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.
Proceedings of the National Academy of Sciences
Computational simulation/modeling
Optimizing infectious disease mitigation under dynamic conditions
3-Aug-2026