The coronavirus is spreading at an exponential rate. Thus far, control measures have been mainly the initiative of individual states, rather than the federal government. This has been the case for social distancing policies and medical resource allocations alike.

This decentralized approach was reiterated in Thursday’s White House press conference. President Trump told reporters that states should try to acquire ventilators and tests on their own before asking the federal government’s assistance. “The federal government’s not supposed to be out there buying vast amounts of items and then shipping, you know, we’re not a shipping clerk.”

However, research shows that in the face of epidemics, there is no substitute for centralized, federal-level actions when designing effective policies. The reason is that states and cities are not isolated from one another. They are interconnected because individuals and goods travel freely among them without any screening or testing. 

This creates what the scientific literature calls network effects. Because of network effects, individual states are less effective than the federal government is in controlling contagion at the national level. And the federal government can only accomplish this if foreign inflows can be controlled.

Consider the case of the common flu. It is far less contagious than the coronavirus is, but its spreading mechanism is similar. Our research shows that there are substantial network effects on the spread of the virus. The implication is that taking these effects into account is crucial in designing effective contagion control policies. In the case of the common flu, this can make such policies up to three times as effective. Only the federal government can achieve such efficiency gains; individual states cannot.  

In particular, two concrete lessons can be drawn from our research on the spread of the common flu.

The first lesson concerns the specification of travel restrictions. Unlike individual states, the federal government can identify the key routes across state boundaries where travel restrictions should be prioritized at a given stage of the epidemic. Specifically, it can identify the crucial origin-destination pairs where travel restrictions would be most effective. 

As an example, New York and Florida have approximately equal population sizes, but the number of identified coronavirus infections is more than 15 times larger in the former. It would therefore be more effective to shut down travel into Florida as opposed to into New York, even if the travel volumes between the two states are the same. Only the federal government can impose such restrictions.

The second lesson is about the allocation of medical resources. For example, it is far from optimal to let individual states decide on how many coronavirus testing kits or ventilators—both in extremely scarce supply—they should attempt to procure, or where in their state to place them. Free, decentralized market mechanisms fail in settings of extreme scarcity where the goal is to save as many lives as possible.

Moreover, an optimally effective allocation of these scarce supplies should not be based on simple metrics such as population sizes or the current number of infected individuals. Once again, the network effects need to be integrated in the analysis, but this cannot be done by the individual states. For instance, New Jersey today has a much lower infection rate than does Washington state. But because of the much higher travel volume from and to New Jersey, it may prove more effective in the long run to have more testing kits there.

There are substantial benefits in acting at the federal level to allocate medical resources where they will be most effective and to determine which, if any, travel routes should be curtailed or shut down. Only the federal government can determine and implement such optimal policies.

Fanyin Zheng is an assistant professor of the Decision, Risk, and Operations Division of Columbia Business School.

More coronavirus coverage from Fortune:

—Financial crisis looms as corporate America presses for coronavirus bailout
—Tax deadline moved to July 15 due to coronavirus
—Death rate in China’s coronavirus epicenter is lower than previously thought
—How working parents are navigating childcare during the coronavirus pandemic
—As oil slides on coronavirus and price war, the market looks for the new normal
—Funerals in the time of coronavirus: How a pandemic is changing the industry
—Listen to Leadership Next, a Fortune podcast examining the evolving role of CEO
—WATCH: World leaders and health experts on how to stop the spread of COVID-19

Subscribe to Fortune’s Outbreak newsletter for a daily roundup of stories on the coronavirus outbreak and its impact on global business.