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Tipping point. Simulation shows how longer sentences for some may drive up rates of imprisonment for many.

Tipping point. Simulation shows how longer sentences for some may drive up rates of imprisonment for many.

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Is prison contagious?

Incarceration in the United States is frequently described as an epidemic, with per capita rates nearly quadrupling in the past 30 years. African-Americans appear to be particularly susceptible: In 2011, they were six times more likely than whites to be incarcerated, making up 38% of the 1.6 million Americans behind bars while accounting for only 13% of the U.S. population. Now, a computer simulation originally developed to track infectious disease suggests the longer prison sentences that blacks often receive may accelerate the rate of “infection.”

Social scientists have long observed that imprisonment behaves like a contagious disease, says Kristian Lum, a statistician at Virginia Polytechnic Institute and State University in Blacksburg. Studies show that those close to an incarcerated person are more likely to become imprisoned themselves. They could be driven to crime by poverty or stress resulting from the jailed person's absence, or become inured to violence through more frequent exposure to criminals. Children whose parents or older relatives are in prison may act out in ways that land them in jail, too. Even if the prisoner's friends and family don't commit more crime, or more violent types of crime, they may attract more attention from the police and be more likely to be arrested for minor infractions.

To find out what makes imprisonment more transmissible among blacks than whites, Lum and her colleagues turned to the world of infectious disease, repurposing a computer simulation used in epidemiology to predict how an epidemic of imprisonment might develop. When a disease changes from just something that's going around to a true epidemic, there's usually a tipping point, Lum explains. For example, the sick people may come into close contact with others who are extremely vulnerable—the elderly, young children, or those who have never been exposed to the infection before. With incarceration, the researchers suspected one such tipping point might be the longer sentences typically given to black offenders.

Incarceration equals the period of contagion, Lum explains. "The longer you're imprisoned, the higher the toll your incarceration takes on your family and friends, and the more likely they are to ‘catch’ your incarceration from you." Sentencing discrepancies are not huge, she notes. For drug possession, according to the U.S. Department of Justice, whites are given an average sentence of about 14 months, whereas black Americans typically get about 17 months for the same offense. Still, the researchers thought the difference might be just enough to tip a problem into an epidemic.

To test their suspicion, the researchers used their epidemiology model to generate a virtual community of about 8000 imaginary people. They assigned each individual a gender, a partner, a given number of children, siblings and friends of various ages, and a given lifespan. All data were drawn from the Census Bureau, Social Security Administration, and Centers for Disease Control and Prevention. In all, the virtual network encompassed about 60,000 friendships and family ties. About 1% of the virtual population was assumed to be in jail. The probability of these virtual inmates' friends and family also going to jail was programmed into the model using previously published statistics.

To observe the effects of differences in sentence length, Lum’s team ran a simulation twice. The first time, the imprisoned individuals were given the 14-month sentence usually assigned to whites for drug possession. The second time, the same virtual group was used; the only difference was that those in jail stayed there for 17 months, a typical sentence for black offenders. Using the lifespans, ages, sentence durations, and probability of arrest that were programmed into the model, the researchers watched each simulation for 50 virtual years.

The disparity in sentencing between whites and blacks emerged as the single factor making the disease of incarceration a true epidemic among blacks, the researchers report online this week in the Journal of the Royal Society Interface. With no differences between the two hypothetical groups other than the length of the sentence, even 3 extra months in prison led to higher incarceration rates over time. In the test for which the shorter sentence was used, incarceration rates actually declined from the starting point of 1% for about the first 5 years and then increased only very slightly, to 0.725%, for the 50-year duration.

In the second simulation, however, the longer sentence clearly fell on the other side of the tipping point. When the virtual inmates were imprisoned for 17 months, incarceration rates throughout the community climbed steadily until just under 3% of the population was in jail 50 years later.

When the model was run indefinitely, it leveled off at incarceration rates of 1% using the shorter sentence and 7% using the longer sentence—a figure that mirrors the difference in rates of white and black incarceration in the United States today.

"According to our model, the tipping point is somewhere between the 14- and 17-month sentences," Lum says. "Below that point, incarceration won't take off and reach high levels in the population, and above that point, it will."

Focusing on the potential effects of the sentence length opens a host of questions for future work, says James Moody, a sociologist at Duke University in Durham, North Carolina. One such question is how differences in a person’s family structure or number of close friends may influence how their incarceration “spreads” through their community. "Contagious processes often contain clear tipping points," he explains. "In this case, the sentence length for black Americans is on one side of this point while that for whites is on the other."

Because a computer simulation is not the real world, the researchers compared their results with California’s incarceration data since the mid-1980s, when mandatory drug sentencing became law and average sentence length for white and black offenders began to diverge. This time, real-world figures and estimates of incarceration were used in the simulations. The model's predictions were borne out almost exactly. In California, from 1986 to 2010, the incarceration rate for blacks climbed from 1% to 2.18%, while for whites it rose from a lower starting point of 0.15% to 0.28%. The model had predicted an increase to 2.25% for individuals assigned the sentence usually given to blacks, and 0.34% for a shorter sentence handed to whites.

Unexpectedly, the simulation also proved accurate in another area, closely reflecting data about recidivism, or going back to jail after release. Results in the simulation almost exactly tracked California figures for the probability of returning to jail based on the number of times incarcerated, the inmate's age upon first being released from prison, the number of months since release, and by the length of the sentence.

"Using the California data showed us that what our model said would happen, did happen," Lum says. "It provides more evidence that incarceration may be infectious because it closely matches real data on a variety of levels."

Statistician David Banks, also at Duke, notes that the model adapted by Lum and colleagues is of a kind often used in weather forecasting, economics, and advertising, as well as in epidemiology. He finds its use to study incarceration innovative, saying that more simulations like this one might provide useful data about the consequences of decisions that affect society. "It's a clean, smartly coded model that might give policymakers more information about consequences, like when they're looking at sentencing guidelines.”

Lum cautions that in the real world, other factors besides sentence duration likely contribute to differences in incarceration rates. Still, she notes, the implications of the study aren't purely racial. "Under this model, small increases in sentence length led to large differences in the rate of incarceration regardless of race. That means harsher sentencing policy may have the unintended consequence of increasing crime, rather than reducing it.”