Application of tests for contagion in point processes to measles, Chlamydia, Lyme disease, and suicide

A recently proposed likelihood-ratio test for identifying causal triggering in point process data is applied to a variety of case counts of diseases of varying infectiousness. The test, suggested by McGovern et al. (2025), involves comparing the likelihood of a fitted Hawkes model to that of a fitted Poisson cluster model, and was shown using simulations to be powerful at discriminating between a process with causal triggering and a process where the clustering is merely due to spatial-temporal inhomogeneity. Here, the test is applied to data on measles, Chlamydia, and Lyme disease in the United States, to see if the test can discern between diseases that are highly contagious, moderately contagious, and not directly contagious from human to human. Measles is a highly contagious disease that spreads rapidly through populations, so it can potentially be modeled accurately using a Hawkes model¹². Chlamydia is a sexually transmitted disease that is not as highly contagious as measles since the level of contact needed for exposure is much higher than for measles². Lyme disease is non-contagious from human to human but cases tend to be highly clustered, as the disease is primarily spread through ticks, and this exposure is much more likely to happen during warmer weather¹⁶. Further, the test is applied to data on adolescent suicides in the United States, in order to investigate the hypothesis that such suicides are an epidemic spread by social contagion. The results show that the test is able to measure the degree of contagion of a disease, and the results suggest that there is indeed a small but statistically significant element of contagion to youth suicides.