Editorial : infectious disease modelling

The aim of this Special Issue is to collect together a group of outstanding applied mathematics research articles that provide new insight into our understanding of infectious diseases and infectious disease modelling. The scope of the articles is broad, encompassing both specific applications of modelling to particular examples of infectious diseases, as well as articles that are devoted to the development of more general theoretical insight.

A 250 μg/week dose of vitamin D was as effective as a 50 μg/d dose in healthy adults, but a regimen of four weekly followed by monthly doses of 1250 μg raised the risk of hypercalciuria

The risk of vitamin D insufficiency is increased in persons having limited sunlight exposure and dietary vitamin D. Supplementation compliance might be improved with larger doses taken less often, but this may increase the potential for side effects. The objective of the present study was to determine whether a weekly or weekly/monthly regimen of vitamin D supplementation is as effective as daily supplementation without increasing the risk of side effects. Participants were forty-eight healthy adults who were randomly assigned for 3 months to placebo or one of three supplementation regimens: 50 μg/d (2000 IU/d, analysed dose 70 μg/d), 250 μg/week (10 000 IU/week, analysed dose 331 μg/week) or 1250 μg/week (50 000 IU/week, analysed dose 1544 μg/week) for 4 weeks and then 1250 μg/month for 2 months. Daily and weekly doses were equally effective at increasing serum 25-hydroxyvitamin D, which was significantly greater than baseline in all the supplemented groups after 30 d of treatment. Subjects in the 1250 μg treatment group, who had a BMI >26 kg/m2, had a steady increase in urinary Ca in the first 3 weeks of supplementation, and, overall, the relative risk of hypercalciuria was higher in the 1250 μg group than in the placebo group (P= 0·01). Although vitamin D supplementation remains a controversial issue, these data document that supplementing with ≤ 250 μg/week ( ≤ 10 000 IU/week) can improve or maintain vitamin D status in healthy populations without the risk of hypercalciuria, but 24 h urinary Ca excretion should be evaluated in healthy persons receiving vitamin D3 supplementation in weekly single doses of 1250 μg (50 000 IU).

Tax Expenditure Management : A Critical Assessment

A tax expenditure is a 'tax break' allowed to a taxpayer or group of taxpayers, for example, by way of concession, deduction, deferral or exemption. The tax expenditure concept, as it was first identified, was designed to demonstrate the similarity between direct government spending on the one hand and spending through the tax system on the other. The identification of benefits provided through the tax system as tax expenditures allows analysts to consider the fiscal significant of those parts of the tax system which do not contribute to the primary purpose of raising revenue. Although a seemingly simple concept, it has generated a range of complex definitional and practical issues, and this book identifies and critical assesses the controversial aspects of tax expenditure and tax expenditure management.

A comparison of finite difference and finite volume methods for solving the space fractional advection-dispersion equation with variable coefficients

Transport processes within heterogeneous media may exhibit non-classical diffusion or dispersion; that is, not adequately described by the classical theory of Brownian motion and Fick's law. We consider a space fractional advection-dispersion equation based on a fractional Fick's law. The equation involves the Riemann-Liouville fractional derivative which arises from assuming that particles may make large jumps. Finite difference methods for solving this equation have been proposed by Meerschaert and Tadjeran. In the variable coefficient case, the product rule is first applied, and then the Riemann-Liouville fractional derivatives are discretised using standard and shifted Grunwald formulas, depending on the fractional order. In this work, we consider a finite volume method that deals directly with the equation in conservative form. Fractionally-shifted Grunwald formulas are used to discretise the fractional derivatives at control volume faces. We compare the two methods for several case studies from the literature, highlighting the convenience of the finite volume approach.

An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

Climate change and reduction of emissions of greenhouse gases from ships : an appraisal

Article 2(2) of the Kyoto Protocol imposes an obligation only on certain developed countries, working through the International Maritime Organisation (IMO), to pursue the reduction of greenhouse gas (GHG) emissions from marine bunker fuels. The IMO recently took the initiative to adopt a new legal instrument for the reduction of shipgenerated greenhouse gas emissions. Some developing countries have suggested that the proposed IMO initiative should strictly adhere to Article 2(2) of the Kyoto Protocol and the principle of Common but Differentiated Responsibility (CBDR). Against this backdrop, this article intends to review the extent to which it is possible to propose an international legal instrument for the reduction of GHG emissions from marine bunker fuels which is applicable only to ships from developed countries considering the complex characteristics of the international shipping industry. This article also examines how far this approach is justifiable even within the framework of the CBDR principle.

Decision and reasons for calling an ambulance : patients’ perspective

Background: Demand for pre-hospital emergency care is increasing in Australia as in many other countries. Using posthoc criteria such as triage, diagnosis and admission status, some authors view a considerable number of these as "inappropriate". Yet, calling an ambulance at the time of emergency is rarely studied from the patients’ or their carers’ perspective. This study interviewed patients about the decision, circumstances surrounding and reasons for calling an ambulance in Queensland, Australia. Methods: A cross-sectional survey of patients attending a sample of eight public hospital emergency departments in Queensland was undertaken between March and May 2011. In total, 911 questionnaires were collected (response rate: 67%), of whom 226 (24.8%) had arrived by ambulance. Results: In 35.6% of ambulance arrivals, the decision to request an ambulance was made by the patient; 25% by a doctor; 20% by a family member, friend or carer. Other callers included nurse, people at work or school, and passers-by. Reasons to request an ambulance included urgency (87%) and severity (84%) of the condition. Other reasons included requiring special care (76%), getting higher priority at the emergency department (34%), not having a car (34%), and financial concerns (17%). Decision to request an ambulance varied significantly according to the time of illness onset (e.g. on the day, week before), and location (e.g. home, outside). Conclusion: The decision to call an ambulance is made mostly by non-medical professionals in a perceived emergency situation. They call the ambulance for different reasons but mainly take into account the patient’s welfare and safety. Better understanding of these reasons will affect the direction and effectiveness of demand management strategies.

