Modelling the effect of seasonal influenza vaccination on the risk of pandemic influenza infection

<p>Abstract</p> <p>Background</p> <p>Recent studies have suggested that vaccination with seasonal influenza vaccine resulted in an apparent higher risk of infection with pandemic influenza H1N1 2009. A simple mathematical model incorporating strain competition and a hypothesised temporary strain-transcending immunity is constructed to investigate this observation. The model assumes that seasonal vaccine has no effect on the risk of infection with pandemic influenza.</p> <p>Results</p> <p>Results of the model over a range of reproduction numbers and effective vaccination coverage confirm this apparent increased risk in the Northern, but not the Southern, hemisphere. This is due to unvaccinated individuals being more likely to be infected with seasonal influenza (if it is circulating) and developing hypothesised temporary immunity to the pandemic strain. Because vaccinated individuals are less likely to have been infected with seasonal influenza, they are less likely to have developed the hypothesised temporary immunity and are therefore more likely to be infected with pandemic influenza. If the reproduction number for pandemic influenza is increased, as it is for children, an increase in the apparent risk of seasonal vaccination is observed. The maximum apparent risk effect is found when seasonal vaccination coverage is in the range 20-40%.</p> <p>Conclusions</p> <p>Only when pandemic influenza is recently preceded by seasonal influenza circulation is there a modelled increased risk of pandemic influenza infection associated with prior receipt of seasonal vaccine.</p

A Metapopulation Model of Tuberculosis Transmission with a Case Study from High to Low Burden Areas

Tuberculosis (TB) is a growing problem worldwide, especially with the emergence and high prevalence of multidrug-resistant strains. We develop a metapopulation model for TB spread, which is particularly suited to investigating transmission between areas of high and low prevalence. A case study of cross-border transmission in the Torres Strait region of Australia and Papua New Guinea (PNG) is considered and a sensitivity analysis is conducted. We find that only 6 of the 50 parameters analysed are important to the cumulative number of clinically active TB patients in the entire region. Of these, only the detection rate in PNG is found to be an important intervention parameter. We therefore give insight into the extent the area with the high burden of TB (PNG in the case study) is dominating the TB dynamics of the entire region. Furthermore, the sensitivity analysis results give insight into the data that most important to collect and refine, which is found to be data relating to the PNG parameters

Modelling the Seasonal Epidemics of Respiratory Syncytial Virus in Young Children

BACKGROUND Respiratory syncytial virus (RSV) is a major cause of paediatric morbidity. Mathematical models can be used to characterise annual RSV seasonal epidemics and are a valuable tool to assess the impact of future vaccines. OBJECTIVES Construct a mathematical model of seasonal epidemics of RSV and by fitting to a population-level RSV dataset, obtain a better understanding of RSV transmission dynamics. METHODS We obtained an extensive dataset of weekly RSV testing data in children aged less than 2 years, 2000-2005, for a birth cohort of 245,249 children through linkage of laboratory and birth record datasets. We constructed a seasonally forced compartmental age-structured Susceptible-Exposed-Infectious-Recovered-Susceptible (SEIRS) mathematical model to fit to the seasonal curves of positive RSV detections using the Nelder-Mead method. RESULTS From 15,830 specimens, 3,394 were positive for RSV. RSV detections exhibited a distinct biennial seasonal pattern with alternating sized peaks in winter months. Our SEIRS model accurately mimicked the observed data with alternating sized peaks using disease parameter values that remained constant across the 6 years of data. Variations in the duration of immunity and recovery periods were explored. The best fit to the data minimising the residual sum of errors was a model using estimates based on previous models in the literature for the infectious period and a slightly lower estimate for the immunity period. CONCLUSIONS Our age-structured model based on routinely collected population laboratory data accurately captures the observed seasonal epidemic curves. The compartmental SEIRS model, based on several assumptions, now provides a validated base model. Ranges for the disease parameters in the model that could replicate the patterns in the data were identified. Areas for future model developments include fitting climatic variables to the seasonal parameter, allowing parameters to vary according to age and implementing a newborn vaccination program to predict the effect on RSV incidence.HCM is funded by National Health and Medical Research Council Fellowship #1034254

We should not be complacent about our population-based public health response to the first influenza pandemic of the 21st century

