Alexandra B. Hogan

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.

Time series analysis of RSV and bronchiolitis seasonality in temperate and tropical Western Australia

Respiratory syncytial virus (RSV) causes respiratory illness in young children and is most commonly associated with bronchiolitis. RSV typically occurs as annual or biennial winter epidemics in temperate regions, with less pronounced seasonality in the tropics. We sought to characterise and compare the seasonality of RSV and bronchiolitis in temperate and tropical Western Australia. We examined over 13 years of RSV laboratory identifications and bronchiolitis hospitalisations in children, using an extensive linked dataset from Western Australia. We applied mathematical time series analyses to identify the dominant seasonal cycle, and changes in epidemic size and timing over this period. Both the RSV and bronchiolitis data showed clear winter epidemic peaks in July or August in the southern Western Australia regions, but less identifiable seasonality in the northern regions. Use of complex demodulation proved very effective at comparing disease epidemics. The timing of RSV and bronchiolitis epidemics coincided well, but the size of the epidemics differed, with more consistent peak sizes for bronchiolitis than for RSV. Our results show that bronchiolitis hospitalisations are a reasonable proxy for the timing of RSV detections, but may not fully capture the magnitude of RSV epidemics.

Age Structures in Mathematical Models for Infectious Diseases, with a Case Study of Respiratory Syncytial Virus

Mathematical modelling plays an important role in understanding the dynamics of transmissible infections, as information about the drivers of infectious disease outbreaks can help inform health care planning and interventions. This paper provides some background about the mathematics of infectious disease modelling. Using a common childhood infection as a case study, age structures in compartmental differential equation models are explored. The qualitative characteristics of the numerical results for different models are discussed, and the benefits of incorporating age structures in these models are examined. This research demonstrates that, for the SIR-type model considered, the inclusion of age structures does not change the overall qualitative dynamics predicted by that model. Focussing on only a single age class then simplifies model analysis. However, age differentiation remains useful for simulating age-dependent intervention strategies such as vaccination.

Potential impact of a maternal vaccine for RSV: A mathematical modelling study

Respiratory syncytial virus (RSV) is a major cause of respiratory morbidity and one of the main causes of hospitalisation in young children. While there is currently no licensed vaccine for RSV, a vaccine candidate for pregnant women is undergoing phase 3 trials. We developed a compartmental age-structured model for RSV transmission, validated using linked laboratory-confirmed RSV hospitalisation records for metropolitan Western Australia. We adapted the model to incorporate a maternal RSV vaccine, and estimated the expected reduction in RSV hospitalisations arising from such a program. The introduction of a vaccine was estimated to reduce RSV hospitalisations in Western Australia by 6-37% for 0-2month old children, and 30-46% for 3-5month old children, for a range of vaccine effectiveness levels. Our model shows that, provided a vaccine is demonstrated to extend protection against RSV disease beyond the first three months of life, a policy using a maternal RSV vaccine could be effective in reducing RSV hospitalisations in children up to six months of age, meeting the objective of a maternal vaccine in delaying an infants first RSV infection to an age at which severe disease is less likely.

Unexpected Infection Spikes in a Model of Respiratory Syncytial Virus Vaccination

Respiratory Syncytial Virus (RSV) is an acute respiratory infection that infects millions of children and infants worldwide. Recent research has shown promise for the development of a vaccine, with a range of vaccine types now in clinical trials or preclinical development. We extend an existing mathematical model with seasonal transmission to include vaccination. We model vaccination both as a continuous process, applying the vaccine during pregnancy, and as a discrete one, using impulsive differential equations, applying pulse vaccination. We develop conditions for the stability of the disease-free equilibrium and show that this equilibrium can be destabilised under certain extreme conditions, even with 100% coverage using an (unrealistic) vaccine. Using impulsive differential equations and introducing a new quantity, the impulsive reproduction number, we showed that eradication could be acheived with 75% coverage, while 50% coverage resulted in low-level oscillations. A vaccine that targets RSV infection has the potential to significantly reduce the overall prevalence of the disease, but appropriate coverage is critical.

A Model for the Spread of an Invasive Weed, Tradescantia fluminensis

Tradescantia fluminensis is an invasive weed and a serious threat to native forests in eastern Australia and New Zealand. Current methods of eradication are often ineffective, so understanding the growth mechanisms of Tradescantia is important in formulating better control strategies. We present a partial differential equation (PDE) model for Tradescantia growth and spatial proliferation that accounts for Tradescantia’s particular creeping and branching morphology, and the impact of self-shading on plant growth. This is the first PDE model to represent a weed that spreads via a creeping growth habit rather than by seed dispersal. We use a travelling wave analysis to investigate how Tradescantia extends to colonise new territory. Numerical simulations and analysis show that the model provides a good qualitative representation of the behaviour of this plant. This model provides a foundation for assessing different control and eradication strategies for Tradescantia.

The Formation and Launch of the Asia Pacific Consortium of Mathematics for Industry (APCMfI)

The Forum “Math-for-Industry” 2014 (FMfI 2014) represented the first opportunity to formally showcase the concept and formation of the Asia Pacific Consortium of Mathematics for Industry (APCMfI). This new initiative is intended to support the development of mathematics and its applications, and to enhance innovation and technology, in order to explore new research fields and improve the quality of life. A primary goal is to develop industrial mathematical research in the common Asia Pacific time zone of the East Asia and Oceania countries and to stimulate the two-way interaction between mathematics in academia and industry.