The growing demand for emergency healthcare

Emergency health is a critical component of health systems; one increasingly congested from growing demand and blocked access to care. The Emergency Health Services Queensland (EHSQ) study aimed to identify the factors driving increased demand for emergency healthcare. This study examined data on patients treated by the ambulance service and Emergency Departments across Queensland. Data was derived from the Queensland Ambulance Service’s (QAS) Ambulance Information Management System and electronic Ambulance Report Form and from the Emergency Department Information System (EDIS). Data was obtained for the period 2001-02 through to 2009-10. A snapshot of users for the 2009-10 year was used to describe the characteristics of users and comparisons made with the year 2003-04 to identify trends. Per capita demand for EDs has increased by 2% per annum over the decade and for ambulance by 3.7% per annum. The growth in ED demand is most significant in more urgent triage categories with decline in less urgent patients. The growth is most prominent amongst patients suffering injuries and poisoning, amongst both men and women and across all age groups. Patients from lower socioeconomic areas appear to have higher utilisation rates and the utilisation rate for indigenous people exceeds those of other backgrounds. The utilisation rates for immigrant people is less than Australian born however it has not been possible to eliminate the confounding impact of age and socioeconomic profiles. These findings contribute to an understanding of the growth in demand for emergency health. It is evident that the growth is amongst patients in genuine need of emergency healthcare and public rhetoric that congested emergency health services is due to inappropriate attendees is unsustainable. The growth in demand over the last decade reflects not only on changing demographics of the Australian population but also changes in health status, standards of acute health care and other social factors.

Numerical solution of an optimal control model of dendritic cell treatment of a growing tumour

A new optimal control model of the interactions between a growing tumour and the host immune system along with an immunotherapy treatment strategy is presented. The model is based on an ordinary differential equation model of interactions between the growing tu- mour and the natural killer, cytotoxic T lymphocyte and dendritic cells of the host immune system, extended through the addition of a control function representing the application of a dendritic cell treat- ment to the system. The numerical solution of this model, obtained from a multi species Runge–Kutta forward-backward sweep scheme, is described. We investigate the effects of varying the maximum al- lowed amount of dendritic cell vaccine administered to the system and find that control of the tumour cell population is best effected via a high initial vaccine level, followed by reduced treatment and finally cessation of treatment. We also found that increasing the strength of the dendritic cell vaccine causes an increase in the number of natural killer cells and lymphocytes, which in turn reduces the growth of the tumour.

Learning in Helicoverpa armigera (Lepidoptera: Noctuidae): a new look at the behaviour and control of a polyphagous pest

Recent experimental evidence has shown that learning occurs in the host selection behaviour of Helicoverpa armigera (Hübner), one of the world‘s most important agricultural pests. This paper discusses how the occurrence of learning changes our understanding of the host selection behaviour of this polyphagous moth. Host preferences determined from previous laboratory studies may be vastly different from preferences exhibited by moths in the field, where the abundance of particular hosts may be more likely to determine host preference. In support of this prediction, a number of field studies have shown that the ‘attractiveness’ of different hosts for H. armigera oviposition may depend on the relative abundance of these host species. Insect learning may play a fundamental role in the design and application of present and future integrated pest management strategies such as the use of host volatiles, trap crops and resistant crop varieties for monitoring and controlling this important pest species

No evidence for change in oviposition behaviour of Helicoverpa armigera (Hubner) (Lepidoptera : Noctuidae) after widespread adoption of transgenic insecticidal cotton

Cotton growing landscapes in Australia have been dominated by dual-toxin transgenic Bt varieties since 2004. The cotton crop has thus effectively become a sink for the main target pest, Helicoverpa armigera. Theory predicts that there should be strong selection on female moths to avoid laying on such plants. We assessed oviposition, collected from two cotton-growing regions, by female moths when given a choice of tobacco, cotton and cabbage. Earlier work in the 1980s and 1990s on populations from the same geographic locations indicated these hosts were on average ranked as high, mid and low preference plants, respectively, and that host rankings had a heritable component. In the present study, we found no change in the relative ranking of hosts by females, with most eggs being laid on tobacco, then cotton and least on cabbage. As in earlier work, some females laid most eggs on cotton and aspects of oviposition behaviour had a heritable component. Certainly, cotton is not avoided as a host, and the implications of these finding for managing resistance to Bt cotton are discussed.

Numerical solutions for thin film flow down the outside and inside of a vertical cylinder

We consider a model for thin film flow down the outside and inside of a vertical cylinder. Our focus is to study the effect that the curvature of the cylinder has on the gravity-driven instability of the advancing contact line and to simulate the resulting fingering patterns that form due to this instability. The governing partial differential equation is fourth order with a nonlinear degenerate diffusion term that represents the stabilising effect of surface tension. We present numerical solutions obtained by implementing an efficient alternating direction implicit scheme. When compared to the problem of flow down a vertical plane, we find that increasing substrate curvature tends to increase the fingering instability for flow down the outside of the cylinder, whereas flow down the inside of the cylinder substrate curvature has the opposite effect. Further, we demonstrate the existence of nontrivial travelling wave solutions which describe fingering patterns that propagate down the inside of a cylinder at constant speed without changing form. These solutions are perfectly analogous to those found previously for thin film flow down an inclined plane.