Analyzing gun violence in Milwaukee on yearly and monthly scales reveals periodic fluctuations, indicating both seasonal trends and long-term shifts. Since 2013, incidents have increased, with a significant rise from 2018 to 2021, peaking at 10,793 in 2021. Monthly data show a consistent pattern of higher incidents during summer (June–August) compared to colder months, though variations exist over the years. The data highlights an intensification of gun violence in Milwaukee, particularly over the last 4 years.

To examine gun violence in the context of neighborhood settings, we analyzed incidents categorized by historical redlining grades, creating four distinct time series across Milwaukee (Fig. 2). Each time series corresponds to one of the redlining grades (A, B, C, and D). Using a decomposition method, we further analyzed these time series by breaking them down into three fundamental components: trend, seasonality, and residual noise. The trend component highlights long-term patterns and underlying changes over time, while the seasonal component captures periodic fluctuations, providing insights into recurring patterns. The residual noise component isolates random variations, allowing us to assess the stability of the data. The results of the decomposition, illustrated in the accompanying figure, enable a comparative analysis of the temporal dynamics across neighborhoods with differing redlining grades.

Time series decomposition of gun violence data (2005–2021) across Milwaukee neighborhoods stratified by historical redlining grades (A, B, C, and D). Each panel illustrates the extraction of three components: trend (long-term patterns), seasonality (recurring temporal cycles), and residual noise (stochastic variability). Using computational models, this analysis reveals significant disparities in temporal dynamics associated with historical redlining practices, emphasizing pronounced differences in gun violence trends across neighborhoods with varying grades

Grade A neighborhoods, with a population of 11,734, experienced 840 gun incidents, resulting in a gun violence rate (GVR) of 7158.68 per 100,000. The trend slope, indicating the rate of change in incidents, was 841.64. In grade B, with a population of 55,768, incidents increased to 7436, yielding a GVR of 13,333.81 and a sharper trend slope of 1260.37, indicating a more rapid increase.

The most concerning findings are in grades C and D neighborhoods. Grade C, with a population of 190,827, experienced 37,463 incidents, leading to a GVR of 19,631.92 and a slope of 1523.86. Grade D, with a smaller population of 119,373, reported 22,687 incidents, resulting in a GVR of 19,005.14 and the highest slope of 1677.70 among all grades.

Table 1 demonstrates a progression in slopes from 841.64 to 1677.70, reflecting the increasing incidence and rapid growth of gun violence across HOLC grades. The slope represents the mean annual increase in gun violence rates per 100,000 residents, calculated using least squares regression to provide a comparative measure of grade-specific trends. These findings indicate that neighborhoods graded C and D not only experience higher baseline rates of gun violence but also exhibit steeper upward trends over time. A statistical test for the equality of regression coefficients (Paternoster et al., 1998) confirmed significant differences in slopes across grades, emphasizing the need for targeted, localized interventions to address these disparities effectively.

Figure 3 presents a bivariate map showing the spatial distribution of poor physical and mental health outcomes in Milwaukee (2014–2018) alongside neighborhoods stratified by historical HOLC redlining grades. Neighborhoods classified as grades C and D are represented by the darkest regions, indicating the highest prevalence of these health outcomes. These areas also exhibit the highest gun violence rates (GVRs) and the steepest upward trends in gun violence. The geographic clustering of gun violence and adverse health outcomes underscores the compounded effects of historical redlining policies and socioeconomic disadvantages in these neighborhoods.

A bivariate map that visualizes the geographic areas where both poor mental and physical health outcomes overlap in Milwaukee (2014–2018). This map highlights regions where these health issues are concentrated, emphasizing the compounded impact on community well-being

Gun violence incidents aggregated at the census tract level showed a statistically significant upward trend (p < 0.01) across most neighborhoods (Fig. 4). The Mann–Kendall (MK) test [28] indicated a widespread increase in gun violence, reflecting a notable escalation in incident frequency over time.

