So, it is fair to say that R0 has an intrinsic value at the beginning of an epidemic when everyone is susceptible, and which depends on the virus itself, local living conditions, and social networks. But even in the same county or country, the rate at which the virus spreads changes with time. Therefore we should think about an effective R0, or Reff, that depends on time and various local conditions. We will discuss how Reff depends on these variables soon, but can the intrinsic value of R0, even in a particular county or nation, be measured accurately?
It is not easy to measure R0 accurately for an epidemic caused by a new virus, as was made vivid in the case of the COVID-19 pandemic. When COVID-19 first began to spread in China, medical authorities did not initially realize that a new virus had emerged. It took some time to isolate the new virus and then to develop a specific test. By this time, basic information about the early stages of the infection was not available. Furthermore, imprecision in estimates of R0 was likely exacerbated because the onset of the epidemic in China coincided with the Lunar New Year, a major holiday there. This accelerated travel (and viral spread) throughout China and encouraged close contact of those infected with their families.
When early efforts to control an epidemic fail, the biggest concerns are that the capacity of the healthcare delivery system will be overwhelmed by the spreading infections and that many people may die. The value of R0 (or Reff) is an important parameter that influences how quickly infections spread, and thus how quickly the number of hospitalized patients and fatalities will grow. In the absence of reliable data, can we estimate the value of R0, and with some assumptions, make useful projections about the future?
Epidemiological Models
Epidemiologists use mathematical models to study how outcomes depend on various scenarios of virus infectivity, nature of local conditions, and policies imposed to mitigate the spread of disease. It is important to understand the essence of these models in order to know what they can and cannot do.
One of the simplest epidemiological models divides the population into four classes of people: (1) those who are susceptible (S) to infection because they are not immune to infection, (2) those who have been exposed (E) to the virus by coming in contact with an infected person, (3) those who progress to infected (I) status after exposure, and (4) those who have recovered (R) from the infection. For all viral infections that we know of, people who recover from a disease are immune for at least some duration. So, it is fair to presume that usually people in the “R” pool are protected from reinfection for a while. These models are called SEIR models for obvious reasons. The essence of these models is to describe the processes shown schematically in the accompanying figure.
The first step describes the rate at which infected people encounter susceptible people and expose them to infection. The second step describes the rate at which exposed people actually become infected. In order to describe how the number of infected people will grow, we need to know the rates at which this sequence of steps occur. The rates depend on the duration of the infectious period and R0. As described above, the latter quantity depends on many factors, such as the social network of people, whether the population under consideration is rural or urban, or whether there was a special event occurring like the Lunar New Year in China or Mardi Gras in New Orleans (super-spreading events). The last step in the process describes the rate at which infected people recover from disease, which depends on the specific viral infection and traits of individual patients.
The various rates required to describe the processes noted above are called the parameters of the model. By knowing or assuming values of the parameters and the number of susceptible, exposed, infected, and recovered people at a particular time point, a well-established mathematical technique called ordinary differential equations can be used to calculate how the number of people in each of these groups will change with time. This is how epidemiological models try to project what the future will look like. Importantly, the parameters required to carry out these calculations are not firmly known for a new virus. R0 is not usually known, and even the number of infected persons at a particular time is not known firmly. This is because without a very rigorous testing infrastructure in place, the number of infected people is difficult to determine. With uncertain values of the parameters, it is difficult to make accurate projections.
Epidemiological models can be made more complicated by adding many additional features that make them more realistic. For example, for COVID-19 one could divide infected people into groups of asymptomatic and symptomatic patients; divide those infected into who requires hospitalization, who does not, and who dies; or stratify the population by age, co-morbidities, geographic location, or other factors. You could also say that the rate at which an asymptomatic infected person transmits the virus is different from a symptomatic one or that patients who are hospitalized take longer to recover. For unknown reasons, some individuals spread the infection to many more than most people. One could try to account for the effects of such super-spreaders, who are characterized by values of Reff that are much higher than the average. Every new feature added to epidemiological models correspondingly requires a new parameter to be specified. So, more complicated models have even more unknown parameters, making projections for future outcomes even more challenging.
Some of the unknown parameters can be estimated by adjusting their values until predictions from the model fit known data. For example, a model could tell us how the daily increase in the number of infected people or those who died changes with time. The parameters can then be adjusted to fit what was really observed for changes in new cases and deaths. As just one example, R0 could be estimated this way. During the early stages of an epidemic, if tests are not readily available, the real-world data are both sparse and noisy. So, the parameters that are estimated in this way are not very accurate. For example, when testing is not widely available, the number of new reported cases is not an accurate reflection of reality. So, one might use only the reported deaths to estimate model parameters as these data are usually more reliable. But the uncertainty in the estimated parameter values is greater if less information is known, just like your answer to a question is less certain if you are given one clue rather than two. So, estimating many parameters accurately by fitting model predictions to match just the known number of deaths is more challenging than if the numbers of both deaths and new infections were reliably known. The more complicated models require estimating more parameters, which makes the estimates even more statistically unreliable. So, the projections that the models make are not numerically accurate. As more data are collected, the parameters are estimated more accurately and the projections get more accurate.
