# Uncovering the impact of randomness in HIV hotspot formation: A mathematical modeling study

## TL;DR

This study shows that random early events in the HIV epidemic can create long-lasting hotspots, especially in small communities, which has implications for public health strategies.

## Contribution

The study introduces a novel mathematical model showing how early random fluctuations drive the formation and persistence of HIV hotspots in small communities.

## Key findings

- Smaller communities are more likely to become HIV prevalence outliers due to early random fluctuations.
- Outliers in small communities can persist over time due to feedback between incidence and prevalence.
- Larger communities require additional factors beyond randomness to form HIV hotspots.

## Abstract

HIV hotspots, regions with higher prevalence than surrounding areas, are observed across Africa, yet their formation and persistence mechanisms remain poorly understood. We hypothesized that random fluctuations during the early stages of the HIV epidemic (1978–1982), amplified by positive feedback between HIV incidence and prevalence, play a critical role in hotspot formation and persistence. To explore this, we applied a network-based HIV transmission model, focusing on randomness in the spatial structure of the epidemic.

We adapted a previously validated agent-based network HIV transmission model, EMOD-HIV, to simulate HIV spread in western Kenya communities. The model includes demographics, age-structured social networks, and HIV transmission, prevention, and treatment. We simulated 250 identical communities, introducing stochastic fluctuations in network structure and case importation. Outliers were defined as communities with prevalence > 1.5x the median, and persistence as meeting these criteria for >70% of 1980–2050. We systematically varied community size (1,000–10,000), importation timing (1978–1982), and importation patterns (spread over 1, 3, or 5 years), and calculated the proportion of outliers and persistent outliers.

HIV prevalence outliers were more common in smaller communities: in 1990, 25.3% (uncertainty interval: 22.3%–28.2%) of 1,000-person communities vs. 9.1% (uncertainty interval: 6.9%–11.4%) of 10,000-person communities. By 2050, 21.6% of 1,000-person communities were persistent outliers, compared to none in larger communities. Autocorrelation of HIV prevalence was high (Pearson’s correlation coefficient 0.801 [95% CI: 0.796–0.806] for 1,000-person communities), reflecting feedback that amplified early fluctuations.

Early random fluctuations contribute to the emergence and persistence of prevalence outliers, especially in smaller communities. Recognizing the role of randomness in prevalence outlier formation in these settings is crucial for refining HIV control strategies, as traditional methods may overlook these areas. Adaptive surveillance systems can enhance detection and intervention efforts for HIV and future pandemics.

In this study, we explored how random events early in the HIV epidemic may have contributed to the formation of HIV prevalence outliers. Using a simulation model of HIV spread in communities in western Kenya, we introduced random variations in the initial spread of the disease and examined how these fluctuations affected infection patterns over time. We found that community-level prevalence exceeding 1.5 times the median could emerge through random variations in an appreciable fraction of small communities, and that outliers were more likely to persist over time in such settings. In contrast, larger communities appeared to need additional factors beyond random chance for outliers to form. Our findings suggest that random fluctuations can influence the development of HIV prevalence outliers, especially in smaller communities. Recognizing this could enhance public health strategies by encouraging more detailed monitoring of HIV in vulnerable areas. By understanding the role of randomness, we can refine approaches to detecting and controlling the spread of HIV and other infectious diseases in the future.