December 20, 2024

The Math Behind Why Mexico’s Cartel War is a Never-Ending Nightmare

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An unsettling silence hangs over the historic center of Culiacán, the capital of Sinaloa. Here, in the heartland of one of the world’s most powerful drug cartels, a violent feud has turned the city’s streets into a ghost town. Since September 2024, this internecine warfare has claimed hundreds of lives, leaving behind a city where normal life has all but evaporated.

As night descends on Paseo del Ángel, once the bustling nightlife quarter of Culiacán, the emptiness feels almost surreal. Restaurants that used to be fully booked every night now sit deserted. Nail salons and pastry shops bear signs that announce they’re up for sale.

“Life in Culiacán has almost disappeared,” Miguel Taniyama, the owner of Clan Taniyama restaurant, remarked with quiet resignation.

For years, Sinaloa — an agricultural region synonymous with the infamous cartel bearing its name — enjoyed a fragile peace. But that calm was obliterated in September when two factions of the cartel turned their guns on each other.

Scenes like these are becoming increasingly common, despite the government’s open war with organized crime. Yet, despite the record number of arrests and fatalities among cartel members, the violence hasn’t stopped. On the contrary, it has accelerated. The scale of death is immense with over 400,000 murders since 2007.

In Mexico, the fight against organized crime has long resembled a game of whack-a-mole. Now, a new study offers a startling insight: the way to stop cartel bloodshed isn’t by locking up more people — it’s by stopping people from joining in the first place.

Cartels: A Perpetual Cycle of Violence

The study, authored by researchers Rafael Prieto-Curiel, Gian Maria Campedelli, and Alejandro Hope, used a decade’s worth of data on homicides, arrests, and cartel interactions in Mexico. The findings are sobering. Mexican cartels now boast an estimated 175,000 members, making them the fifth largest employer in Mexico, right between the grocery chain Oxxo and telecoms company América Móvi.

Cartels lose members constantly through conflict with rivals and arrests by the state. Yet they replenish their ranks at an alarming rate, recruiting at least 350 people every week. This relentless cycle of violence is self-sustaining.

It’s a sobering conclusion that needs to be taken to heart by the authorities: increasing arrests does not reduce violence. Instead, it might make things worse.

Diagram showing how Cartels change in membership numbers
Model diagram representing the four reasons why a cartel changes in size. Credit: Science.

Understanding the inner workings of cartels is notoriously difficult. They operate in secrecy, making data hard to come by. So, to shine light on the cartels, the researchers used public data to cast an indirect view.

The study models cartel dynamics using a mix of statistics and network theory. The researchers accounted for the losses cartels suffer through violent clashes and law enforcement’s efforts to incapacitate them and then used this data to infer the strength of Mexican cartels.

Despite setbacks, the researchers found that cartels continue to grow. They estimate that between 2012 and 2022, cartel membership rose by 60,000 members.

“One of the biggest issues about cartels is that they are like a black box. We will never be able to go into a city and ask, ‘Are you a cartel member?’ So, we needed to come up with another idea — and that idea is mathematics,” Prieto-Curiel told ZME Science during an interview at the Falling Walls conference in Berlin.

“We try to understand with a system of equations how cartels change in size and how they manage to prevail as an institution despite the number of losses that they have through either killing or arrests. Given the data that we actually have, like the number of homicides and arrests in the country, we can understand the inside of the cartels in Mexico. And that’s what we did,” added the researcher, who used to be a former Mexico City police officer; now a mathematician at the Complexity Science Hub in Vienna.

A Mathematical Black Box

Cartels have an uncanny ability to adapt. When authorities crack down on one group, others move in to seize territory, recruit new foot soldiers, and expand their networks. Taking into account publicly available data and cartel dynamics, the researchers crafted a series of equations that can offer valuable insight into one of the most dangerous underground operations in the world. The model considered four forces that shape cartel size: recruitment, arrests (or incapacitation), conflict with rival cartels, and internal breakdown (saturation).

Graphs showing the recruitment and loss rates of the cartelsGraphs showing the recruitment and loss rates of the cartels
Between 2012 and 2022, researchers estimate that 285,000 people worked as cartel members, but only 60% were still active by 2022. Roughly 18% of them are dead, and 20% were incapacitated. B – Number of employees from the top 10 companies in Mexico and the combined size of cartels [45]. We estimate that cartels had 175,000 members by 2022, with an interval between 160,000 and 185,000 members combined. C – Of the 175,000 active cartel members, roughly 17.9% are part of CJNG, 8.9% of Cartel de Sinaloa, and 6.2% from Nueva Familia Michoacana, the top three cartels in terms of size. Credit: Science.

