# Introducing the Mathematical Modelling of Infectious Disease Dynamics Collection

In recent months, the words “infection” and “outbreak” have not been far from anyone’s mind as we’ve faced the emergence of a new coronavirus, COVID-19. Across the globe, efforts are underway to control and limit the spread of the virus, and to find ways to treat those infected. As we watch these events unfurl, it is evident that there is still a lot that we, as a global community, do not yet understand about the dynamics of infectious diseases. The ways in which diseases spread are a concern that we all have a stake in?research that helps further our understanding of infectious diseases can influence each of our lives.

One distinct community of researchers working on understanding infectious disease dynamics is the mathematical modelling community, consisting of scientists from many different disciplines coming together to tackle a common problem through the use of mathematical models and computer simulations. Mathematics may sound like an unlikely hero to help us overcome a global epidemic; however, the insights we gain from studying the dynamics of infectious diseases by using equations describing fundamental variables are not to be underestimated. By approaching infectious diseases from a mathematical perspective, we can identify patterns and common systems in disease function, and it enables us to find some of the underlying structures that govern outbreaks and epidemics. Mathematical modellers make use of available data from current and previous outbreaks to predict who may get infected, where vaccination efforts will be most effective, and how to limit the spread of the disease.

Today at PLOS, we are launching a collection of new research papers submitted to a call for papers during the latter half of 2019 entitled “Mathematical Modelling of Infectious Disease Dynamics”, hosted by PLOS Biology, PLOS Computational Biology and PLOS ONE. The aim of this collection is to bring together different disciplines such as mathematics, biology, medicine and physics in order to shed light on the important topic of how mathematical models can help us understand infectious disease dynamics, and to present this research to the broad readership of these three journals and beyond. The accumulation of vital new research in a comprehensive collection will be a useful resource for understanding how infectious diseases operate, and how we can tackle them in real-time as well as in the future.

At PLOS we remain committed to our primary Open Access mission?ensuring that science is made as widely available as possible, and not locked behind paywalls. This is especially important in outbreak scenarios, such as the current COVID-19 epidemic, where it is critical that any new and relevant research be made easily accessible around the world, immediately at the time of publication.

Several of the papers in this collection present new methods that can be utilized in a range of scenarios. For instance, Patel and Sprouge developed a new estimator for predicting the basic reproduction number R0, which is the expected number of host cells infected by a single infected cell. This can be used for instance to understand the early stages of HIV infections, and for assessing the effectiveness of various therapies.

If two pathogen species, strains, or clones don’t interact, surely we can estimate the proportion of coinfected hosts as the simple product of the individual prevalences? A paper in PLOS Biology by Frédéric Hamelin, Nik Cunniffe and co-workers shows that this assumption is false; even if pathogens don’t interact, death of coinfected hosts causes net prevalences of individual pathogens to decrease simultaneously. The authors reinterpret data from previous studies accordingly.

Unusually large outbreaks of mumps across the United States in 2016 and 2017 raised questions about the extent of mumps circulation and the relationship between these and prior outbreaks. In this PLOS Biology paper, Shirlee Wohl, Pardis Sabeti and co-authors paired epidemiological data from public health investigations with analysis of mumps virus whole-genome sequences from 201 infected individuals. This allowed them to reconstruct mumps transmission links not evident from more traditional approaches and also revealed connections between apparently unrelated mumps outbreaks.

Endo and colleagues present a model of a phenomenon to which we can all relate, but which is still not well understood – the spread of infection within the household. They modelled the fine structures of family life to understand how disease typically enters and spreads through the household. Their findings support the idea that children are the most likely culprits of bringing disease into the household, and showed that there is a high level of transmission within generations, as well as between mother and child.

Rotavirus, the leading cause of diarrhea globally in children under 5, shows a biennial pattern of emergence in the US, while in many other high-income countries it exhibits an annual pattern. Ai and colleagues modelled the effect that higher vaccine coverage may have on this phenomenon, and found that increasing vaccine coverage from the current 70-75% to 85% would not only reduce the number of rotavirus cases, but also shift occurance to a more predictable annual epidemic pattern.

