In the third week of February, as the COVID-19 epidemic was still flaring in China, I arrived in Kolkata, India. I woke up to a sweltering morning—the black kites outside my hotel room were circling upward, lifted by the warming currents of air—and I went to visit a shrine to the goddess Shitala. Her name means “the cool one”; as the myth has it, she arose from the cold ashes of a sacrificial fire. The heat that she is supposed to diffuse is not just the fury of summer that hits the city in mid-June but also the inner heat of inflammation. She is meant to protect children from smallpox, heal the pain of those who contract it, and dampen the fury of a pox epidemic.

The shrine was a small structure within a temple a few blocks from Kolkata Medical College. Inside, there was a figurine of the goddess, sitting on a donkey and carrying her jar of cooling liquid—the way she has been depicted for a millennium. The temple was two hundred and fifty years old, the attendant informed me. That would date it to around the time when accounts first appeared of a mysterious sect of Brahmans wandering up and down the Gangetic plain to popularize the practice of tika, an early effort at inoculation. This involved taking matter from a smallpox patient’s pustule—a snake pit of live virus—and applying it to the pricked skin of an uninfected person, then covering the spot with a linen rag.

The Indian practitioners of tika had likely learned it from Arabic physicians, who had learned it from the Chinese. As early as 1100, medical healers in China had realized that those who survived smallpox did not catch the illness again (survivors of the disease were enlisted to take care of new victims), and inferred that the exposure of the body to an illness protected it from future instances of that illness. Chinese doctors would grind smallpox scabs into a powder and insufflate it into a child’s nostril with a long silver pipe.

Vaccination with live virus was a tightrope walk: if the amount of viral inoculum in the powder was too great, the child would succumb to a full-fledged version of the disease—a disaster that occurred perhaps one in a hundred times. If all went well, the child would have a mild experience of the disease, and be immunized for life. By the seventeen-hundreds, the practice had spread throughout the Arab world. In the seventeen-sixties, women in Sudan practiced tishteree el jidderee (“buying the pox”): one mother haggling with another over how many of a sick child’s ripe pustules she would buy for her own son or daughter. It was an exquisitely measured art: the most astute traditional healers recognized the lesions that were likely to yield just enough viral material, but not too much. The European name for the disease, variola, comes from the Latin for “spotted” or “pimpled.” The process of immunizing against the pox was called “variolation.”

Lady Mary Wortley Montagu, the wife of the British Ambassador to Constantinople, had herself been stricken by the disease, in 1715, leaving her perfect skin pitted with scars. Later, in the Turkish countryside, she witnessed the practice of variolation, and wrote to her friends in wonder, describing the work of one specialist: “The old woman comes with a nut-shell full of the matter of the best sort of small-pox, and asks what vein you please to have opened,” whereupon she “puts into the vein as much matter as can lie upon the head of her needle.” Patients retired to bed for a couple of days with a fever, and, Lady Montagu noted, emerged remarkably unscathed. “They have very rarely above twenty or thirty in their faces, which never mark; and in eight days’ time they are as well as before their illness.” She reported that thousands safely underwent the operation every year, and that the disease had largely been contained in the region. “You may believe I am well satisfied of the safety of this experiment,” she added, “since I intend to try it on my dear little son.” Her son never got the pox.

In the centuries since Lady Montagu marvelled at the efficacy of inoculation, we’ve made unimaginable discoveries in the biology and epidemiology of infectious disease, and yet the COVID-19 pandemic poses no shortage of puzzles. Why did it spread like wildfire in Italy, thousands of miles from its initial epicenter, in Wuhan, while India appears so far to have largely been spared? What animal species transmitted the original infection to humans?

But three questions deserve particular attention, because their answers could change the way we isolate, treat, and manage patients. First, what can we learn about the “dose-response curve” for the initial infection—that is, can we quantify the increase in the risk of infection as people are exposed to higher doses of the virus? Second, is there a relationship between that initial “dose” of virus and the severity of the disease—that is, does more exposure result in graver illness? And, third, are there quantitative measures of how the virus behaves in infected patients (e.g., the peak of your body’s viral load, the patterns of its rise and fall) that predict the severity of their illness and how infectious they are to others? So far, in the early phases of the COVID-19 pandemic, we have been measuring the spread of the virus across people. As the pace of the pandemic escalates, we also need to start measuring the virus within people.

Most epidemiologists, given the paucity of data, have been forced to model the spread of the new coronavirus as if it were a binary phenomenon: individuals are either exposed or unexposed, infected or uninfected, symptomatic patients or asymptomatic carriers. Recently, the Washington Post published a particularly striking online simulation, in which people in a city were depicted as dots moving freely in space—uninfected ones in gray, infected ones in red (then shifting to pink, as immunity was acquired). Each time a red dot touched a gray dot, the infection was transmitted. With no intervention, the whole field of dots steadily turned from gray to red. Social distancing and isolation kept the dots from knocking into one another, and slowed the spread of red across the screen.

This was a bird’s-eye view of a virus radiating through a population, seen as an “on-off” phenomenon. The doctor and medical researcher in me—as a graduate student, I was trained in viral immunology—wanted to know what was going on within the dots. How much virus was in that red dot? How fast was it replicating in this dot? How was the exposure—the “touch time”—related to the chance of transmission? How long did a red dot remain red—that is, how did an individual’s infectiousness change over time? And what was the severity of disease in each case?

What we’ve learned about other viruses—including the ones that cause AIDS, SARS, and smallpox—suggests a more complex view of the disease, its rate of progression, and strategies for containment. In the nineteen-nineties, as researchers learned to measure how much H.I.V. was in a patient’s blood, a distinct pattern emerged. After an infection, the virus count in the blood would rise to a zenith, known as “peak viremia,” and patients with the highest peak viremia typically became sicker sooner; they were least able to resist the virus. Even more predictive than the peak viral load was the so-called set point—the level at which someone’s virus count settled after its initial peak. It represented a dynamic equilibrium that was reached between the virus and its human host. People with a high set point tended to progress more rapidly to AIDS; people with a low set point frequently proved to be “slow progressors.” The viral load—a continuum, not a binary value—helped predict the nature, course, and transmissibility of the disease. To be sure, every virus has its own personality, and H.I.V. has traits that make viral load especially revealing: it causes a chronic infection, and one that specifically targets cells of the immune system. Yet similar patterns have been observed with other viruses.