The numbers are stark. By 2022, cartels had between 160,000 and 185,000 active members. This means cartels rival some of Mexico’s largest employers, like the retail giant Walmart. In 2012, the researchers estimated there were 115,000 cartel members.

In order to sustain these numbers, the cartels have to recruit at least 370 people per week, otherwise they would collapse. Week after week, they manage to hit this quota and perhaps even more.

The study took into account a total of 150 active cartels in Mexico as of 2020. These cartels were identified through open-source data, including reports from national and local newspapers, and narco (narcotics) blogs.

“We take one equation for each cartel, so we got a system of 150 equations. Each equation tells you the size of that cartel and why it changes according to the different structure conflicts and so on. We take this equation and then when we solve it,” said Prieto-Curiel.

The Brutal Food Chain

At the top of the food chain looms Cártel Jalisco Nueva Generación (CJNG). Its reach extends across 77 state-level conflicts, like tentacles spreading out to strangle territories in its grip. With an estimated 28,764 members, CJNG has built a fortress of alliances in 55 different regions.

Then there is the Sinaloa Cartel, an empire whose name has echoed through decades of narco history. It commands an army of 17,825 members, locked in rivalries that span 19 states, but also bolstered by alliances in 34 regions. Once the undisputed giant, it now shares the battlefield with other rising forces.

Other major cartels include La Nueva Familia Michoacana with 10,736 estimated members and the Cártel del Noreste with 8,992 members. La Unión Tepito, an urban cartel entrenched in the heart of Mexico City, counts 7,561 members.

Lower down the food chain are countless smaller organizations, often no more than 200 members strong. But each group, no matter its size, feeds the same cycle of violence. The clashes between the ten largest cartels generate only 15% of fatalities. The rest — the bulk of the bloodshed — comes from a relentless war waged by and against smaller, fragmented cartels, who are often targeted for elimination or used as pawns in bigger gang rivalries by the major cartels.

The researchers estimate that if current trends continue, the violence in Mexico will worsen significantly over the next five years. By 2027, they predict:

  • 40% more cartel-related casualties compared to 2022 levels.
  • A 26% increase in cartel membership, further solidifying the cartels’ hold on the country.

Why Arrests Aren’t Working

Graphs showing the cartel-related deaths in Mexico projected to 2027Graphs showing the cartel-related deaths in Mexico projected to 2027
Weekly cartel-related deaths (top) and cartel size (bottom) if trends continue, incapacitation doubles, recruitment is reduced by half and recruitment is reduced to zero. Credit: Science.

The traditional strategy of incapacitation — arresting cartel members and putting them behind bars — seems logical. After all, fewer criminals should mean less crime. But the study shows this approach is flawed. For every cartel member arrested, new recruits step in, often drawn from communities where opportunities are scarce and violence is a constant presence.

Roughly 37% of cartel members over the past decade were either killed or jailed, yet there are more cartel criminals than ever.

The authors found that even if arrests doubled, this approach would lead to an 8% increase in weekly casualties and a 6% growth in cartel membership. Arresting more cartel members destabilizes the power balance between cartels, triggering more violent conflicts as groups scramble to fill the void left by imprisoned leaders.

This is exactly what happened in the sunbaked city of Culiacán, home to one million people. Last summer the son of the Sinaloa cartel’s jailed founder Joaquin “El Chapo” Guzman reportedly double-crossed the cartel’s other co-founder, Ismael “El Mayo” Zambada. Zambada was arrested on U.S. soil on July 25 after allegedly being kidnapped in Mexico and delivered to U.S. authorities against his will.

The ensuing war between the cartel’s “Mayos” and “Chapitos” has left more than 400 people dead and hundreds missing in just a few months, according to the state prosecutor’s office. Many of the victims were tortured by electrocution and even hot chiles, while others were “fed dead or alive to tigers.”

President-elect Donald Trump promises to escalate the battle against Mexican drug gangs. Trump said that “we need a military operation” against the traffickers, although he’s provided few details. His Vice-president, JD Vance, said that hundreds of thousands of American soldiers “are pretty pissed off”. He added, “I think we’ll send them in to do battle with the Mexican drug cartels.” If that were indeed the case, this could end in disaster, ironically making cartels stronger than ever in the long run.

