Rangers in South Africa's Kruger National Park, one of the world's most popular safari destinations, did not have to wait long for their first battle of the New Year.

Within days of the birth of 2013, rangers stationed near the park's border with Mozambique were in a gunfight with poachers who fled, leaving behind a high-calibre rifle and a bag full of rhino horns. The dehorned carcass of a female white rhinoceros was found nearby together with her two-month-old calf which survived despite having been slashed 18 times with machetes.

It was an all too typical encounter. By last Friday five rhinos had already been killed this year in South Africa, including three in the Kruger.

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But the Kruger killings are just a tiny corner of a much wider poaching disaster hitting Africa and also India's greatest wildlife reserve, the Kaziranga, on the banks of the mighty Brahmaputra River. An epic rhino and elephant slaughter is under way which conservationists fear may lead to the extinction of these magnificent animals within the lifetimes of the youngest living humans.

At the current rate of killing, they predict that wild elephants and rhinos will be extinct within 15 to 40 years.

Poachers, financed by sophisticated international gangster syndicates, are wiping out tens of thousands of Africa's elephants each year, more than at any time in the past two decades, with the underground ivory trade becoming increasingly militarised.

Thousands of the world's remaining rhinos in the wild – at the beginning of 2011 there were 28,000 in Africa and Asia – have been slaughtered in the past year to satisfy demand for their horns by increasingly affluent East Asians, mainly in China and Vietnam. Economic booms in these countries have created a vast middle class, pushing up the price of ivory, "white gold", to £1130 per kilogramme on the streets of Beijing and Hanoi, compared with £63 per kilo eight years ago.

The black market price of rhino horn on those same streets is even more spectacular – £38,000 per kilo, making it twice the value of an equivalent weight of gold. Rhino horn, made of keratin, the same substance as human finger nails, has for centuries been used in traditional Asian medicines for treating fevers and arthritis, although scientists have long established it has no healing qualities. Now it is being peddled as a treatment for cancer.

Powdered horn sells as if it were cocaine, a "drug" of choice for the wealthy to snort, believing it improves sexual performance. "There are websites right now promoting rhino horn as better than Viagra for men," laments Tom Milliken, director of Traffic, the global wildlife-trade-monitoring network backed by the World Wildlife Fund (WWF).

"We're fighting a war out here, and right now we're losing," says Juan Pinto, a wildlife guide in the Kruger Park – at 13,000 square miles nearly half the size of Scotland and home to more rhinos than any other reserve on earth.

Kruger, with some 12,000 white and black rhinos, and Kaziranga National Park, with more than 2000 Indian one-horned rhinos, are together the homes of more than half of the world's surviving wild rhinos. The African onslaught is mirrored in the Kaziranga, where a new India-China road being driven through the heart of the park is making it easier for Chinese gangsters to move their booty.

The rhino poaching orgy began in 2008 after a Vietnamese government officer claimed to have been cured of cancer after ingesting powdered horn. South Africa, home to 90% of the African continent's surviving rhinos, last year lost two of the animals every day to poaching gangs. Until 2008, it lost fewer than 15 rhinos a year. Killings have since grown exponentially: hitting 333 in 2010, 448 in 2011, a record 668 last year, and the slaughter continues.

Two months ago WWF announced that in the course of just one month two of the world's rhino sub-species became extinct. One was the Vietnamese Javan rhino. Its last survivor was shot in the leg in Cat Tien National Park, near Hanoi, its horn removed and left to die of septicemia.

The official extinction of the West African black rhino was, sadly, expected. After decades of heavy poaching and weak protection, it was last seen in 2000 in Cameroon.

In Cameroon's Bouba Ndjida National Park, which employed only six poorly paid rangers, 300 of the park's surviving 450 elephants were last year slaughtered for their ivory in a single bout by janjaweed militiamen who rode 700 miles on horseback and camel from Sudan's Darfur Province. The tusks were sold in Khartoum before heading to China, Vietnam and Laos. The money raised is likely to have been used to buy more automatic weapons, feeding the civil war that plagues Sudan and to be used in further cross-border raids for ivory. John Scanlon, secretary-general of the Convention on International Trade in Endangered Species of Wild Fauna and Flora (CITES), said: "This incident of poaching elephants is on a massive scale but it reflects a new trend across many range states, where well-armed poachers with sophisticated weapons decimate elephant populations, often with impunity."

