models of drug killing are possible, and the malaria drug development pipeline urgently needs to adopt a new approach to assessing drug efficacy.
Malaria causes almost half a million deaths every year. In particular, malaria is common in areas with seasonal variations in the transmission rate. During the dry season, the number of mosquitoes is very low, there are few new infections, and few clinical malaria cases. However, shortly after the beginning of the rainy season both mosquitoes and malaria parasites become abundant. There is evidence that some people carry the parasites over the dry season and humans thus serve as a parasite reservoir. We consider a mathematical model in order to characterize these “carriers”. The model includes stochastic infectious mosquito bites with the rate of bites depending on the season and deterministic within-host dynamics. Each infectious mosquito bite inoculates a new parasite strain. For the within-host dynamics we consider parasite concentration, strain-specific immunity, and general immunity. Simulations indicate that children who are more exposed to mosquitoes and older children have lower parasite multiplication rates, i.e., their parasites grow slower. Thus, they have longer lasting infections and they can carry parasites through the dry season.
In this talk, I will present a gradient recovery technique based on an oblique projection for the virtual element method on polygonal meshes. I will give a short introduction to the virtual element method and introduce the gradient recovery operator and its construction. Finally, I will present some numerical results showing the comparison between convergence rates of the standard gradient and the recovered gradient.
We are developing a tomographic reconstruction algorithm for residual strain fields from Bragg-edge strain images. The Finite element approach is used to model a longitudinal ray transform which is expressed in terms of the same finite element mesh used to model equilibrium within the system. This model is not based on the usual structural finite element method where displacement is unknown. In our case, the elastic strain is unknown at the nodes. A linearly constrained least-squares optimisation problem is used to find the solution.
Dye-Sensitized Solar Cells (DSSCs) play a vital role in renewable energy as a third-generation photovoltaic device. The efficiency and current-voltage characters of a typical DSSC are usually derived from the density of conduction band electrons within the nanoporous semiconductor of the DSSC. Given the known fractal geometry of the commonly used semiconductor Titanium Dioxide ($\text{TiO}_2$), a natural direction for mathematically modelling DSSCs uses fractional diffusion. With Caputo fractional derivatives on time and space we solve this fractional diffusion equation analytically and numerically to investigate the effect of the fractional derivative on the diffusion process in an operating DSSC.
Ecosystem engineers are species which invade an already occupied habitat with an existing resident species and "engineer" the habitat to better suit their needs and survival. Although an obvious example would be the human species, a better example would be beavers, which builds dams to protect themselves from predators and allow easy access to food during winter. We will present a ordinary differential equation mathematical model to describe the state of the habitat and the population dynamics. The behaviour of the model will be classified and the model
extended to include stochastic and time delay effects.
Locusts are short horned grasshoppers that exhibit two behaviour types depending on their local density. These are; solitary, where they will actively avoid other locusts, and gregarious, where they will actively seek them out. It is in this gregarious state that locusts can form massive and destructive swarms or plagues. It is hypothesised that compact discrete food sources can lead to a greater likelihood that these outbreaks will occur. By modifying a previous gregarization model to include locust hunger and food interaction, we were able to test this hypothesis.