Two of the papers published in the collection are concerned with malaria. Kim and colleagues modelled the effectiveness of relapse control methods for Plasmodium vivax, finding that current vector control methods may have a negative effect on controlling disease prevalence, but that a shift towards control at a higher vector control level may be more efficient. Meanwhile, Wang and colleagues have constructed a stacking model for malaria prediction by combining two traditional time series models and two deep learning methods. Utilising malaria incidence data from Yunnan Province, China, they find that the ensemble architecture outperforms each of the sub-structure models in predicting malaria cases.

There are two papers in the collection that look at improving prediction of dengue infections. Leibig and colleagues present a network model of how international air travel can affect the spread of dengue across the world. By modelling the number of dengue-infected passengers arriving at various airports each month, the authors were able to study how dengue may be imported into different countries, and which routes would be the most likely for dengue-infected passengers to arrive by. Secondly, Liu and colleagues developed a model for predicting the spread of dengue infections that incorporates climate factors such as mean temperature, relative humidity and precipitation and applied this to data from dengue infections in Guangzhou, China, in order to help inform best practices in the early stages of a dengue outbreak.

The development of diseases can be influenced by personal factors such as age, which two of the papers in the collection address. Ku and Dodd developed a model for accounting for population aging when looking at tuberculosis incidence, as the impact of demographic change on disease forecasting is still not well understood. They applied the model to historical data of TB cases in Taiwan from 2005-2018, and used this to forecast what the incidence may look like until 2035. On the other end of the age spectrum, Rostgaard and colleagues used a Markov model to study the relationship between Epstein-Barr virus and infectious mononucleosis. Most people are typically infected with Epstein-Barr virus in early childhood, while infectious mononucleosis can sometimes follow in adolescence or later in life. The authors developed a statistical model to probe some of the uncertainties surrounding the origin and dynamics of infectious mononucleosis.

Some of the papers in the collection address new and emerging diseases. Dodero-Rojas and colleagues used the SEIR model to study the last three Chikungunya outbreaks in Rio de Janeiro, Brazil, and estimated their respective Basic Reproduction Numbers, R0. They also expanded their findings to include predictions for the Mayaro virus, which is an emerging disease in South America, and found that it has the possibility to become an epidemic disease in Rio de Janeiro.

The ability to accurately forecast disease patterns is crucial for ensuring that the right resources are in place to handle outbreaks. Morbey and colleagues looked at seasonal patterns in respiratory disease in England, and found that although syndromic indicators were affected by the timing of the peaks in seasonal disease, the demand for hospital beds was the highest on either 29th or 30th December, regardless of the timing of the syndromic peaks. Asadgol and colleagues also addressed seasonal patterns, this time in cholera in Iran, and predicted the effect of climate change on cholera incidence from 2020-2050 using an artificial neural network.

Given the interdisciplinary nature of the topic, we are grateful to countless authors, reviewers, Academic Editors and Guest Editors for making this collection a reality. We are especially grateful to our Guest Editor team, Konstantin Blyuss (University of Sussex), Sara Del Valle (Los Alamos National Laboratory), Jennifer Flegg (University of Melbourne), Louise Matthews (University of Glasgow) and Jane Heffernan (York University) for curating the collection. While 14 papers are included in this collection today, we’ll keep adding new papers as they are published, so please keep checking back for updates.

Guest Editor Konstantin Blyuss sums up the importance of this collection: “A recent and ongoing outbreak of coronavirus COVID-19 has highlighted the enormous significance of mathematical models for understanding the dynamics of infectious diseases and developing appropriate strategies for mitigating them. Mathematical models have helped identify the important factors affecting the spread of this infection both globally, and locally using country-specific information. They have also elucidated the effectiveness of different containment strategies and provided quantitative measures of disease severity”.

