“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.
“By the way, viral mutations are more frequent in bats, whose immune system is astonishingly weak, while their social network is extensive and characterized by a lot of interaction.”
So we’re talking about maximum rate of infection – that is, of becoming a carrier – of 50 percent. That’s still a lot of patients, a lot of hospitalizations and mainly a lot of deaths.
“Again, the most interesting issue for decision makers is the mortality rate. When we look at the dry data, we see a very high mortality rate, of 4 to 7 percent, in countries like Italy and Spain, alongside far lower numbers in countries like Germany and South Korea.
“And then there’s China, though it’s very difficult to believe the numbers coming out of there – and in any event no country in the West can allow itself to adopt the measures that China adopted to contain the spread. Now ask yourself: How do you check the mortality rate in all those countries? You take the total number of deaths and divide it by the total of reported patients.”
So the research is biased.
“Very biased. If I can only carry out few tests, I will test those who have the highest chance of becoming ill, and then, when I check the mortality rate among them, I will get very high numbers. But there is one country we can learn from: South Korea. South Korea has been coping with corona for a long time, more than most Western countries, and they lead in the number of tests per capita. Therefore, the official mortality rate there is 0.9 percent. But even in South Korea, not all the infected were tested – most have very mild symptoms.
“The actual number of people who are sick with the virus in South Korea is at least double what’s being reported, so the chance of dying is at least twice as low, standing at about 0.45 percent – very far from the World Health Organization’s [global mortality] figure of 3.4 percent. And that’s already a reason for cautious optimism.”
Let’s move from percents to people.
“Just a minute. Although we’re both Westernized countries, we are absolutely not South Korea. South Korea has one of the highest proportions of elderly people in the world, whereas Israel tops the graph in fertility, and we have a very young population. So, if we use the upper limit [of mortality] of South Korea and normalize the mortality rate for the population in Israel, we are talking about the probability of a mortality rate of 0.3 percent among those who have been infected.
“Now we’ll go to a severe scenario in which no one is immune and every second person is sick, so that the disease is incapable of spreading further – namely, a situation where there’s a maximum infection rate of 50 percent.
“We are a country of nine million citizens. So in the worst-case scenario, we are talking about 4.5 million Israelis who will become ill with the coronavirus. Multiply 4.5 million by 0.3 percent and you get 13,500 Israelis who are liable to die from the disease. By comparison, 700 to 2,500 Israelis die every year of complications from other respiratory ailments.”
But German Chancellor Angela Merkel talked about a rate of infection of 70 percent in Germany.
“And Netanyahu talked about a mortality rate of between 2 percent and 4 percent. And do you know what’s most absurd? That in the final analysis [U.S. President Donald] Trump was right. Not that the coronavirus is just plain flu – it absolutely isn’t – but as he put it: ‘This is just my hunch – way under 1 percent’ [will die].’
“We must be cautious, of course, but at the moment a high probability is emerging that the risks are far lower than what the World Health Organization presented. Under two assumptions – that the health system doesn’t collapse and that life continues as usual – we are not likely to see more than 13,500 victims of the coronavirus in Israel.” (About 45,000 people die in Israel in a normal year, which would make for a rise of approximately one-third.)
But, social distancing should lead to fewer cases of infection and death, no?
“No, because we won’t be able to isolate ourselves completely or forever. At some stage, we will have to resume a regular routine, and then the R0 will stabilize at 2 again. Effectively, we are delaying the inevitable. I have no criticism of the decisions made until now. On the contrary: With such a large area of uncertainty, Israel’s decision makers are considering not only a reasonable scenario but also a margin of safety.
“In my opinion, the Health Ministry deserves tremendous credit for being ahead of the world by having instituted no few measures. In the same breath, the public needs to understand that these measures of social distancing mean that we will find ourselves with corona for a longer period, even to 2023.”
“Take the swine flu, from 2009. Reliable models show clearly that it was contained in Israel because its appearance coincided with the Jewish holidays in the fall [when people weren’t out much in public]. From the virus’ point of view, the timing wasn’t good for it in Israel. By contrast, in the United States there was significant infection in 2009-2010. But in the end, it balances out. So we saw swine flu in Israel both in 2009-10 and in 2010-11, whereas in the United States it just came and went. The American population as a whole was exposed to the virus at high rates, so those who fell ill and recovered served as a ‘human shield’ for those who did not get sick.”
So what you’re saying is to tear the bandage off in one fell swoop, and explose everyone at once, the way they tried to do in Britain.
“We need to make decisions based on the most precise models possible. What should be done? Of course, we must significantly increase testing, using the rapid PCR test, and that is what is actually being done. In parallel, serologic tests should be conducted. These differ from regular tests in that they examines an individual’s immunological reaction to exposure. That’s the only way we will be able to get an accurate picture of the distribution of the virus in Israel, and thereby also of the mortality rates.”
What will that test be able to tell us?
“It will solve the riddle of the young people: It’s still not clear whether young people are infected by the coronavirus but don’t develop symptoms, or are simply immune and thus don’t become infected. This is different from most respiratory ailments. With those illnesses, like RSV or flu, this is a key population: The 5-to-19 age group is not at risk but they are responsible for infecting others.”
Because children don’t wash their hands, and they drool on themselves?
“It’s not only a function of hygiene, it’s mainly a function of contact between people. Picture the average old person. How many different people does he encounter in a day? And what is the nature of those encounters? The older we get, the less we caress and kiss others. Also, children constitute the only age group that comes into contact with all other age groups – not just theirs. That’s why it is the key population in spreading respiratory diseases.”
As soon as we know whether children infect others with corona, we will know whether the schools can be opened.
“Yes. And there are also other potential pockets of infectiousness that can be isolated on a specific basis. In a study based on cellphone data that we conducted in Israel recently on contact networks of flu, we found two locales that are more ‘responsible’ than their relative proportion of the population should be for spreading infectious diseases: Tel Aviv and Petah Tikva.
“Regarding Tel Aviv it’s clear. It’s the hub. A million Israelis enter the city [on a normal] day. The Tel Avivians are like Saudi sheikhs – they just wait for people to come to them. Whereas Petah Tikva is the exact opposite: Everyone flees. But seriously, Petah Tikva is a very diversified city socioeconomically, with a rich mosaic of ultra-Orthodox. Orthodox, secular, poor, rich. That’s what makes it, together with Tel Aviv, a focal point for the spread of respiratory ailments: Petah Tikvans encounter everyone. Whereas, in most places, people tend to meet up with people who are like themselves. I myself live in Ramat Gan. My neighbors are from [the mostly ultra-Orthodox city of] Bnei Brak, but it’s not reasonable to assume that I will be infected by them. [Yamin is not Haredi.] We saw cases of measles [in 2019] in Bnei Brak and Brooklyn of a sort that did not get to Ramat Gan. On the map of viruses, Bnei Brak is closer to Brooklyn than Ramat Gan. So, with a high probability, we can say that our situation is not good – but it’s not apocalyptic.”