One may not always equate disease with natural disasters, other examples being earthquakes or hurricanes, but they are part of the history of people and communities and they are a product of nature, in these cases a most virulent kind that does not involve the destruction of property.
The world does not see epidemics of the scope that existed before the discovery of vaccines or development of modern hygiene practices. But even into the 20th century, in many regions where our ancestors lived, communities were often attacked by diseases. If you want to count the types and numbers of epidemics that we know about just in recorded history, there is a list on Wikipedia (List of Epidemics).
Very commonly in past centuries, smallpox, cholera, influenza and plague killed thousands of people, sometimes millions, before they were checked or ran out of steam. Today most are confined to less-well developed regions of the world, where living conditions are poor and good hygiene virtually non-existent. In developed countries we have learned how to control or eradicate most of them through maintaining ourselves in better health and with inoculations. We still see small pockets of sicknesses we thought we had rid ourselves of in areas where people have determined they do not need vaccines, but thankfully they are small in number.
Family historians will undoubtedly come across examples in their own families where ancestors contracted and even died of diseases we don’t hear much about any more. I wrote about the Scourge of Phthisis (Tuberculosis) in 2015 and how it had killed great-grandmothers of my wife and me. I have come across references to this particular malady in many records.
I know that the main community in which my Shepheard ancestors lived – Cornwood, Devon, England – according to the church burial register, was visited by cholera, measles, typhus, smallpox and whooping cough. These were recorded only by two incumbents in two periods between 1770-1772 and 1799-1823. We do not have causes of death in church records for the other years between 1685 and 1993 but can reasonably surmise that, at least in the early centuries, disease was also a factor in the deaths of residents. A high proportion of the deaths in this area, prior to the 20th century, were children and infants as I described in a post title Trends in Ages of Death in Cornwood Parish, Devon in 2015.
One of the last major epidemics in modern times was the Spanish Flu in 1918-20. Estimates put the death toll between 75 million world-wide. Not since the Plague of Justinian in 541-545 (25-50 million, 40% of population) or the Black Death in 1346-50 (75-200 million, 30-60% of population), has the number been so high. Hundreds of thousands more died during the Great Plague of the 1660s. Early European explorers brought diseases with them to foreign shores, unleashing devastating results to indigenes populations, completely eradicating many communities. While this was not strictly caused by only natural conditions, the result was the same.
Not all death or burial records indicate what the causes of death were. In the case of many people, especially children dying within a short period it may be useful too look at whether disease was the reason. Information about those events may be found in newspapers or other historical publications.
Disease, particularly when widespread is no less a disaster than an earthquake or hurricane. While not caused by geologic or atmospheric processes it is still a part of nature.