#### Konstantin Blyuss

Guest Editor, PLOS ONE, PLOS Biology, and PLOS Computational Biology

Konstantin Blyuss is a Reader in the Department of Mathematics at the University of Sussex, UK. He obtained his PhD in applied mathematics at the University of Surrey, which was followed by PostDocs at Universities of Exeter and Oxford. Before coming to Sussex in 2010, he was a Lecturer in Complexity at the University of Bristol. His main research interests are in the area of dynamical systems applied to biology, with particular interest in modelling various aspects of epidemiology, dynamics of immune responses and autoimmunity, as well as understanding mechanisms of interactions between plants and their pathogens

#### Sara del Valle

Guest Editor, PLOS ONE, PLOS Biology, and PLOS Computational Biology

Dr. Sara Del Valle is a scientist and deputy group leader in the Information Systems and Modeling Group at Los Alamos National Laboratory. She earned her Ph.D. in Applied Mathematics and Computational Science in 2005 from the University of Iowa. She works on developing, integrating, and analyzing mathematical, computational, and statistical models for the spread of infectious diseases such as smallpox, anthrax, HIV, influenza, malaria, Zika, Chikungunya, dengue, and Ebola. Most recently, she has been investigating the role of heterogeneous data streams such as satellite imagery, Internet data, and climate on detecting, monitoring, and forecasting diseases around the globe. Her research has generated new insights on the impact of behavioral changes on diseases spread as well as the role of non-traditional data streams on disease forecasting.

#### Jennifer Flegg

Guest Editor, PLOS ONE, PLOS Biology, and PLOS Computational Biology

Jennifer Flegg is a Senior Lecturer and DECRA fellow in the School of Mathematics and Statistics at the University of Melbourne. Her research focuses on mathematical biology in areas such as wound healing, tumour growth and epidemiology. She was awarded a PhD in 2009 from Queensland University of Technology on mathematical modelling of tissue repair. From 2010 – 2013, she was at the University of Oxford developing statistical models for the spread of resistance to antimalarial drugs. From 2014 – April 2017 she was a Lecturer in the School of Mathematical Sciences at Monash University. In May 2017 she joined the School of Mathematics and Statistics at the University of Melbourne as a Senior Lecturer in Applied Mathematics.

#### Louise Matthews

Guest Editor, PLOS ONE, PLOS Biology, and PLOS Computational Biology

Louise Matthews is Professor of Mathematical Biology and Infectious Disease Ecology at the Institute of Biodiversity, Animal Health and Comparative Medicine (BAHCM) at the University of Glasgow. She holds a degree and PhD in mathematics and has over 20 years research experience as an epidemiologist, with a particular focus on diseases of veterinary and zoonotic importance. Her current interests include a focus on drug resistance; antibiotic resistance in livestock; the community and the healthcare setting; anthelminthic resistance in livestock; and drug resistance in African Animal Trypanosomiasis. She is also interested in the integration of economic and epidemiological approaches such as game theory to understand farmer behaviour and micro-costing approaches to promote adoption of measures to reduce antibiotic resistance.

#### Jane Heffernan

Guest Editor, PLOS ONE, PLOS Biology, and PLOS Computational Biology

Jane Heffernan is a Professor in the Department of Mathematics and Statistics at York University, and York Research Chair (Tier II). She is also the Director of the Centre for Disease Modelling (CDM), and serves on the Board of Directors of the Canadian Applied and Industrial Mathematics Society (CAIMS). She is also very active in the Society for Mathematical Biology (SMB). Dr. Heffernan’s research program centers on understanding the spread and persistence of infectious diseases. Her Modelling Infection and Immunity Lab focuses on the development of new biologically motivated models of infectious diseases (deterministic and stochastic) that describe pathogen dynamics in-host (mathematical immunology) and in a population of hosts (mathematical epidemiology), as well as models in immuno-epidemiology, which integrate the in-host dynamics with population level models. More recently, Heffernan is focusing on applying mathematics and modelling to studying pollinator health and disease biology.

Featured Image : Spencer J. Fox, CC0

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