As many, I'm troubled by the recent shootings in the US (in Buffalo, NY, and then in Uvalde, TX). My colleagues and I published a paper in 2015 where we found that the occurrence of a mass killing in the US tends to incite subsequent events in the following 1-2 weeks. This is, of course, highly troublesome. And a number of questions arise: Is this pattern generalizable outside of the US? Does it apply to events of a smaller scale (e.g., petty crimes, or singular murders)? With a few caveats, I think the answer to both questions is 'yes'.
The reason mass killings incite subsequent mass killings, we hypothesized in our paper, is because the widespread attention and media reports which spread the news, and promote the ideation for carrying forward further crimes. But the fundamental mechanisms of copying what others do run more deeply in our veins, and we need to rethink how information is reported for crimes such that our inner nature does not promote more crime.
The question about how to report crimes is tightly linked with the question about the motivations behind violent acts. Both phenomena (the reporting of news and the violent act) seek to spread a message. If they both end up sending the same message (explicitly or implicitly, intentionally or unintentionally), they will reinforce each other and will induce contagion. Hence, a critical question to ask is what is the message that criminals (and mass killers in particular) want to spread, and how to report the news in a way that (hopefully) negates the message of the killer.
The psychological and sociological research on the motives of criminals has a long history. For example, we know that the perpetrators of homicides (mass shootings included) usually think their acts were morally justified. The acts are motivated by what the perpetrators perceive were moral transgressions committed to them by the victim (or by some institution or group of people, in the case of mass killings). In the book "Seductions of Crime: Moral and Sensual Attractions in Doing Evil", the sociologist Jack Katz argues that crimes typically originate from moral rage, and are linked with emotions like humiliation, righteousness, arrogance, ridicule, cynicism, defilement, and vengeance.
For these reasons, I think contagion is present in smaller scale events as well. Since (a) most acts of violent crime are moral in nature, (b) moral acts are something that as humans we like to display publicly, and (c) humans have an innate tendency to imitate virtuous displays of morality and be recognized by others for "acting morally", crimes, as a consequence, are all expected to be contagious at least to some extent. This is possibly known by the perpetrators of crimes at a subconscious level, which may explain why researchers have observed that mass murderers tend to also seek fame with their acts. That is, they seek credit for events they think are in the service of a higher moral good. So a recommendation that has emerged from these observations is that these events should be reported, but no information about the killer should be provided (their history, possible motivations, etc). The following are interesting references on this subject: