By Oded Carmeli
“The virus spreads in a geometric progression,” Benjamin Netanyahu declared last week, going on to explain to the lay public what that means: “One person infects two people. Each of them infects two more. The four infect eight, the eight infect 16, the 16 infect 32, the 32 infect 64, the 64 infect 128 – and so on and so forth.”
According to the prime minister’s logic, 100 percent of the Israeli population will become carriers of the coronavirus within a short time. On the other hand, according to that same logic, 100 percent of the population will also come into contact with each other within a short time. Is this really the situation?
“We do not move about in space like particles,” says Dan Yamin, of Tel Aviv University’s industrial engineering department. “Try to remember what you did yesterday. Even without all the social distancing measures, you probably would have met the same people you met today. We move across networks of social contact. So, from a certain stage, it will be difficult to infect even those who bear a potential for becoming infected, because the carriers don’t wander around looking for new people to infect.”
Dr. Yamin is an engineer, not a physician. But in 2008, when he was a graduate student at Ben-Gurion University in Be’er Sheva, a certain research study caught his eye.
“It was an analysis of a dynamic model for the spread of smallpox,” Yamin, 38, says. “The researchers used tools from game theory. It was so interesting that I decided to conduct a similar study on influenza – which turned into a doctoral thesis on disease-spread models.
“If, 40 or 50 years ago, epidemiology researchers came exclusively from the field of medicine, today we understand that in order to predict the spread of diseases, it’s also necessary to understand how humans behave as a collective, to be able to analyze big data and to have the ability to create models and perform mathematical simulations – and for that you need engineers.”
Yamin encountered his first real epidemiological crisis while doing postdoctoral work at the the Center of Infectious Disease Modeling and Analysis at Yale University’s school of public health.
“At Yale we worked for three weeks, with almost no sleep, to create models based on engineering tools for the spread of Ebola. The dilemma of the Liberian health ministry regarded whom to prioritize, given a serious shortage of isolation facilities. The Liberians assumed that it would make more sense to quarantine those who were ill with less serious symptoms, because the others could not be saved in any case.
“We showed that it was precisely the patients with the most acute symptoms who are the most infectious, both because of the high viral load [meaning, the amount of a virus in one’s body] and also because of the increase in the number of encounters between people: The acute patients were dying, so everyone came to take their leave from them,” Yamin says. “I was pleased that Liberia adopted our recommendations and isolated those who were seriously ill. In retrospect, we know that that new policy helped curb the epidemic.”
Yamin currently heads the Laboratory for Epidemic Modeling and Analysis in TAU’s engineering faculty. His primary field of work is development of models for the spread of infectious diseases, with an emphasis on viruses responsible for respiratory ailments, such as flu and RSV (respiratory syncytial virus), which causes bronchitis. He is actually somewhat optimistic about the models he has developed for the spread of the coronavirus, which is also a respiratory disease.
“The big, open question is what the chance is of dying from the virus,” Yamin explains.
“When you ask epidemiologists what the most important datum is concerning a virus, they will say it’s the rate of the basic reproductive ratio, or R0 [often called “R nought”] – the average number of people a sick person will infect. That’s an interesting question, but a theoretical one.
“The R0 of measles is 12, meaning that each person who is ill with measles infects 12 people on average. However, only 5 percent of the population can actually be infected, because most of us have been immunized or had measles in the past. So that is the upper limit of its spread.”
But we know that the R0 of the coronavirus is 2, and we still don’t know whether anyone is naturally immune to the disease.
Yamin: “The overwhelming majority of people are apparently not immune, because it’s not a common disease. After all, there is no precedent for such an infectious and violent type of virus from the corona family, so it’s safe to assume that the majority has not been exposed to the virus before this and that they can be infected. However, that’s not to say that the majority of the population will actually contract the disease.
“The basic principle is that a virus with an R0 of 2 in a non-immune population can be expected to infect 50 percent of the population. After that the R0 will reach a value of 1 or less, and the disease will be contained. By the way, it will recede in a converging exponential; in other words, the coronavirus can be expected to disappear from this region with the same dizzying speed with which it entered our lives.”
But we don’t know for certain whether a person can be infected twice.
“No, but with the majority of viruses, if you’re infected and you have recovered, you won’t be re-infected, because of immunological memory. And if you are infected again, the symptoms will be less acute the second time. The exception to the rule is influenza: Its mutation frequency is so high that you can be infected by it year after year. Last year alone, the flu underwent 17 mutations. Whereas the last time we heard about corona was 17 years ago, with SARS. In other words, the coronavirus did not undergo mutations at the same frequency as the flu. Of course, the mutations themselves are a function of the number of infections: The more infections there are, the greater the likelihood that mutations will occur. But in practice, the most rapid mutations occur in animals, and they only infect us then, and obviously it’s less probable that we will be infected again by a bat in the near future.