Spatial trends in gun violence across Milwaukee (2005–2021) Census tracts are classified using the Mann–Kendall trend test to detect statistically significant changes in gun violence over time. Purple shades indicateincreasing trends, green shades represent decreasing trends, and white areas show no significant change. This map reveals persistent spatial inequalities in violence trajectories across the city

The analysis revealed seven distinct spatiotemporal patterns of gun violence in Milwaukee: consecutive hot spots, new hot spots, sporadic hot spots, oscillating hot spots, persistent cold spots, diminishing cold spots, and historical cold spots. Each pattern corresponds to specific socioeconomic and demographic conditions, highlighting areas that may require tailored interventions, resource allocation, and targeted crime-prevention strategies.

As shown in Table 2, the hot spot zones with consistently high gun violence rates highlight significant socioeconomic challenges. These areas have a median household income of $35,666.28, with 31% of residents living in poverty. Health issues are prevalent, with 17.28% of the population reporting poor physical health and 19.28% experiencing mental health problems. The population is diverse, with a significant African American presence.

Regarding employment and education, 38.46% of residents are full-time, and 8.64% have attained higher education. Recent new hot spots, with increased gun violence, exhibit a median income of $37,197.63 and a high poverty rate of 36.61%, within a racially diverse area where Whites, African Americans, and Hispanics account for 54.48%, 31.54%, and 19.82% respectively. Oscillating hot spots, with fluctuating gun violence, show a median income slightly above Milwaukee’s average. In contrast, sporadic hot spots, characterized by irregular gun violence surges and a predominantly African American population, have the lowest median income and a poverty rate of 33.58%.

Contrastingly, historical cold spot regions, characterized by fewer gun violence incidents, exhibit a more prosperous socioeconomic profile, with a median income of $51,253.38 and an 18.55% poverty rate. These areas are predominantly White (80.75%), with healthier employment (56.84%) and higher education attainment (31.08%). Persistent cold spots represent the city’s affluent enclaves, boasting the highest median income at $62,871.97 and a 14.10% poverty rate.

An examination of gun violence (rate per 1000 persons) alongside poor mental health (percentage of adults reporting ≥ 14 days of poor mental health in the past month) revealed distinct spatial correlations (Fig. 5). Overall, the findings indicate that neighborhood-level mental health challenges and gun violence rates are related, though the form and strength of this relationship vary across Milwaukee.

The spatial relationship between gun violence and the prevalence of poor mental health in Milwaukee (2014–2018). a Gun violence hotspots. b Areas with high prevalence of poor mental health. c The local correlation, revealing mostly positive linear relationships with more complex interactions in central areas

The analysis identified five relationship types between gun violence and mental health indicators: not significant, positive linear, concave, convex, and undefined complex. A “Not Significant” relationship indicates no statistically valid association, while a “Positive Linear” relationship shows that increased mental health challenges correspond with higher gun violence incidents. The “Concave” and “Convex” relationships reflect downward and upward curving connections, respectively, as mental health challenges rise. The “Undefined Complex” relationship reveals a significant correlation but does not fit the other patterns.

Most areas exhibited a positive linear or concave relationship between mental health challenges and gun-related incidents, indicating that as mental health challenges increase, gun violence also rises. However, central city neighborhoods, with the highest prevalence of poor mental health and gun violence, showed a more complex relationship that warrants further investigation. These areas, with a median income of $25,204.33, a poverty rate of 41.83%, and 61.61% African American residents, reported 21.70% poor mental health and only 5.85% with a bachelor’s degree or higher.

Areas with a positive linear trend had a higher median household income ($50,065.16) and lower poverty rate (21.07%), with a demographic composition of 58.47% Whites and 25.74% African Americans. Poor mental health was reported by 16.47%, the full-time employment rate was 49.49%, and 18.36% held a bachelor’s degree or higher. In contrast, areas with a concave relationship had a median household income of $42,999.10 and a poverty rate of 32%. These areas were evenly split between Whites (43.24%) and African Americans (45.12%). Poor mental health affected 18.07%, with 43.16% employed full-time and 18.42% holding a bachelor’s degree or higher.

The interplay of gun violence and mental health in Milwaukee is shaped by unique socioeconomic factors, necessitating targeted interventions and policies.