Unfortunately, this is kind of a hard question to answer given its scope and the relative lack of information that we would have regarding "serial killers" in pre-modern history. In a vague, general sense, my answer would be that serial killers a. are never really rampant and b. have probably always been present in similar (if not more) numbers throughout human history. The problem is, prior to the advent of centralized legal systems and equally centralized, formal methods of enforcement of those legal systems, it's relatively hard to find hard and fast examples of serial killers as we would understand them. We know, for example, the identities of a number of serial killers across history starting from the Roman Republic. Some have become famous in their own right, such as Elizabeth Bathory or Gilles de Rais, others not so much. Because of the often suspect legal practices of their times and the politicization of legacies/spread of rumors, the guilt of these individuals is often questioned. A famous example is the aforementioned Gilles de Rais, companion of Joan of Arc and purported child rapist/murderer, whose guilt a number of individuals (including even Aleister Crowley), have questioned throughout history. The Werewolf of Bedburg, Peter Stubbe, provides similar issues, in that he may well have not committed the crimes he was accused of but was instead used as a stand-in by desperate local authorities looking to quell rising tensions among the populace. And these questionable cases are just the ones we know about! Even given the relative lack of population density in places like Europe compared to the modern era, a serial killer in, say, 1400s England could probably have gone relatively unnoticed if he/she was clever enough about choosing victims and committing their murders. Even more difficult to track would be slave owners in slave owning societies, who could, depending on the society (such as ancient Rome), quite easily have preyed on their slaves without very many questions from any sort of authority. If, for example, Roman estate owner Titus Coelius Balbinus buys a lot of slaves for his country villa and some of them go missing under mysterious circumstances, it's doubtful any authority figure is going to follow up on what became of them. In places with even less explicitly recorded history, such as among certain indigenous cultures, the likelihood of us possessing records of the operations of a serial killer are very low. What changes in the modern era is the combination of evolving crime investigation techniques and centralized legal systems, the rise of mass media, and a more interconnected society make it far easier for knowledge of these crimes to be spread. Instead of isolated incidents going relatively undetected, serial killers suddenly become well-reported crimes that gain national or international attention. In short, it's reasonable to assume that there have always been people we would classify as serial killers operating within human societies, but because they are so sparse to begin with as a demographic and our records are equally sparse about them, it's hard to make a definitive judgment on the subject.