In the 18th century New York City faced many health problems, yellow fever and smallpox epidemics specifically. Tottenville was mainly country, not as open to the conditions in Manhattan at the time. My research so far hasn’t found any information specifically to Tottenville, but I would think there must have been some impact, especially in the latter half of the century with all the British stationed on Staten Island during the Revolutionary War.

Yellow Fever

Yellow fever is a viral disease spread through mosquito bites. It got this name from the yellowed appearance of the skin and eyes caused from the built-up toxins in the body from damage to the liver. After contracting yellow fever some people develop even more serious illnesses that lead to bleeding, shock, organ failure, and sometimes death.

In 1702 a Yellow Fever outbreak caused 570 deaths. From 1743 to 1745 there was another Yellow Fever epidemic. At the time a correlation with dockyard areas was noted, but mosquitos causing it was not known.

“The press was reluctant to publish the extent of yellow fever due to fears of people leaving the city and the economy suffering. New Yorkers falsely believed the disease was not contagious, and by 1798, the dispersion of yellow fever had reached epidemic proportions claiming the lives of thousands. Various efforts were made to clean up certain neighborhoods most widely affected by the disease, but other than quarantining infected ships, the newly formed health department did little to prevent the sickness from spreading.”

https://www.mcny.org/story/germ-city-epidemics-throughout-new-yorks-history?gclid=CjwKCAjwldHsBRAoEiwAd0JybRaVjvSwnJF0W3SDi--sPNnluzoTZGr8POB2Xd4JKzF5U1TlJ8royRoCFBcQAvD_BwE

Smallpox

Smallpox is an airborne disease, with the tendency to spread the smallpox virus quickly, with the added chance of infection from contaminated clothing or bedding. 

In 1731 during a 3-month smallpox epidemic hundreds died with another 549 dying in 1732.

Benjamin Franklin’s four-year-old son, Francis Folger Franklin, died of smallpox on November 21, 1736.

“In 1736 I lost one of my Sons, a fine Boy of 4 Years old, taken by the Small Pox in the common way. I long regretted that I had not given it to him by Inoculation, which I mention for the Sake of Parents, who omit that Operation on the Supposition that they should never forgive themselves if a Child died under it; my Example showing that the Regret may be the same either way, and that therefore the safer should be chosen.”~ Benjamin Franklin, quoted in Franklin on Franklin by Paul Zall

In 1746 there was another outbreak of smallpox.

In 1759 the information about inoculation began to circulate through the free distribution of pamphlets.

“At the suggestion of his friend Benjamin Franklin, English physician William Heberden wrote a pamphlet called "Some Account of the Success of Inoculation for the Small-Pox in England and America: Together with Plain Instructions By which any Person may be enabled to perform the Operation and conduct the Patient through the Distemper." https://www.historyofvaccines.org/timeline/all?timeline_categories[]=49

In 1775 smallpox was a factor during the Revolutionary War.

“George Washington’s siege of Boston was complicated by smallpox infection inside the city. British troops occupying Boston had been variolated or exposed to smallpox in the past. But Washington’s Continental Army troops were more vulnerable. Most had never been exposed to smallpox and were not previously variolated. Washington himself had survived a case of smallpox while on the island of Barbados in 1751.” https://www.historyofvaccines.org/timeline/all

In 1777 “George Washington, commander-in-chief of the Continental Army, based at his headquarters in Morristown, New Jersey, ordered mandatory inoculation for troops if they had not survived a smallpox infection earlier in life—possibly in reaction to the inability of Benedict Arnold’s troops to capture Quebec from Britain the year before, when more than half of the colonial troops had smallpox. Recruits passing through Virginia were inoculated at Alexandria.” https://www.historyofvaccines.org/timeline/all

Washington Inoculates an Army https://www.battlefields.org/learn/articles/washington-inoculates-army