Taking appropriate protective measures during pandemics
Optimal containment measures exhibit a clear threshold depending on the severity of the disease
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A new model determines the optimal strength of containment measures for infectious diseases, taking into account the costs of both the disease and containment.
view moreCredit: Max Planck Institute for Dynamics and Self-Organization (MPI-DS)
- Optimal containment measures exhibit a clear threshold depending on the severity of the disease
- Cost-benefit analysis: Optimal regulation requires balancing the societal costs of protective measures against those of infections
- Threshold structure: Mild diseases do not require general containment, while severe diseases require countermeasures. Surprisingly, the transition is not gradual but occurs abruptl
- Adaptation: When external conditions change seasonally or due to vaccinations, the model calculates how measures can be dynamically and optimally adjusted
In the event of a pandemic, every society is confronted with the question: How can the spread of an infectious disease be effectively contained without restricting daily life more than necessary? Measures such as mandatory mask-wearing or contact restrictions can reduce the spread of disease but also entail social, economic, and psychological costs.
Optimization of countermeasures
Researchers from the Theory of Complex Systems group at the Max Planck Institute for Dynamics and Self-Organization (MPI-DS) developed a model to optimize such countermeasures while taking containment costs into account. Using numerical methods, it calculates the optimal intensity of intervention based on the characteristics and severity of a disease. The aim of the study was not to make statements about specific diseases or to propose specific measures, but rather to identify general principles of optimal pandemic control. The flexible optimization model can also be combined with different disease models: “Through this, we hope to contribute to preparations for possible future outbreaks,” explains Laura Müller, the study’s first author.
Abrupt transition at optimal level of containment
The research group investigated general patterns of optimal infection control using a classical mathematical model in which individuals are either susceptible, infected, or temporarily immune following recovery. “Surprisingly, it becomes very clear that optimal measures follow a threshold structure,” explains Viola Priesemann, professor and group leader at the MPI-DS. “For mild diseases, the model shows that it is optimal not to impose any containment measures. However, once the disease reaches a certain severity, a high level of containment is optimal.”
Which combination of measures is chosen is a societal and political question and depends on the characteristics of the disease. “It is very surprising that the transition in the idealized model occurs absolutely abruptly,” Priesemann further emphasizes. Measures that represent a compromise between optimal intervention and no control at all ultimately result in higher overall costs: Either they are more extensive than necessary or they are insufficient to effectively curb the spread of infection.
Seasons and vaccinations influence the course of infection
The researchers also examined the influence of fluctuating infection rates over the course of the year. Their findings showed that optimal containment in winter must increase in tandem with the higher probability of infection. With such optimized containment of infectious diseases like influenza, there would be at most a small wave of infection in the spring instead of the typical waves of infection during the winter months. Mathematically, it can be calculated that this small wave occurs exactly 3 months after the peak of seasonality.
The new optimization framework also allows to determine how measures can optimally be reduced during vaccination campaigns.
In addition, it is possible to calculate the costs incurred when measures are implemented too late: Due to the exponential growth at the beginning of a pandemic, even minor delays in launching measures lead to notably higher infection rates. In the case of severe diseases, this results in considerable additional costs; in the case of mild diseases, however, it does not.
The study is based on a simplified mathematical model and therefore cannot make direct statements about individual diseases or specific pandemic situations. However, it has identified a novel, fundamental principle of optimal infection control: the clear threshold that emerges when containment costs are factored in at a very general level. Such principles provide guidance when society and policymakers need to develop strategies, even when the exact details of disease spread are not yet known. The results can thus help provide a stronger scientific basis for future decisions. Which measures are ultimately implemented, however, remains a societal and political decision.
Journal
Proceedings of the National Academy of Sciences
Method of Research
Computational simulation/modeling
Article Title
Optimizing infectious disease mitigation under dynamic conditions
Article Publication Date
3-Aug-2026
Machine learning turns routine water quality data into early warnings for pathogen health risks
New ML-QMRA framework predicts microbial contamination and translates it into potential public health risks
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A machine learning-quantitative microbial risk assessment (ML-QMRA) framework for predicting potential health risks from pathogens in drinking water sources
view moreCredit: Bingbing Guo, Jing Wang, Chicheng Yan, Chao Tang, Kun Yin, Lei Jiang & Changzheng Cu
Safe drinking water depends not only on treatment, but also on knowing when harmful microorganisms may be present in source waters. Researchers have now developed a data-driven framework that uses routinely measured water quality indicators to predict pathogen concentrations and estimate their potential health risks.
