Hungarian team applies game theory to determine how a government can fight novel pathogen

The COVID-19 pandemic has made the world aware of the deadly consequences of a new pathogen for which there was little preparation and no initial vaccine. 

But what if another novel pathogen strikes? What lessons from COVID-19 can guide government responses? A Hungarian-led team of scientists has used a game theory model to analyze the problem and provide policy guidelines for governments to deal most effectively with a novel pathogen.

The mathematical model had two "players," the government versus the pathogen. The model considered a few potential scenarios for a state in acting against an epidemic-causing pathogen whose properties are not yet known.

The work appears in Nature's Scientific Reports, Sept. 30.

Two findings of note.

• First, the study found that the "presence and length of a pre-symptomatic infectious state of the disease" has the "greatest effect" on the probability of the pathogen to cause a pandemic.

• Second, surprisingly, the research showed that even if a nation (or state) wants to provide care for everyone who needs it and "minimize the cost of lockdowns," it should not "strive for the great expansion of its health care capacities...."

Why game theory?

Current Science Daily talked with co-author Ádám Kun how the researchers came up with using game theory as a way to help a government most efficiently deal with an epidemic caused by a new pathogen.

Kun is at the Institute of Evolution, Centre for Ecological Research and Eötvös Loránd University in Budapest.

"It's a classic example of having a hammer and seeing everything as a nail," Kun said. "We have been studying game-theoretical situations, mostly among animals, for decades. Societal situations generally can be analyzed as game-theoretical ones as well. Examples are vaccination, mask-wearing, obeying social distancing.

"Game theory is a field in mathematics that deals with situations where the outcome--the payoff--for any given participant depends not only on its behavior--strategy--but on the behavior of the others as well," he added. 

The name comes from the analysis of poker-games by 20th Century mathematician John von Neumann.

Kun noted that game-theoretical situations on a government level had dealt with "a fixed pathogen and optimized for economic outcome," but other elements should be included.

"A government has to be prepared for a future, yet unknown pathogen, and it also has obligations toward its citizens, like trying to provide hospital care," he said. 

The scenarios

The mathematical model used in the study considered the worst possible case for a nation, in which a vaccine would not be developed in time to stop the pathogen. In the model, the pathogen, nature, moves first, forcing a response from the state.

The model assumed that the government had the objective of guaranteeing hospital care for those who needed it, and at the same time maximizing people's freedom by limiting lockdown time. It did not consider a case with the most restrictive measures. 

In looking for the optimal way for a government to reach its objectives, the model considered the revenue stream to the state in different scenarios. How could a nation best meet the short-term costs of health care while balancing shutdown of some economic activities such as retail stores, arts, entertainment, recreation, manufacturing, travel, restaurants and hotels.

The epidemiological variables in the model considered the number of susceptible, exposed, infectious, and recovered people (SEIR). Factored in were different scenarios for times involved in each stage, including hospitalizations. The optimal controls for an epidemic included quarantines for people with symptoms, quarantining of household members together, increased hospital capacity and selective prohibition of certain activities and closing certain venues.

Lessons learned

The mathematical model found that the optimal mandated controls on public activity varied, depending on the length of time people were pre-symptomatic. A longer period of being pre-symptomatic allowed the pathogen to spread and increased the number of days people needed to be hospitalized. In such cases longer periods of lockdown are beneficial.

One surprising finding, the researchers state, is that, "The state should not try to increase hospital bed capacity recklessly, as its cost could be minimized with fewer beds and still being able to provide hospitalization to all needing citizens."

"There is an optimal level of investment into preparation," Kun added. "In our model, that was the amount of mothballed hospital capacity the state has. A larger hospital capacity means a quicker course for an epidemic which translates to less economic restriction, hence less economic loss. But hospital capacity also has a cost, and when everything is considered it is better to endure restrictions a little longer." 

Unexpected outcomes

Kun described what he called "surprising outcomes." 

"For example," he said, "one of the aims of the state was to have a healthy workforce large enough to run critical infrastructure, general stores at any given moment during the epidemic. But at no point in our calculation was there any shortage of general workforce, not even close. Hospital capacity and medical personnel are the real bottleneck.

"Also, while we allowed non-critical stores to be closed, the optimal solution never required them to do so," he added. "People just do not spend too much time in stores and have few interactions with others there. Controlling big events, restaurants and tightly packed offices and factories proved to be enough."

Future applications

Regarding how he thought the game theory model of a nation against nature could be used in the future, Kun said, "Models like ours are simple representations of reality. They are useful for thinking about a situation. But at the same time these models also offer a framework into which more detailed data could be fed, so that it can help actual governments to deal with their own population and their own economy.

"During the COVID-19 pandemic, governments quickly found that they had scientists who could advise them based on state-of-the-art epidemiological models," he added. "They might also realize, that mathematical epidemiology, coupled with game theory and optimization, can help them to prepare for the next pandemic."

Kun also noted that "pathogens don't have to cause a deadlier disease than COVID-19 to be a serious threat. What if the disease is not deadly, but debilitating and would cause a huge loss of working hours? In other words, what if something like long-COVID were a common outcome."

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József Garay, Ádám Kun et al. "State-controlled epidemic in a game against a novel pathogen." Scientific Reports 15716, Sept. 20, 2022. https://doi.org/10.1038/s41598-022-19691-7