The killing with automatic rifles this month by poachers of an entire family of 12 elephants in Kenya's iconic Tsavo National Park and Conservation Area, stretching across an area nearly as extensive as the whole of Scotland, attracted widespread media attention. The poachers hacked from the dead animals 22 tusks worth £175,000 on Asian markets.

The attack was the latest in a surge of elephant deaths that has seen the number of animals killed for their ivory in Kenya increase sevenfold in five years, from fewer than 50 in 2007 to 360 in 2012, according to Kenya Wildlife Service official figures.

Experts such as Iain Douglas-Hamilton, a legendary wildlife researcher who founded the Kenya and UK-based Save The Elephants organisation, argues that many more elephants are being killed in the wilderness and their carcasses never found. The current crisis is graver than the mass slaughter of Africa's elephants in the 1970s and 1980s which led in 1989 to an official global ivory trade ban, says Douglas-Hamilton, adding: "We have fewer elephants left now, but the demand for ivory is far greater. The only thing that will radically alter the situation is somehow to lower that demand."

The Kenyan killings are, however, nothing compared with the orgy of slaughter going on elsewhere in Africa.

A country like Gabon, four times the area of Scotland with billions of pounds of oil money, endless swathes of virgin equatorial forest and a population of only 1.5 million, ought to be a secure reservoir for its estimated 60,000 to 80,000 elephants. The country, whose national parks director Professor Lee White is of Scottish parentage, has conservation policies seen by wildlife experts as among the best in Africa. Nearly 20% of Gabon's territory is devoted to national parks: its ranger staffing has been increased sixfold in the past decade. Last year, Gabon publicly burned five tonnes of confiscated elephant tusks to demonstrate its commitment to fighting the illegal ivory trade.

But as the price of tusks keeps rising, Gabon's elephants are now also being slain. The elephants, despite Gabonese leaders' best intentions, are being squeezed in a lethal vice between an insatiable lust for ivory in Asia and desperately poor hunters and traffickers in central Africa. Both greed and poverty are killing Gabon's and all Africa's elephants.

What makes the stakes particularly high in Gabon is that its elephants are among the last of Africa's rare forest elephants – smaller than their savannah cousins in countries like Kenya and with attractive, extra-tough pink-coloured ivory that is especially prized in Asia.

A decade ago there were 700,000 forest elephants roaming central Africa's jungles. Now there are fewer than 100,000, with most of them in Gabon. A century ago many forest elephants had tusks so long that they scraped the ground: now perhaps a dozen of these magnificent beasts survive deep in the Gabon jungle.

Conservationists scratch their heads almost in vain on how to halt this rolling disaster. The poachers are usually better armed than the game guards: they have night-vision goggles and are often supported by helicopters to spot animals and remove the booty. International agreements limiting or prohibiting trade in wildlife products are easily breached with prices so high.

In desperation, the South African Parks Board has brought out of retirement an old apartheid-era Afrikaner general, Johan Jooste, to revamp its anti-poaching strategy in the Kruger Park. A former practitioner of "total war" against the now ruling African National Congress, General Jooste says: "We are going to take the war to these armed bandits and we aim to win it." The general has been reinforced with specialised army units and has been given improved firearms for his rangers, and aircraft and drones to patrol the skies above Kruger.

Past animosities have been widely abandoned in the new war against poaching. Former South African Army paratrooper Rian Labuschagne manages Zakouma National Park in southern Chad where there is a war on against poachers, and the elephant population is down to fewer than 450 from 4,350 a decade ago. There has been only one confirmed birth of an elephant calf in Zakouma in the past two years.

But, again, enforcement is seen as only part of the solution. According to Traffic, the key is to reduce demand for the product in the first place – "to take away the market."

Traffic, based in Cambridge but with offices throughout the world, is targeting Vietnam and China with programmes designed to reduce demand.

"Efforts now really need to focus in on the underlying social motivations that drive people to buy these products – whether it is as a symbol to show off their success or social status, or as a gift to impress their peers or business partners," says Steven Broad, Traffic's executive director. Traffic aims to persuade people that live elephants and rhino are better for the future of humankind than piles of tusks and horns from dead animals.

It will be a formidable task, but it can be done, argues Broad. He points to Japan, once a major market for illegal ivory and South Korea and Yemen – both once target markets for rhino horn, but no longer so. "Attitudes can be changed, but it's not an overnight process," Broad says. " Traffic is in this for the long term, in the belief that we will ultimately be successful."