An image from a jihadist website shows Isis militants after they allegedly seized an Iraqi army checkpoint in Salahuddin

The “global war on terror” was shot down in a hail of ridicule. Sceptics scoffed that President George W Bush’s GWOT was not global and it was not a war — since terrorism is a tactic, not an enemy. On taking office as US president in 2009, Barack Obama quietly dropped the term.

The GWOT may have been a clumsy phrase and an inexact idea but, sadly, linguistic quibbles have not removed the underlying issue. However you want to label it, the world has a problem with jihadi violence — and it is getting worse.

There are two specific ways in which the threat from militant Islamism has worsened over the past five years. First, jihadi groups are operating in more parts of the world. Second, the frequency of attacks and number of deaths is increasing.

The massacre of 148 people, mainly children, at a school in Peshawar on December 16 was the worst atrocity in Pakistan since 2007. It was followed, this month, by the murder of up to 2,000 people by Boko Haram in Nigeria, and the killing of 17 in two separate attacks in Paris.

Three brutal attacks on three separate continents give the impression that the frequency of Islamist terror attacks is rising. That impression is confirmed by the data.

A recent study by the Rand Corporation identified 49 Salafist-Jihadi groups operating around the world in 2013, compared with 28 in 2007. These groups staged 950 recorded attacks in 2013, up from 100 six years earlier. And that Rand report was published before a big surge in violence in Nigeria. A recent US state department report estimated that 18,000 people were killed by terrorism in 2013 — but also noted that the number of Americans killed was very low and going down.

That decline in the numbers killed by terrorism in the west ensured the problem received only sporadic attention in the US and Europe. But, in the rest of the world, the number of lawless areas in which jihadi militias can freely operate and train has increased.

A decade ago, the main area of concern for western counter-terrorism efforts was Afghanistan and the border areas of Pakistan — with Somalia another significant worry. But now the self-styled Islamic State of Iraq and the Levant (Isis) controls a large swath of Syria and Iraq, including Mosul, Iraq’s second-largest city.

In Africa, Boko Haram — possibly inspired by the success of Isis — has also seized territory and now controls a part of northern Nigeria the size of Belgium, as well as threatening neighbouring states such as Cameroon and Niger. Much of Libya has slipped into violent anarchy and jihadism is also endemic in Yemen.

The obvious questions are why the problem is escalating and what needs to be done. In the solipsistic world of US politics, it is natural for politicians to assume the problem somehow begins in Washington. Democrats cite President Bush’s decision to invade Iraq. The Republicans claim President Obama withdrew from Iraq prematurely.

Actually, recent history teaches ambiguous lessons about the impact of western military intervention. The failure of the US to intervene earlier in Syria is sometimes blamed for the rise of Isis. On the other hand, western military intervention in Libya helped to reduce the country to anarchy — creating space for jihadi groups to thrive. In reality, this is a problem that is not primarily about US foreign policy and the iniquities of the west. In recent years, every single permanent member of the UN Security Council has been hit. The US was struck on September 11 2001. The UK experienced the 7/7 bombings that killed London commuters in 2005. Russia has waged a long and brutal struggle with Chechen jihadis. China has experienced a bombing in Tiananmen Square and killings around the country. Now France has been struck. India, too, is on the frontline.

Tempting as it is for western powers to make common cause with all countries that have been hit by Islamist terror, it is also politically difficult since that potentially involves accepting the Russian narrative on Chechnya, the Israeli narrative on Gaza and the Chinese view of Xinjiang.

The factors behind the recent upsurge in violence include the increased fragility of several states in the aftermath of the revolutions in the Arab world — as well as the amplifying effect of social media, which allows jihadi messages to spread fast and to reach ever-larger audiences.

As Islamist militias have gained ground, so the conflict with them has come increasingly to resemble a conventional war. There are now several parts of the world where regular armies are battling jihadi groups for control of territory. American and European air-forces are bombing Isis. The Nigerian army, aided by troops from Chad and Niger, is fighting Boko Haram — albeit not very effectively. The French army deployed in Mali to beat back a jihadi threat. The Pakistanis, goaded by the attacks on Peshawar, have renewed military action against the Taliban.

Solving the problem of jihadi violence, over the long-run, will be more about the battle of ideas than a battle of armies. But, in the meantime, there are military campaigns against Islamist movements under way in Africa, Asia and the Middle East. It turns out there may be a “war on terror”, after all.

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