The study, published in Biocontaminant, combines machine learning with quantitative microbial risk assessment, or QMRA, to create an ML-QMRA framework for drinking water source monitoring. The approach could complement conventional microbial testing by providing faster estimates of contamination risks from readily available water quality data.
“Routine monitoring already generates a large amount of environmental information. Our goal was to determine whether these commonly measured variables could also help us anticipate microbial contamination and translate those predictions into meaningful health risk estimates,” said Changzheng Cui, corresponding author of the study from East China University of Science and Technology.
The researchers collected 95 surface water samples from two drinking water sources in a major city in Eastern China between May 2024 and December 2025. They monitored three commonly used indicator bacteria, fecal coliforms, Escherichia coli, and Enterococcus faecalis, together with six pathogens: Pseudomonas aeruginosa, Salmonella spp., Shigella spp., adenovirus, norovirus, and enterovirus.
The results revealed an important limitation of conventional microbial indicators. Although the three fecal indicator bacteria were significantly correlated with one another, their relationships with viral pathogens were generally weak or inconsistent. This means bacterial indicators alone may not always reflect viral contamination accurately.
To improve prediction, the team compared six machine learning approaches, including Multiple Linear Regression, Least Squares Boosting, Decision Tree, Support Vector Machine, Random Forest, and Multilayer Perceptron models.
Random Forest and Decision Tree models performed particularly well, and all optimized models achieved R² values above 0.75. The Decision Tree model showed especially strong performance for P. aeruginosa, with an R² above 0.90. Independent data collected in January and February 2026 were also used for temporal validation, supporting the ability of most models to make predictions beyond the original training period.
The researchers then linked predicted pathogen concentrations to QMRA calculations expressed as disability-adjusted life years, or DALYs. Most estimated risks remained below the World Health Organization benchmark of 10⁻⁶ DALYs per person per year, but Salmonella spp., Shigella spp., and enterovirus showed probabilities of exceeding this benchmark under unfavorable exposure conditions.
The analysis also identified disinfection efficiency as the dominant factor influencing estimated health risk, emphasizing the importance of stable and effective drinking water treatment.
To make the machine learning models more transparent, the researchers used SHapley Additive exPlanations, or SHAP. Turbidity was among the strongest predictors for fecal indicator bacteria, accounting for 41.6% to 62.1% of predictive importance in those models. Temperature, dissolved oxygen, rainfall, and other water quality variables contributed differently across individual pathogens.
The study shows that routine physicochemical measurements can provide useful predictive information about pathogen levels and their associated potential health risks. However, the authors stress that the framework still requires validation across different watersheds, seasons, treatment systems, and land-use conditions.
Future integration of ML-QMRA models with real-time monitoring systems could help water managers identify periods of elevated microbial risk earlier and support more targeted water safety interventions.
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Journal reference: Guo B, Wang J, Yan C, Tang C, Yin K, et al. 2026. A machine learning-quantitative microbial risk assessment (ML-QMRA) framework for predicting potential health risks from pathogens in drinking water sources. Biocontaminant 2: e012 doi: 10.48130/biocontam-0026-0009
https://www.maxapress.com/article/doi/10.48130/biocontam-0026-0009
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About Biocontaminant:
Biocontaminant (e-ISSN: 3070-359X) is a multidisciplinary platform dedicated to advancing fundamental and applied research on biological contaminants across diverse environments and systems. The journal serves as an innovative, efficient, and professional forum for global researchers to disseminate findings in this rapidly evolving field.
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Journal
Biocontaminant
Method of Research
Experimental study
Article Title
A machine learning-quantitative microbial risk assessment (ML-QMRA) framework for predicting potential health risks from pathogens in drinking water sources
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