# The opposite effect of an embargo

July 01, 2015

If Albert Camus could have read the article by physicists from the Max Planck Institute for Dynamics and Self-Organization, the plague in his famous novel might have ended differently. The researchers investigated in a mathematical model how diseases spread, if the infection risk varies locally. Their surprising result: in certain situations shut-off policies can lead to a higher percentage of infected individuals.

Commuters between Göttingen and Hannover or pig transports between breeding farms and feed lots gave them the idea: David Lamouroux, Jan Nagler, Theo Geisel and Stephan Eule asked, how changing places influences the spread of infectious diseases. They investigated this with a mathematical model that varies the risk of infection depending on the location. This spatially different risk of infection is influenced by several factors: “How infectious is the disease in itself and how often are people or animals in contact with each other at the same place”, Dr Stephan Eule, physicist at the Max-Planck Institute for Dynamics and Self-Organization explains.

Infection risks differ from place to place

The mathematical model describes the basic properties of animal transport: animals are transported from breeding to feeding lots and stay there. So far, epidemic scientists disregarded either transport, as if all animals were on the same farm, or they concentrated on the transport: “David Lamouroux noticed that those epidemiological models all used the same infection risk everywhere, so we analysed what happens when we change that,” Stephan Eule explains. When the scientists allowed animal transport between farms with different infection risks in the model, they discovered a paradoxical effect: the fraction of infected animals increased at the farm with high risk and decreased where the risk was low. However, the intuitive expectation would be more infected animals at the low-risk farm, because the transport also brings more infected animals with it. The effect occurred at realistic infection risks and transport rates.

Transport makes the difference

How can this effect be explained? An analogy helps: a pile of fast burning coals will be burnt earlier than a pile of slow burning coals. If you exchange coals between the two piles, that with the fast burning variant gets more fresh pieces and produces even more burnt coal. The intuitive reaction during an animal disease – shutting down the transport between the farms of high infection risks to other farms – may thus have the opposite effect. The scientists simulated this in their study. They calculated how the fraction of infected animals changes, if one transport-route between farms with low, middle and high infection risk has been cut off. When they allowed transport between the high and the middle-risk farm, the fraction of sick animals decreased in both farms. If transport was allowed only between the middle and the low-risk farm, the fraction of animals increased in both farms.

Whether this effect would also occur among humans with their more complex movement patterns, i.e. whether the citizens in Camus' novel stricken by the plague and devastated by isolation stood a chance, the scientists cannot yet definitely decide. This is the aim of a future research project. Yet, this result from physicists at the Max-Planck Institute for Dynamics and Self-Organization in Göttingen already shows that the current shut-off policy should be carefully revised when it comes to livestock treatment.

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