Recruitment: The Achilles Heel of Cartels

If arrests don’t work, what does? The answer lies in prevention. The study shows that cutting recruitment in half would reduce cartel-related homicides by 25% and shrink cartel membership by 11%. This strategy, the researchers argue, is more effective and sustainable.

“The only thing that would decrease violence… was lowering the number of people who joined the organizations in the first place,” Prieto-Curiel said.

The study calls for structural investments in a proactive strategy that targets individuals at risk rather than a traditional reactive approach.

Yet this would be no small feat. Reducing recruitment means addressing the social and economic conditions that push people toward cartels in the first place. Young men, who make up the bulk of cartel recruits, often face bleak futures. Cartels offer not just money, but a sense of purpose and belonging. Breaking this cycle requires massive investment in education, job creation, and community support.

The researchers emphasize that even if recruitment were to drop to zero overnight, it would still take years to return to the levels of violence seen a decade ago. The cartel population is simply too large, and their networks too entrenched.

A Call for Change

Rafael Prieto-Curiel. Credit: ZME Science.Rafael Prieto-Curiel. Credit: ZME Science.
Rafael Prieto-Curiel. Credit: ZME Science.

Mexico’s fight against cartel violence is at a crossroads. The data makes it clear: the current strategy of arrests and crackdowns is a losing battle. The cartels are too resilient, their recruitment pipelines too robust. To truly reduce violence, Mexico must pivot toward a proactive approach.

This means providing alternatives to the cartel life. It means investing in youth, creating opportunities where there are none, and breaking the cycle of poverty and violence that feeds the cartels.

“Tackling recruitment has a triple effect: first, it lowers the number of cartel members, reducing the violence they can create by having fewer killers. Second, it lowers the number of targets, so fewer people are vulnerable to suffering more violence. And third, it reduces the cartel’s capacity for future recruitment,” the authors wrote in their study.

However, it’s all a daunting challenge. For instance, Prieto-Curiel pointed out that recruitment isn’t driven solely by poverty, challenging a common misconception:

“Those regions in which you have more cartel presence are not the poor ones, those cities with a higher cartel presence are not the poor ones,” he told me.

Prieto-Curiel criticized how media, particularly shows like Narcos, glamorize cartel leaders and distort reality for vulnerable youth:

“In the past 10 years… in Netflix, they are showing these cartel capos as the hero, as the person that is successful, that has all the houses, that travels with the cars. But that is not true.”

He argued that such portrayals create dangerous misconceptions, making cartel life seem attractive. The reality, he stressed, is that most cartel members face grim outcomes:

“When you see that member of the cartel being successful, what you’re not seeing is that there are the other 174,999 members of a cartel… They are the ones that get arrested, murdered, killed.”

“It’s a harsh reality,” Prieto-Curiel said. “When a young person joins a cartel, the chances they will be dead or in prison within 10 years are extremely high.”

He estimated that 50% to 60% of new recruits end up dead or incarcerated within a decade.

“The chances that they will finish dead in the next 10 years is 100 times higher than a person in the street.”

He also pointed to the way cartels use social networks to recruit. When one person joins, it often pulls in their family, friends, and neighbors. “The chances are that not only you, but your whole network, will end up dead or in prison,” he warned.

As the mathematician was telling me all of this, I couldn’t help but wonder if he was concerned for his safety. When confronted with this, Prieto-Curiel seemed unphased, although I couldn’t help noticing that he obviously thought about it.

“It is tricky to do research on organized crime, and I admit that sometimes I feel nervous about going back to Mexico. That is tricky, right?”

However, he says that his work relies solely on mathematical modeling and publicly available data, not specific information about individual cartel members.

“I don’t have any specific data about any member of a cartel… I use only equations. And I use not even an equation for the character, but I use a number of homicides to try to estimate this.”

“For me, a question was not, ‘Who is a member of a cartel here?’… I hope that I’m in less risk thanks to that.”

Nonetheless, he acknowledged that research in social sciences, particularly on sensitive topics like organized crime, can still touch on political or institutional interests, making researchers vulnerable:

“In all aspects of research, we are in the risk of touching the nerves here and there of either political parties, institutions, companies.”

In Mexico, the stakes couldn’t be higher. Without a change in strategy, the violence will continue, claiming more lives and destabilizing more communities. The path forward seems more clear now – but it requires courage, vision, and a willingness to invest in Mexico’s most vulnerable citizens.

If Mexico hopes to break free from the cycle of cartel violence, the solution lies not in more arrests, but in fewer recruits. The country’s future depends on it.

The findings were reported in the journal Science.