# ODU Mathematician John Adam Adapts Predator-Prey Model for Insurgency Study

John Adam interprets the world around him with the help of his beloved math, whether he's contemplating the rise and fall of insurgencies in Colombia, the pattern of a rainbow, spontaneous combustion of haystacks or an outbreak of swine flu on an oceanliner.

The University Professor of mathematics and statistics at Old Dominion University has wielded his expertise across the board in recent months, most notably in his new book, "A Mathematical Nature Walk," published by Princeton University Press, which arrived in bookstores in June.

But perhaps his most intriguing application of mathematics and modeling is an experiment he conducted for the United States military. It has to do with insurgents in Colombia who are driven by the financial rewards of the cocaine trade. At times during the last few decades, the drug cartels have had a great deal of success exploiting poor farmers and others of their countrymen to ramp up the cocaine trade. Yet at some times, particularly recently, the authorities seem to have the upper hand, giving the civilians a chance to escape the grasp of the cartels.

Adam was invited to apply his unusual modeling ideas to circumstances in the South American country by two researchers at ODU's Virginia Modeling, Analysis and Simulation Center-the acting director, John Sokolowski, and social sciences researcher Catherine Banks. They had a grant from the U.S. Marine Corps Systems Command to develop computational models that predict and track insurgencies.

The beauty of Adam's work on insurgencies comes from its simplicity, from the fact that he uses what may be one of the most common-and most easily understood-mathematical models. It's often referred to as a predator-prey model. His paper, "A Two-Population Insurgency in Colombia: Quasi-Predator-Prey Models-A Trend Towards Simplicity," was published in the journal Mathematical and Computer Modeling. Sokolowski and Banks are co-authors.

Here in its basic form is how the model works, say with tuna as the predators and mullet as the prey. Population numbers of both fish species are interdependent because if the tuna population falls, the mullet population rises, which, in turn, could lead to the tuna population rebounding and the mullet population falling.

A variation of this model can be expressed by the scenario of one person with swine flu boarding an ocean liner. For the sake of the story, let's say he is not yet showing symptoms, boards without incident and the ship sets sail. Also, we will stipulate that at the outset the flu victim is the sole predator and the other 999 people on board are prey.

Mathematicians such as Adam can model the inevitable spread of the swine flu. "Another way to think of it is if one person has a juicy bit of information," Adam explained. "How will the rumor spread? As with the illness, it spreads when someone who has it comes together with someone who doesn't have it. It doesn't spread if both people who come together already know the rumor-or already are infected-and it doesn't spread if both of these people don't know the rumor-or are not infected."

Also, there can be certain forces that push a predator-prey model in a particular direction. Say tuna populations are depleted by fishermen. This theoretically would give mullet a chance to expand their numbers. But a toxic algae bloom that killed mullet could also drive down the population of tuna.

What does this have to do with insurgencies in Colombia? Adam and his co-authors posited an interdependency with the narco-insurgents as the predators and the susceptible populations as the prey. Then they went looking for forces that influence the model.

Several forces promote the insurgencies, namely a weak government, ineffective military and police forces, and the economic plight of the average citizen. "Unending conflict makes it difficult for the country to mature; and many of Colombia's citizens perceive an absence of state and no rule of law as they experience the government's inability to provide for domestic security," according to the research paper. It follows that a high civilian death toll-it totaled 100,000 between 1980 and 2004-would indicate that insurgents had the upper hand. The same could be said for a high number of kidnappings and extortions.

More recently, a hard-line approach to the insurgents instituted by President Alvaro Uribe seems to have helped to turn the tide. He increased the size of the Colombian military and improved training. He instituted a policy of no dialogue with the insurgents and, latching onto the United States' war on terrorism, he successfully labeled drug lords as terrorist leaders. Specific factors that reflect the strength of the government and a secure existence for civilians include the number of insurgents who were captured or killed-for example, 100,000 in 2004 alone-and the 63 percent decrease in terrorist attacks between 2002 and 2006.

"Certainly it appears that general mathematical representations of insurgency models using population dynamics are feasible," Adam and his co-authors wrote in the paper's conclusion. "If data on insurgency strength as a function of time is known but a detailed 'factor analysis' is not possible, such models may still be able to represent insurgent behavior by means of these mathematical representations."

Adam said he does not know if the U.S. military or government will want to pursue his lines of reasoning. "But it was a very interesting project for me and I think it had interesting results," he added.

Admittedly, his mathematical adventures don't usually involve death tolls and kidnappings. In fact, his new book, "A Mathematical Nature Walk," is downright pastoral, even if it does mention exploding haystacks. The book ($27.95, available at the University Bookstore on Monarch Way) is an entertaining and informative collection of puzzles from the natural world. It includes 96 questions about many natural phenomena, and then shows how to answer them using mostly basic mathematics.

One question considers how to arrive at the weight of a pumpkin just by looking at it, and another examines why large haystacks are prone to spontaneous combustion.

The ODU professor, who was born in England, said the book was the subject of a feature article in the Scottish edition of The Sunday Times, perhaps on the strength of one question about the Loch Ness Monster. The article is at http://entertainment.timesonline.co.uk/tol/arts_and_entertainment/books/book_reviews/article6493067.ece.

Adam also is the author of "Mathematics in Nature" and co-author with Lawrence Weinstein, an ODU physics professor, of "Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin."

**This article was posted on: July 30, 2009**

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