Mathematical modelling of infectious diseases
The field of disease ecology – the study of the spread and impact of parasites and pathogens within their host populations and communities – has a long history of using mathematical models. As such, it represents one of the richest areas of research at the interface of pure ecological theory and data. However, as with any field, there is the danger that those working in one particular area, or using one particular technique, will end up communicating primarily with themselves, resulting in discrete silos of research, with little cross-talk between sub-disciplines. For such an applied topic as disease control this could lead to theory that is irrelevant, or unable to be connected to the kind of data available to empiricists working on natural disease systems. This Special Issue was put together with the aim of presenting a snapshot of the current state of the field, with each paper describing existing or potential links between models and data as appropriate, and outlining areas for closer integration of theory and data in the future.
The papers in this Special Issue cover a range of topics, from highly conceptual to applied, across a diversity of systems, covering human diseases, livestock and wildlife conservation. Despite the diversity of topics and systems covered, a number of common points were raised by many of the authors. In particular, several emphasised how hard it is to accurately measure even basic properties of natural disease systems, such as true infection prevalence or transmission. However, despite this apparently-bleak situation, many authors describe a number of excellent analytical methods for bringing empirical data and mathematical models closer together than has previously been possible, often allowing the integration of data from multiple different sources. As seen with the recent ebola outbreak, and constant threats of newly emerging diseases (e.g., Zika virus), the ability to rapidly obtain decent parameter estimates from sparse data is only going to become more valuable.
However, as described by several authors, major obstacles still exist to prevent the seamless joining of theory and empirical approaches in disease ecology. Not least, there may still be a tendency for theoreticians and empiricists to focus on fundamentally different aspects of the system – either those that are mathematically convenient for the theoreticians, or those that are logistically easy to measure, for the empiricists – and these are rarely likely to be the same thing. As such perhaps the most important recurring point throughout this Special Issue is that there is a general need for closer integration of theoreticians and empiricists from the start of a project. To make the most of recent advances in parameter estimation techniques, it is essential that both empiricists and theoreticians embark together on an iterative process of study design, data collection, model development, and project refinement to ensure the theory is relevant and the data collected are interpretable. The papers in this Special Issue provide a roadmap of how this may be achieved for many key topics within the wider field of disease ecology.
Main image: ‘Extract from Mathematical modelling of infectious diseases’ special issue cover. Illustration: Flow chart and photograph illustrate the cattle-brucellosis system in Tanzania described in Mafalda et al. Photo credit: Jo Halliday.