## Typhoid Mary within a Contact Network

Mary Mallon immigrated to New York City from Ireland in the early 1880’s. During her early years in the city, she worked as a cook in nine families, eight of which contracted typhoid. A sanitary engineer investigated these cases and traced their origin back to Mary Mallon, who quickly earned the nickname “Typhoid Mary.” She was a healthy carrier of Salmonella typhiv, also known as typhoid.

Mallon’s job as a cook put her in contact with many people, though the process of cooking her food typically killed all pathogens. However, her signature dish was Peach Melba, made of fresh peaches and ice cream, which quickly infected the families for whom she worked. The health department analyzed the situation and the threat that Mary posed. During the year 1907, when the investigation was taking place, 3,000 New Yorkers contracted typhoid and Typhoid Mary was likely the main contributor to the outbreak.

At the time, there was no immunization or treatment and about 10% of cases were fatal. The problem posed by Mary Mallon could not be ignored. To understand the best solution available at the time, consider the following model.

We will use the general model R0 = pk, where p is the probability that the disease transmits at each contact point, k is the number of people that each person comes into contact with, and pk is the expected number of new cases that are caused by one existing case. If R0 > 1 the disease persists indefinitely, but if R0 < 1 the disease dies off in a finite number of steps. Therefore the goal of the sanitation engineers at the time was to achieve R0 < 1.

Since the health department wished to cut the spread of the disease off at patient zero, we will limit our focus to Typhoid Mary herself. As a cook who specialized in serving raw fruit, the chances of transmission were high. Eight out of nine families she worked for experienced cases of typhoid, and one report claimed that half of the members in a given family became ill. So for simplicity sake, let’s say that p = (8/9) (1/2) = (4/9). One outbreak occurred in the Warren household, which held about twelve people. Taking this to be a typical house size during this time, including servants, cooks, and family members, Mary came into contact with approximately 108 people while working as a cook, so let’s say that k=108. When we calculate R0 based on Mary’s history, we find that R0 is somewhere on the order of 48.

In order to lower R0 below 1, the sanitation engineers could lower p, k, or both. The initial solution was to lower p and k drastically by quarantining Mary on North Brother Island. There, she was no longer a cook, which drastically lowered the chances of transmission (p), and she came into contact with only a few doctors, dropping k nearly to zero. This lowered R0 below 1 and temporarily slowed the spread of the epidemic.

Mary Mallon, however, was not content to remain confined on her island. As a healthy carrier, she never experienced any symptoms and felt she had been unjustly accused of spreading illness through her cooking. She tried in vain to sue the health department in 1909, but in 1910 a new health commissioner joined the health department and decided to return Mary Mallon to the city. The health department released her on the strict orders that she was not to serve as a cook ever again because of the threat she posed.

Mary took a job as a laundress and was under the constant supervision of the health department for some time. The goal was not to limit k but to keep p as low as possible. The health department eventually ceased to supervise her. However, five years later, there was an outbreak of typhoid at a maternity hospital and the health department found Mary Mallon working in the kitchens. Some research revealed that Mary had been working in the kitchens at a variety of restaurants and inns since her release from quarantine.

These incidents made it clear that it was impossible for the health department to only lower the probability (p) of spread outward from Mary because of her refusal to cooperate. Therefore the only way to control the spread was to quarantine her again, effectively lowering p and k to a minimum. She remained on North Brother Island until her death. In total, she spent twenty-six years of her life in isolation on the island.

Around this time, many other healthy carriers of typhoid were identified throughout the city. All carriers who worked as cooks were banned from cooking; some listened but others, like Mary Mallon, did not. The health department relied on reducing p in these cases rather than reducing k. Nobody besides Typhoid Mary was quarantined.