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Cause and Dynamics of a Silent Epidemic: Confronting the Dropout Crisis and Keeping Children in Schools

A Mathematical Analogy with an Infectious Diseases Approach

By Anuj Mubayi

In 2014, the U.S. high school graduation rate was 83.2 percent. In 2013, the average four-year cohort dropout rate for all Chicago high schools was 26.2%. Researchers from Arizona State University (ASU), Northeastern Illinois University (NEIU), and the University of Texas at Arlington (UTA) developed a data-driven mathematical model to study the influence of student environment on high school dropout patterns. This modeling study includes a 2013 survey—designed by researchers using a sampled Chicago high school, which is particularly vulnerable to student dropouts—to parameterize the model, making it unique among these types of investigations.

Bechir Amdouni, a high school teacher and graduate student at NEIU, and I (formerly of NEIU and now a professor at ASU) spearheaded the research project after visiting a local high school in South Chicago and witnessing the seriousness of the dropout problem firsthand. Upon interacting with students and faculty at the high school, we realized that academic achievement shaped by peer influence and parental guidance might offer significant support to vulnerable students; such influences may be affecting dropout rates in this community. Marlio Paredes, a dynamical systems expert at the University of Puerto Rico-Cayey, and Christopher Kribs, a specialist in mathematical education and mathematical epidemiology from UTA, joined us to formally design the study.

Methods and Analysis

Despite the complexity of dropout dynamics, previous studies have argued that the U.S. government’s policies are not supported by mechanistic-based temporal research; thus, dropout rates in many parts of the country are rising rapidly. Our study aims to identify driving mechanisms and develop, analyze, and test a mathematical model to better understand high school dropout dynamics; this is followed by analysis, calibration, and simulation. Our dynamic model uses an analogy from susceptible-infected-recovered-type infectious disease models via a set of nonlinear differential equations. Bifurcation analysis identified two tipping point quantities: a threshold that evaluates the generation point of the critical mass of academically vulnerable students in a school, and a threshold that captures conditions under which the number of failing students becomes large enough to increase dropout rates. The resulting model, based on students’ academic performance in core courses, can imitate four different situations:

(i) A ‘healthy’ school, in which all students perform very well academically
(ii) An institution where some students fail core courses but academic failure does not cause dropouts  
(iii) A school with low dropout rates
(iv) A school with extremely high dropout rates

Following model formulation, we developed and administered a precise survey instrument to a group of ninth through twelfth grade students in a Chicago public school. We used data about the school’s enrollment and attempted to identify factors that correlated with the establishment and maintenance of high dropout levels.

Findings and Implications

Our research team studied the effects of multiple mechanisms—including effective teaching, school demographic factors, peer influences on and off campus, parental influences, and student academic performances—on the dynamics of dropout rates. We found that parental involvement and peer interactions have the highest impact, and hence decided to further study their impact on student outcome.

Students’ academic achievement is most directly related to the level of parental involvement, or lack thereof.  Survey analysis revealed that over half of the dropouts did not live with their parents, reinforcing the potential effect of social, economic, and emotional environments on students’ educational development.

In our sample, more than 50% of students were in frequent contact with individuals who are of the mindset that attending school is a waste of time. Preemptively identifying vulnerable students and increasing parental involvement lowers the number of disaffected friends, thus raising the question of how to monitor or effectively restrict “good” students from mixing with failing students or dropouts. However, if negative social interactions (social mixing) increase beyond a certain threshold, the impact of parental involvement becomes less significant (see Figure 1). And if intervention is left until students are actively failing at school, attempts at parental guidance are futile.

Figure 1. Parental guidance and peer influence are most influential on student dropoff rates. Although preemptive parental involvement can keep students in school, that involvement loses significance as the quantity of negative social interactions increases. Image adapted from [1].

The study thus suggests that peer interaction, like parental guidance, is critical to the development of higher dropout rates. However, separating students based on negative peer interactions and behaviors towards one another raises many practical issues regarding curriculum. For example, if there is a major shortage of skilled faculty in similar schools, who will teach these separated groups of students?

Chicago public schools use metrics, such as dropout rates, to evaluate school performance. If this metric is low, schools may lose funding or even face closure (50 schools closed in the U.S. in 2013). Therefore, teachers feel a continuous pressure to not fail students, which raises other issues. Do students passing with very low grades deserve to pass, or are their passing grades a result of pressure of a potential school closing? If they graduate, do they enroll in a college or university? Have they truly gained quality education in high school?

Numerous factors contribute to dropout rates, making its investigation quite challenging. This study serves as a starting point to begin to understand these complexities, though some limitations exist. Future studies must consider higher sample sizes, a greater number of schools per sample, data stratification based on race and ethnicity, and construction and analysis of dynamical models that capture peer influences depending on class year, age group, social context, and neighborhood.


The factors we consider in this analysis are different from those typically investigated in existing dropout-related studies. Moreover, unlike cross-sectional and longitudinal approaches, our research focuses particularly on the dynamics of dropout rates, likely the most effective way to identify critical factors and design a lasting intervention. In summary, while parental influence can deter student dropout up to a certain point, the amount of time vulnerable students spend with friends who have already dropped out is also significant. We included general positive and negative trends as part of the study hypotheses, but the ways in which they interact and limit each other are complex. The model—while still a gross oversimplification of human interaction—allowed us to capture some of that complexity.


[1] Amdouni, B., Paredes, M., Kribs, C., & Mubayi, A. (2017). Why do students quit school? Implications from a dynamical modelling study. Proceedings of the Royal Society A, 473(2197).

  Anuj Mubayi is an assistant professor of applied mathematics in the School of Human Evolution and Social Change as well as the Simon A. Levin Mathematical Computational and Modeling Science Center at Arizona State University. He is co-director of the Mathematical and Theoretical Biology Institute’s summer training program for undergraduate students. The program aims to improve dropout rates for college students, specifically underrepresented minorities, and encourage and train them for the challenges of graduate-level research in biology and applied mathematics. 


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