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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. (2023), 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 model. 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 measles. 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 weather. 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. 

ABSTRACT Variants of the Epidemic‐Type Aftershock Sequence (ETAS) and Short‐Term Earthquake Probabilities (STEP) models have been used for earthquake forecasting and are entered as forecast models in the purely prospective Collaboratory Study for Earthquake Predictability (CSEP) experiment. Previous analyses have suggested the ETAS model offered the best forecast skill for the first several years of CSEP. Here, we evaluate the prospective forecasting ability of the ETAS and STEP one‐day forecast models for California from 2013 to 2017, using super‐thinned residuals and Voronoi residuals. We find very comparable performance of the two models, with slightly superior performance of the STEP model compared to ETAS according to most metrics. 

Abstract This article reviews some of the statistical issues involved with modeling SARS-CoV02 (Covid-19) in Los Angeles County, California, using Hawkes point process models and SEIR models. The two types of models are compared, and their pros and cons are discussed. We also discuss particular statistical decisions, such as where to place the upper limits on y-axes, and whether to use a Bayesian or frequentist version of the model, how to estimate seroprevalence, and fitting the density of transmission times in the Hawkes model. 

The rate of spread of an emerging epidemic is frequently characterized via the doubling time, which is the time it takes for the number of cases to double. This paper explores different ways to estimate doubling time, and investigates the estimation of doubling time in relationship to parameters in the HawkesN model and the SQUIDER (Susceptible, Quarantine, Undetected Infected, Infected, Dead, Exposed, Recovered) model. We observe an approximately exponential relationship between the productivity parameter κ in the HawkesN model and doubling time. We also evaluate the performance of the models in forecasting doubling times and compare to empirical doubling times using daily reported statewide totals for SARS-CoV-2 infections in California, and find that the HawkesN model forecasts doubling times more accurately, with 3.6% smaller root mean squared errors in Spring 2020, 79.4% smaller root mean squared errors in Autumn 2020, and 5.4% smaller root mean squared errors in Summer 2021. The HawkesN and SQUIDER models appear to forecast daily rate doubling times accurately at most times, though the SQUIDER forecasts of daily rate doubling times are far more volatile and thus occasionally have much larger errors, particularly in Fall 2020. 

We present a fast, accurate estimation method for multivariate Hawkes self-exciting point processes widely used in seismology, criminology, finance and other areas. There are two major ingredients. The first is an analytic derivation of exact maximum likelihood estimates of the nonparametric triggering density. We develop this for the multivariate case and add regularization to improve stability and robustness. The second is a moment-based method for the background rate and triggering matrix estimation, which is extended here for the spatiotemporal case. Our method combines them together in an efficient way, and we prove the consistency of this new approach. Extensive numerical experiments, with synthetic data and real-world social network data, show that our method improves the accuracy, scalability and computational efficiency of prevailing estimation approaches. Moreover, it greatly boosts the performance of Hawkes process-based models on social network reconstruction and helps to understand the spatiotemporal triggering dynamics over social media.