Modeling Disruptions to Sex Trafficking Networks with Other Forced Illegal Activities

Figures & data

Table 1. Summary of Forced Activities from the Expertise of Our Advisory Group.

Forced Criminal Behaviors	Forced (Legal) Labor Activities
Stealing or Theft	Housework for trafficker or trafficker’s family
Selling Drugs	Childcare for trafficker or trafficker’s family
Transporting Drugs	Driving people around
Check Fraud	Doing hair, nails, or make-up for the trafficker, other victims or the trafficker’s family
	Working a legal job and giving wages to trafficker

Figure 1. Or modeling approach and areas where help is needed from trafficking experts. From Sharkey et al. (2021).

Figure 2. The human trafficking data pyramid. From Kosmas et al. (2023).

Figure 3. An example of control where the trafficker forces the victim to work different illegal activities.

Table 2. An Overview of the Mathematical Notation Capturing the Inputted Data in an Instance of the Interdiction Model.

Sets
M	Set of all markets, m
V	Set of victims, j
A	Set of intervention activities, i
T	Set of traffickers, t
D	Set of days, d
Rjd	Set of required criminal activities of victim j for day d
Parameters
${\mathrm{r}}_{\mathrm{m}\mathrm{j}\mathrm{d}}$	Revenue generated in market m by victim j ($/hour) for day d
$\mathrm{u}{\mathrm{b}}_{\mathrm{t}\mathrm{j}\mathrm{d}}$	Capacity of trafficker t to control victim j (“up-time hours”) for day d
${\mathrm{C}}_{\mathrm{m}\mathrm{d}}$	Market capacity (hours) for markets m for day d
${\mathrm{U}}_{\mathrm{j}\mathrm{m}\mathrm{d}}$	Capacity of victim j to work in market m (hours) for day d
${\mathrm{b}}_{\mathrm{j}}$	Resources required to remove victim j
${\mathrm{a}}_{\mathrm{i}}$	Resources required to implement market-level intervention activity i
${\mathrm{P}}_{\mathrm{i}\mathrm{m}}$	Percent of market m disrupted by intervention activity i
B	Overall budget level for intervention activities

Table 3. Initial Inputs for Networks with a Nickel and Dime Market Focus and Victims with Substance Abuse Disorders.

Market/Illegal Activity	Lowest Hourly Revenue	Typical Hourly Revenue	Highest Hourly Revenue	Hours per day (range)	Number of days per week
Nickel and Dime	$0	$100–$300	$1000+	1–8 hrs	Every day
Strip Club	N/A	N/A	N/A	N/A	0
Escorting	N/A	N/A	N/A	N/A	0
Drug Trafficking	$50	$250	$1200	1–3 hrs	Every day
Fraud	N/A	$3,750	N/A	8 hrs	Once per year
Theft				1–10 hrs	Every day

Table 4. Initial Inputs for Networks Where Victims Participate in Diverse Commercial Sex Markets.

Market/Illegal Activity	Lowest Hourly Revenue	Typical Hourly Revenue	Highest Hourly Revenue	Hours per day (range)	Number of days per week
Nickel and Dime	$0	$30–$50	$5000	Up to 12 hrs	6 days
Strip Club	$0	$100	$5000	Up to 8 hrs	Every day
Escorting	$0	$1000	$40000	Up to 16 hrs	Every day
Drug Trafficking	N/A	N/A	N/A	N/A	N/A
Fraud	N/A	N/A	N/A	N/A	N/A
Theft	N/A	N/A	N/A	N/A	N/A

Table 5. Impacts, in Terms of Fractions, of Interventions on the Available Hours in Each Illegal Market.

Practical Example		Nickel and Dime Sex Market	Theft	Illegal Drugs	Fraud
Nickel and dime market criminal justice focus	I1	0.2	0	0	0
Targeted demand reduction	I2	0.15	0	0	0
“Street-based” criminal justice focus	I3	0.15	0	0.15	0
Drug trafficking reduction	I4	0	0	0.2	0
Fraud reduction	I5	0	0	0	0.2
Universal basic income	I6	0.05	0.05	0.05	0.05

Table 6. Input Data into Our Instances and Its Justification.

