How mathematical modelling contributes to control of infectious diseases

Mathematic modeling has recently demonstrated that a broad range of non-pharmaceutical interventions may contribute to preventing dissemination of infectious diseases in both pandemic and non-pandemic situations. In particular, hand hygiene, use of face masks, physical distancing, quarantine, isolation, regular screening and contact tracing have all shown to be valuable, powerful instruments in the toolbox of public health officials, concludes Thi Mui Pham, who received her PhD on February 23 in Utrecht.

A mathematical model can be used as a conceptual tool to understand and to quantify dynamic behavior of infectious diseases. More specifically, infectious disease models serve three aims: (1) understanding the dynamics of disease spread, (2) predicting the future course of an outbreak, and (3) ultimately devising and evaluating measures and interventions for disease control. Using these models, one is able to translate epidemiological assumptions of biological processes into a mathematical framework in a transparent and systematic way. As such, mathematical models allow us to test our understanding of the epidemiology of a disease by comparing model results and observations from the real world. They complement traditional experimental approaches, in particular when experimental manipulation of the studied system is not feasible, for example during a pandemic.

In her thesis, Thi Mui Pham (Infectious Disease Modelling group, Research Program Infectious Diseases, UMC Utrecht) elucidated the important role of mathematical models for infectious disease control with a focus on the transmission of the SARS-CoV-2 virus in the community and in hospital settings, as well as the transmission of Pseudomonas aeruginosa in intensive care units. The most important findings of her studies were:

• Self-imposed measures (handwashing, mask-wearing, physical distancing) as a reaction to the COVID-19 epidemic can be effective in mitigating and delaying it. They can even prevent a large epidemic if they are adopted fast and if the measure has a high efficacy;
• Hand hygiene may be optimized by the frequency and the moment at which it is applied to reduce viral respiratory tract infections. She found that immediate hand washing after contamination is consistently more effective than at fixed time intervals;
• Many hospital-acquired COVID-19 cases may remain unidentified if their definition relies on a cutoff of days after symptom onset: Patients may be discharged or have a symptom onset prior to this cutoff. Screening or quarantining hospital patients at discharge may be effective in preventing further transmissions into the community;
• In a simulation study, the use of highly effective personal protective equipment in all hospital wards was the most effective intervention to limit SARS-CoV-2 transmission in hospitals in the Netherlands. The role of contact tracing beyond community settings was highlighted since it can detect more infections among tested individuals than regular screening interventions;
• Modeling of environmental contamination as a transmission route for Pseudomonas aeruginosa showed that persistent contamination of the environment may cause outbreaks in intensive-care units but its exact contribution depends on the specific setting.

The thesis by Thi Mui Pham provided new insights into how biological and clinical research problems may be translated into a mathematical or statistical framework, and how the level of detail and the model choice not only highly depends on the objective, but also on the availability of data. Thi Mui Pham: “As mathematical modelers of infectious diseases, we face the trade-off between a simpler model that is easy to understand and to analyze, or following a more complex approach leading to a more realistic representation of the system, but that requires, in exchange, more intricate analysis tools and detailed input. If problems need to be addressed on a population level, simpler models with an aggregated structure maybe be sufficient to capture the relevant transmission dynamics. Simple statistical or simulation models linked with appropriate data may provide first quantitative evidence without the need of a full mechanistic transmission model. To account for stochastic effects in smaller populations such as hospitals, more complex models such as agent-based models may be more appropriate but also need to be equipped with more detailed data.”

Finally, Thi Mui Pham and her co-authors identified gaps in data collection in particular on behavioral responses and hospital patient data that need to be addressed to improve infectious disease model building and to reduce the reliance on arbitrary assumptions. Model-informed data collection and the synthesis of multiple data sources are thought to hugely improve epidemic response, but sustainable data sharing and thus the collaboration of many different research groups, disciplines, and countries will be essential.