We now have definitive proof that Islamic State was the prime force behind the Easter Sunday suicide attacks in Sri Lanka that killed at least 359 people. Although many had hoped that the elimination of Islamic State as a territorial entity in Iraq and Syria ended the threat from the group, the facts show otherwise.

To make sense of terrorist campaigns, I lead a research team at the University of Chicago to compile data on suicide attacks and online videos and messages by Islamic State, also known as ISIS, and other terrorist groups around the world. We have detailed information on more than 6,300 suicide attacks since the early 1980s when the phenomenon began and analysis of the content of more than 5,000 militant videos, many seeking to inspire and recruit fighters.

On Tuesday, ISIS released on the online platform Telegram a photograph of the Sri Lankan suicide bombers, standing in front of the ISIS flag, clearly ready to carry out their deadly strikes. ISIS also released a one-minute video of the bombers pledging allegiance to Abu Bakr al-Baghdadi, the leader of ISIS. For decades, suicide terrorist groups have routinely released martyr videos - the last video testimonials of individuals who carry out suicide attacks for the group. ISIS has just done this and it stands as direct evidence that ISIS was behind the suicide attacks in Sri Lanka.

Most important, the facts show that ISIS's attacks are not simply a spasm of violence against Christians, but focused on a simple strategic goal: to punish the United States, its Western allies and Russia for their role in rolling back ISIS as a territorial entity in Iraq and Syria.

How, exactly, did Islamic State drive the attacks in Sri Lanka? Is ISIS more dangerous as a virtual entity than as a territorial actor?

The answer is that ISIS is playing a role as both a territorial actor and an online entity. For years, the Islamic State controlled territory larger than the size of Great Britain in Iraq and Syria - essentially the largest terrorist training camp in the world. Tens of thousands of Iraqis and Syrians fought for the group. Crucially, thousands of "foreign fighters" from countries around the world also flocked to join ISIS in Iraq and Syria. Most of these fighters were trained and hardened in the cauldron of battle after battle as the international coalition and its local partners systematically dismantled ISIS areas of control.

Today, there are thousands of dedicated Islamic State fighters moving around and fleeing Iraq and Syria, many of them seeking to return to their home countries. This "reverse diaspora" can serve as trained fighters and also serve to develop associations with local terrorist groups, amplifying their power.

That's why, even as ISIS was virtually eliminated as a territorial entity, ISIS attacks in the West and around the world have continued. Since January 2018 - when ISIS lost nearly all of its territory in Iraq and Syria - the group has been involved via coordination or inspiration in over 25 terrorist attacks around the world, many of them suicide attacks, killing over 850 people.

The Easter Sunday suicide attacks against Westerners and churches strongly fits the signature attacks of Islamic State's ongoing international campaign of terrorism.

Further, on April 8, Islamic State announced a new "Campaign of Vengeance for the blessed al-Sham Province," threatening to attack in Iraq, Syria, Egypt, Somalia, Libya, Russia and the West. Over a dozen of these attacks have already occurred, and ISIS has been proud to claim responsibility for many of these. The Easter Sunday suicide attacks were simply the next step of this campaign of vengeance.

ISIS is not the first international terrorist group to continue posing a threat after its main base of operations was disrupted. This also happened with al-Qaida.

In 2001, the United States and its allies destroyed al-Qaida's terrorist training camps in Afghanistan and many thought that the group was done for good. However, from 2002 to 2004, al-Qaida operatives who fled Afghanistan coordinated or inspired 15 suicide attacks in many different countries around the world - for instance, killing at least 200 in Bali in October 2002 and nearly 200 in Madrid in March 2004, focusing on Westerners and churches as revenge for its losses.

Today, Islamic State has thousands of foreign fighters who came to fight in Iraq and Syria who are now heading back home. As we go forward, it is crucial to avoid the two extreme reactions of complacency or fear mongering. Both of these extremes play into the hands of ISIS. Instead, we need to realize that a moderate threat from ISIS and its affiliates is likely to continue for years to come, and so it is important to deal with the underlying political and social roots of terrorism as our best long-term security strategy.

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Robert A. Pape is professor of political science and director of the University of Chicago Project on Security and Threats.