Background: More than a year after an influenza pandemic was declared in June 2009, the World Health Organization declared the pandemic to be over. Evaluations of the pandemic response are beginning to appear in the public domain. Discussion. We argue that, despite the enormous effort made to control the pandemic, it is now time to acknowledge that many of the population-based public health interventions may not have been well considered. Prior to the pandemic, there was limited scientific evidence to support border control measures. In particular no border screening measures would have detected prodromal or asymptomatic infections, and asymptomatic infections with pandemic influenza were common. School closures, when they were partial or of short duration, would not have interrupted spread of the virus in school-aged children, the group with the highest rate of infection worldwide. In most countries where they were available, neuraminidase inhibitors were not distributed quickly enough to have had an effect at the population level, although they will have benefited individuals, and prophylaxis within closed communities will have been effective. A pandemic specific vaccine will have protected the people who received it, although in most countries only a small minority was vaccinated, and often a small minority of those most at risk. The pandemic vaccine was generally not available early enough to have influenced the shape of the first pandemic wave and it is likely that any future pandemic vaccine manufactured using current technology will also be available too late, at least in one hemisphere. Summary. Border screening, school closure, widespread anti-viral prophylaxis and a pandemic-specific vaccine were unlikely to have been effective during a pandemic which was less severe than anticipated in the pandemic plans of many countries. These were cornerstones of the population-based public health response. Similar responses would be even less likely to be effective in a more severe pandemic. We agree with the recommendation from the World Health Organisation that pandemic preparedness plans need review

Proceedings EMAC-2007

This Special Section of the ANZIAM Journal (Electronic Supplement) contains the refereed papers from the 8th Biennial Engineering Mathematics and Applications Conference (EMAC 2007) held at the University of Tasmania in July 2007. The EMAC series of conferences is held under the auspices of the Engineering Mathematics Group (EMG) (a special interest group of the Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) division of the Australian Mathematics Society) and Engineers Australia. The meeting provides a forum for researchers interested in the development and use of mathematical methods in engineering and applied mathematics. A further theme of the conference is the mathematical education of applied mathematicians and engineers

Editorial: Infectious Disease Modelling

The aim of this Special Issue on Infectious Disease Modelling 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 Theoretical Investigation into Phase Change Clothing Benefits for Firefighters under Extreme Conditions

We investigate the thermal performance of protective clothing that has an embedded phase change layer. Heat absorption due to phase change within the material is used to limit the thermal penetration of heat into the material and hence to the firefighter. The distribution of temperature within the fabric and skin during the exposure to an extreme firefighting situation is determined. To determine the protective nature of the clothing, we also include a model of the skin as three layers with differing thermal properties namely the epidermis, dermis and the subcutaneous layer. In our model, we have also incorporated the air gap between the garment and the body. The mathematical model is used to predict the duration of fire exposure during which the garment is able to protect the firefighter from getting first and second degree burns

Modelling the introduction of Wolbachia into Aedes aegypti mosquitoes to reduce dengue transmission

Infecting Aedes aegypti mosquitoes with the bacteria Wolbachia has been proposed as an innovative new strategy to reduce the transmission of dengue fever. Field trials are currently being undertaken in Queensland, Australia. However, few mathematical models have been developed to consider the persistence of Wolbachia- infected mosquitoes in the wild. This paper develops a mathematical model to determine the persistence of Wolbachia-infected mosquitoes by considering the competition between Wolbachia-infected and non-Wolbachia mosquitoes. The model has four steady states that are biologically feasible: all mosquitoes dying out, only non-Wolbachia mosquitoes surviving, and two steady states where non-Wolbachia and Wolbachia- infected mosquitoes coexist. The stability of the steady states is determined with respect to the key parameters in the mosquito life cycle. A global sensitivity analysis of the model is also conducted. The results show that the persistence of Wolbachia-infected mosquitoes is dominated by the reproductive rate, death rate, maturation rate and maternal transmission. For the parameter values where Wolbachia persists, it dominates the population, and hence the introduction of Wolbachia has great potential to reduce dengue transmission. doi:10.1017/S144618111200013