Math Notation	Description	Input Data	Validation and Justification
M	Set of all markets	Nickel and Dime Commercial Sex Market; Drug Trafficking; Theft; Fraud	AG expertise; similar activities discussed Jacobs and Richard (2016) and Roe-Sepowitz (2019)
V	Set of victims	Analysis includes 5 and 6 victims	AG expertise; similar to number of victims pimps reported in Horning et al. (2020)
A	Set of intervention activities	Hypothetical, with a focus on disrupting nickel and dime commercial sex market. Considered 6 interventions.	Currently, we test hypothetical impacts of interventions and leave estimating the effectiveness to future research
T	Set of traffickers	Analysis focused on 1 trafficker	This is a common type of trafficking network
D	Set of days	All 7 days of the week	Helps to represent the changes in the activities of victims during the course of the week as reported by the AG
Rjd	Set of required criminal activities of victim j for day d	Focused on Nickel and Dime Commercial Sex Market; there was a 1/7 probability of this market being included on a particular day	AG expertise indicated that the required activities typically focused on calls to the trafficker from sex buyers. If revenues in this market are higher than all other revenues, the victim would complete work in this market first, without the required activity.
$r_{mjd}$	Revenue generated in market m by victim j ($/hour) for day d	Nickel and Dime: Set probabilities of low, typical, and high ranges from Table 2 to ensure that the traffickers’ expected weekly revenues from this market was $32000 Drug Trafficking: Used the associated probabilities for low, typical, and high ranges from Nickel and Dime to generate expected hourly revenues Theft: Assumed to be $25 per hour Fraud: $3750/8	Nickel and Dime: We used the AG survey ranges and associated probabilities with each range to ensure that the expected weekly revenue was $32000, which was similar to findings of Dank et al. (2014) and Horning et al. (2020) on the weekly revenues of traffickers. Drug Trafficking: Based on AG survey. Theft: Assumed to be the lowest hourly revenue, results would be similar for any hourly revenue with this property Fraud: Given that the fraud activity would occur for one day for 8 hours and generate $3750, we have adjusted the hourly revenue accordingly.
$u{b}_{tjd}$	Capacity of trafficker t to control victim j (“up-time hours”) for day d	Uniformly generated between 8 and 16 hours	This will allow the victim to participate in all Nickel and Dime activities, as well as a number of hours in other criminal activities. This helps simulate situations when not enough money was made in the Nickel and Dime market
$C_{md}$	Market capacity (hours) for markets m for day d	Nickel and Dime: 30 hours for 5 victim networks; 36 hours for 6 victim networks Drug Trafficking: 12 hours for 5 victim networks; 18 hours for 6 victim networks Theft: Uncapacitated Fraud: Uncapacitated	Nickel and Dime: These were chosen so that the available market was about 1.5 times the expected number of hours the trafficker could meet with their set of victims. Drug Trafficking: Most days the network could meet all demand, if they focused on this market. Theft: Assumed to be always available. Fraud: Assumed that the availability of the action is the limiting factor
$U_{jmd}$	Capacity of victim j to work in market m (hours) for day d	Nickel and Dime: Uniformly generated from 1 and 8 hours Drug Trafficking: Uniformly generated from 1 and 3 hours Theft: Uniformly generated from 1 to 10 hours Fraud: Roughly, a 1/365 chance of it being 8 hours; 0 otherwise	AG survey. They indicated that there were times when conditions allowed a victim to spend very little time in the nickel and dime market. They also indicated that fraud was often only done once per year.
$b_j$	Resources required to remove victim j	Arbitrarily large	We did not consider removing victims in this analysis.
$a_i$	Resources required to implement market-level intervention activity i	Assumed to be 1	Given our focus on hypothetical interventions, we assumed each intervention to cost the same amount in order to understand which intervention(s) might be most effective. The study used hypothetical interventions due to lack of data. Future research should identify the effectiveness and costs of such interventions.
$P_{im}$	Percent of market m disrupted by intervention activity i	Hypothetical; provided in Table 4	Given our focus on hypothetical interventions, and the traditional difficulty in measuring effectiveness of such interventions, we hypothesized these parameters. Future research should identify the impacts of such interventions.
B	Overall budget level for intervention activities	Varying; will consider budgets ranging from 1 through 6.	This range allows us to understand which interventions are prioritized.

Table 7. The Number of Hours Victims Were Forced to Work in the Nickel and Dime Market and the Number of Available Hours in the Nickel and Dime Market for Instance 1 of the Six Victim Network Analysis.

Budget	Selected Interventions	Sun	Mon	Tues	Wed	Thurs	Fri	Sat
0	None	(29, 36)	(32, 36)	(27, 36)	(23, 36)	(34, 36)	(27, 36)	(28, 36)
1	N+D focus	(28.8, 28.8)	(28.8, 28.8)	(27, 28.8)	(23, 28.8)	(28.8, 28.8)	(27, 28.8)	(28, 28.8)
2	N+D focus, SB CJ focus	(23.4, 23.4)	(23.4, 23.4)	(23.4, 23.4)	(23, 23.4)	(23.4, 23.4)	(23.4, 23.4)	(23.4, 23.4)
3	N+D focus, SB CJ focus, Demand Red	(18, 18)	(18, 18)	(18, 18)	(18, 18)	(18, 18)	(18, 18)	(18, 18)
4	N+D focus, SB CJ focus, Demand Red, UBI	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)
5	N+D focus, SB CJ focus, Demand Red, UBI, Drug Red	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)	(16.2, 16.2)

Figure 4. Revenues of six victim trafficking networks as the number of interventions increases.

Figure 5. Revenues of five victim trafficking networks as the number of interventions increases.

Table 8. Optimal Intervention Strategies as the Budget Increases for All Five Victim Networks and Instances 1, 2, and 5 for Sic Victim Networks.

		Intervention Budget Level
Practical Intervention Example		1	2	3	4	5	6
Nickel and dime market criminal justice focus	I1	1	1	1	1	1	1
Targeted demand reduction	I2	0	0	1	1	1	1
“Street-based” criminal justice focus	I3	0	1	1	1	1	1
Drug trafficking reduction	I4	0	0	0	0	1	1
Fraud reduction	I5	0	0	0	0	0	1
Universal basic income	I6	0	0	0	1	1	1

Figure 6. Percentage changes in forced illegal activities at three interventions for six victim networks.

Figure 7. Percentage changes in forced illegal activities at three interventions for five victim networks.

Figure 8. An overview of the modeling, data collection, and analysis in this paper.

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