Luck.

Yersinia pestis is an Asian-origin disease. It spread west and created an outbreak in 541AD in Constantinople, then the plague happened about 800 years later in the worst epidemic in recorded history, in which a port city controlled by Venice, named Ragusa, would begin keeping all sailors on a road just outside town or on an unsettled island near the town for 30 days, "trentino." Later it was increased to 40, "quarantino" which gives us the term quarantine. This helped, and a lot, though Ragusa would still see outbreaks in the 14th century.

In 1665 there was another major outbreak, this time in London. It would likely have reached America, but officials took action resluting in sheltering/quantining people, slaughtering animals, no funeral services and graves away from people/churches, burning of furniture, etc. Parliment moved to Oxford. Wealthy elite and anyone with money (like lawyers and physians) fled to the countryside. As recorded in the National Archives of the United Kingdom, in 1666 King Charles II issued the following orders;

RULES AND ORDERS

To be observed by all Justices of Peace, Mayors, Bayliffs, and other Officers, for prevention of the spreading of the Infection of the PLAGUE.

Published by His Majesties Special Command.[Orders 1-5 say that no stranger was allowed to enter a town unless they had a certificate of health. No furniture was to be removed from an infected house. There were to be no public gatherings such as funerals and all houses were to be kept clean.]

… …

(6). That Fires in moveable Pans, or otherwise, be made in all necessary publique [public] Meetings in Churches, &c. and convenient Fumes to correct the Air be burnt thereon.

(7). That care be taken that no unwholsom Meats, stinking Fish, Flesh, musty Corn, or any other unwholesome Food be exposed to sale in any Shops or Markets.

(8). That no Swine, Dogs, Cats or tame Pigeons be permitted to pass up and down in Streets, or from house to house, in places Infected.

(9). That the Laws against Inn-Mates be forthwith put in strict execution, and that no more Alehouses be Licensed then are absolutely necessary in each City or place, especially during the continuance of this present Contagion.

(10). That each City and Town forthwith provide some convenient place remote from the same, where a pest-house, huts, or sheds may be erected, to be in readiness in case any Infection should break out; which if it shall happen to do, That able and faithful Searchers and Examiners be forthwith provided and Sworn to Search all suspected bodies, for the usual signs of the plague, viz. Swellings or Risings under the Ears or Arm-pits, or upon the Groynes [groin]; Blains, Carbuncles, or little Spots, either on the Breast or back, commonly called Tokens.

(11). That if any House be Infected, the sick person or persons be forthwith removed to the said pest-house, sheds, or huts, for the preservation of the rest of the Family: And that such house (though none be dead therein) be shut up for fourty days, and have a Red Cross, and Lord have mercy upon us, in Capital Letters affixed on the door, and Warders appointed, as well to find them necessaries, as to keep them from conversing with the sound.

(12). That at the opening of each Infected house (after the expiration of the said Fourty Days) a White Cross be affixed on the said door, there to remain Twenty days more; during which time, or at least before any stranger be suffered to lodge therein, That the said house be well Fumed, Washed and Whited all over within with Lime; And that no Clothes, or Householdstuff be removed out of the said house into any other house, for at least Three months after, unless the persons so Infected have occasion to change their habitation.

(13). That none dying of the Plague be buried in Churches, or Church-yards (unless they be large, and then to have a place assigned for that use (where other bodies are not usually buried) Boarded or Paled in Ten foot high) but in some other convenient places, and that a good quantity of unslakt Lime be put into the Graves with such bodies, and that such Graves be not after opened within the space of a year or more, less they infect others.

(14). That in case any City, Burrough, Town or Village be so visited and Infected, that it is not able to maintain its own poor, That then a Rate be forthwith made by the adjoining Justices of the Peace, and confirmed at the very next Quarter Sessions, for that use, upon the neighbouring Parishes, according to the Statute 1 Jacobi [James 1], so that such visited poor may have sufficient Relief; want and nastiness being great occasions of the Infection.

(15). That you your selves use your utmost endeavours, not only to see these Directions punctually observed, and be in a readiness to render an Accomt [Account] as often as you shall be required, but that you strictly enjoyn all high Constables, petty Constables, Headburroughs and other Officers, to execute their respective Duties according to their places; and if any shall fail herein, to use the utmost severity against them according to Law.

What relates to Physitians, Chysurgeons, and such other persons as are necessary for the preservation and help of such who shall be Infected, the same is left to your particular care and direction.

Lastly, That you take special care, that not onely [only] the Monethly Fasts, but that the publique prayers on Wednesdays and Fridays also, be strictly and constantly observed according to his Majesties Proclamation; And that such Collections as shall be then made, be strictly applied to the relief and necessities of the poor in Infected places, by which means God may be inclined to remove his severe hand both from amongst you and us.

Then in September of 1666, over 13,000 London homes burned in the Great Fire that impacted the old city inside the Roman walls. Historians disagree as to the impact this had; while it certainly cleansed the city of thousands of rats and fleas, it left the largest and poorest slums of London untouched by flames. For whatever cause, the plague stopped just before it became inevitably spread to the new world.

What the rats likely did bring was leptospirosis, a strong case for which was made in New Hypothesis for Cause of Epidemic among Native Americans, New England, 1616–1619 by John S. Marr and John T. Cathey;

In the years before English settlers established the Plymouth colony (1616–1619), most Native Americans living on the southeastern coast of present-day Massachusetts died from a mysterious disease. Classic explanations have included yellow fever, smallpox, and plague. Chickenpox and trichinosis are among more recent proposals. We suggest an additional candidate: leptospirosis complicated by Weil syndrome.

It is estimated as many as 9 in 10 in impacted coastal tribes, like Tisquantum's home village Patuxet, died. He himself would even die from "Indian fever" but not until after returning from a trip to England. While it wasn't yersinia pestis, in the end the result was the same for them.