Analysing combustion waves in a model with chain branching

We analyse the travelling wave solutions in an adiabatic model with two-step chain branching reaction mechanism. We show that the behaviour of the combustion waves are similar to the case of the corresponding nonadiabatic one-step reaction, namely there is residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. We also analyse how the speed of the travelling wave solutions and the residual amount of fuel left behind the fuel change, as control parameters are varied. References V. V. Gubernov, G. N. Mercer, H. S. Sidhu and R. O. Weber, Evans function stability of nonadiabatic combustion waves, Proc. R. Soc. Lond. A, 460, 2004, 2415--2435.doi:10.1098/rspa.2004.1285 G. Joulin, A. Linan, G. S. S. Ludford, N. Peters and C. Schmidt-Laine, Flames with chain-branching/chain-breaking kinetics, SIAM J. Appl. Math., 45, 1985, 420--434. A. Linan, A theoretical analysis of premixed flame propagation with an isothermal chain-branching reaction Insituto Nacional de Technica Aerospacial ``Esteban Terradas'' (Madrid), USAFOSR Contract No. E00AR68-0031, Technical Report No. 1, 1971. A. Makino, Fundamental aspects of the heterogeneous flame in the self propagating hightemperature synthesis (SHS) process, Prog. Energy Combust. Sci., 27, 2001, 1--74. A. G. Merzhanov and E. N. Rumanov, Physics of reaction waves, Rev. Mod. Phys., 71, 1999, 1173--1211. doi:10.1103/RevModPhys.71.1173 H. Pitsch, and M. Bollig, 1994, FlameMaster, A Computer Code for Homogeneous and One-Dimensional Laminar Flame Calculations, RWTHAachen, Institut fur Technische Mechanik, 1994. A. L Sanchez, G. Balakrishnan, A. Linan and F. A. Williams, Relationships between bifurcation and numerical analyses for ignition of hydrogen-air diffusion flames, Combust. Flame, 105, 1996, 569--590. A. L. Sanchez, A. Lepinette, M. Bolling, A. Linan, and B. Lazaro, 2000, The reduced kinetic description of lean premixed combustion, Combust. Flame, 123, 2000, 436--464. K. Seshadri, N. Peters and F. A. Williams, 1994, Asymptotic analyses of stoichiometric and lean hydrogen-air flames, Combust. Flame, 96, 1994, 407--427. P. L. Simon, S. Kallidasis and S. K.Scott, Inhibition of flame propagation by an endothermic reaction, IMA J. Appl. Math., 68, 2003, 537--562. doi:10.1093/imamat/68.5.537 J. K. Bechtold and C. K. Law, The structure of premixed methane-air flames with large activation energy, Combust. Flame, 97, 1994, 317--338. doi:10.1016/0010-2180(94)90024-8 J. Warnatz, U. Maas and R. W. Dibble, Combustion: physical and chemical fundamentals, modelling and simulation, experiments, pollutant formation, Springer, Berlin, 1996. R. O. Weber, G. N. Mercer, H. S. Sidhu and B. F. Gray, Combustion waves for gases ($Le = 1$) and solids ($Le \rightarrow 1$), Proc. R. Soc. Lond. A, 453, 1997, 1105--1118. doi:10.1098/rspa.1997.0062 C. K. Westbrook and F. Dryer, Simplified reaction mechanisms for the oxidation of Hydrocarbon Fuels in Flames, Combust. Sci. Tech., 27, 1981, 31--43. Ya. B. Zeldovich, G. I. Barenblatt, V. B. Librovich and G. M Makhviladze, The mathematical theory of combustion and explosions Consultants Bureau, New York, 1985. J. W. Dold, R. O. Weber, R. W. Thatcher and A. A. Shah, Flame Ball With Thermally Sensitive Intermediate Kinetics Combust., Combust. Theory Mod., 7, 2003, 175--203. J. W. Dold and R. O. Weber, Reactive-Diffusive stability of planar flames with modified Zeldovich--Linan kinetics. In: F. J. Higuera, J. Jime'nez and J. M. Vega (Eds), Simplicity, Rigor and Relevance in Fluid Mechanics. A volume in honor of Amable Linan, CIMNE (Barcelona), 2004. V. V. Gubernov, G. N. Mercer, H. S. Sidhu and R. O. Weber, Evans function stability of combustion waves. SIAM J. Appl. Math., 63, 2003, 1259--1275. doi:10.1137/S003613990140024

A comparison of critical time definitions in multilayer diffusion

There are many ways to define how long diffusive processes take, and an appropriate “critical time†is highly dependent on the specific application. In particular, we are interested in diffusive processes through multilayered materials, which have applications to a wide range of areas. Here we perform a comprehensive comparison of six critical time definitions, outlining their strengths, weaknesses, and potential applications. A further four definitions are also briefly considered. Equivalences between appropriate definitions are determined in the asymptotic limit as the number of layers becomes large. Relatively simple approximations are obtained for the critical time definitions. The approximations are more accessible than inverting the analytical solution for time, and surprisingly accurate. The key definitions, their behaviour and approximations are summarized in tables. doi:10.1017/S144618111200002