In spite of these challenges, models can be useful for making qualitative projections and estimating the relative effects of different public health measures on mitigating the spread of disease. In particular, models can be used to make projections for how public health measures may affect future hospitalizations and deaths, and the most important factors to control in order to keep these numbers low. This is very useful information for officials and leaders who have to make decisions with limited data during a spreading epidemic.
Effects of Public Health Measures on Mitigating a Spreading Epidemic
Testing, Quarantine, and Contact Tracing
The traditional method of epidemic control is to isolate those who are infected, identify all individuals they contacted, and quarantine them during the infectious period. Contact tracing requires a dedicated team to interview and track down all contacts during the infectious period. For logistical reasons, this is easier to do when the number of infected individuals is low. Therefore, this is a very effective way of epidemic control in the early stages of an epidemic.
Countries that receive some advance warning of a possible pandemic coming to their shores and become very vigilant can be very effective at controlling epidemics early on by extensive testing, quarantine, and contact tracing. During the SARS epid
emic in 2003, early and quick action by authorities isolated those who were infected and identified the people with whom they came in contact. In the Hanoi hospital where Carlo Urbani raised the alarm that a new virus was present, the infection quickly spread to 40 hospital workers. Recognizing that this was a dangerous and infectious virus, the hospital staff locked themselves in to prevent the virus from spreading to the surrounding community. Vietnam closed its borders immediately, and a short six weeks later, with no new infections, Vietnam declared victory over SARS. Similar stories and timetables played out in Hong Kong, Toronto, and Singapore.
The characteristics of the virus that caused SARS helped make it easier to contain. It is a lethal virus, with most patients getting very sick, making it easier to identify those who are infected even without extensive testing. The peak infectious period of SARS-CoV-1 occurs after symptoms begin. Since hospitalization follows quickly after symptoms begin, spread within the community is limited. Hospital workers and close family members are the most vulnerable, and they can be quickly quarantined. The control and eradication of SARS, a virus with an R0 now estimated to be about 3, within a few months of detection, is a powerful example of the effectiveness of isolation, contact tracing, and quarantine. But SARS-CoV-2 has very different characteristics compared with SARS-CoV-1, with many infected persons being asymptomatic and peak infectiousness at or before the onset of symptoms. Can isolation and contact tracing be a useful strategy for a virus like that which caused COVID-19?
Vigilance and quick action in terms of testing, quarantining, and contact tracing allowed some countries to manage the spread of the COVID-19 epidemic well. South Korea, Hong Kong, Vietnam, Taiwan, and Singapore were watching the growing epidemic in China with increasing trepidation. Almost immediately after China’s announcement of an infectious outbreak caused by a new virus, these countries began monitoring the temperature of all passengers arriving on flights from China, especially from Wuhan. South Korea was able to identify its first case of COVID-19 on January 20, 2020, when a passenger from Wuhan arrived at the airport in Korea with fever. This person was isolated, and the country immediately began to ramp up testing nationwide over the next 2 weeks. Hearing this news, Taiwan restricted its borders to China on January 23 and started ramping up testing. Thus, both countries embarked on a program of extensive testing relatively early in the epidemic and then isolating infected persons, which limited the spread of the virus. Quarantine and contact tracing measures reduces the value of Reff quickly. Early on, South Korea reported a value of Reff less than 2 and Taiwan a value less than 1. These values of Reff also reflect that the population of these two countries cooperated with social distancing recommendations.
The situation in the United States was different. That country detected its first case of COVID-19 in Washington State on the same day as South Korea, on January 20, 2020. This patient arrived on a plane from Wuhan a few days earlier, and went to a local clinic on January 19 with cough and fever because he was aware of the epidemic in Wuhan and thought it prudent to seek medical help. He tested negative for influenza, and because he didn’t seem seriously ill, he was sent home while awaiting results of his nasal swab test for SARS-CoV-2 performed by the CDC in Atlanta. After the test came back positive on January 20, he was hospitalized and put into isolation and released two weeks later after clearing the infection. On January 31, 2020, the United States banned incoming travel from China. But US citizens could still enter the country after this date.
Over the next month, about 15 cases were identified sporadically across the United States in addition to 44 infected Americans identified on a cruise ship. In late February, a patient with no history of travel to China or any known exposure to an infected patient tested positive for SARS-CoV-2. This signaled a new stage of the epidemic in the United States. As this person’s infection could not be traced to international travel, they were likely infected by someone in the local community. Epidemiologists call this stage of spreading of an epidemic “community spread.” The CDC initiated a sentinel testing program with the goal of testing patients with mild respiratory illnesses for COVID-19 in six different cities. During the second week of March, 5 percent of patients tested in Chicago were positive for SARS-CoV-2. But a test was still not widely available, as the virus undoubtedly continued to spread. In mid-March, the CDC finally allowed tests other than its own to be used. The lack of widespread testing and contact tracing during the first 8 weeks or more of the epidemic in the United States made it difficult to contain the spread of the virus. Testing, isolation, and contact tracing were no longer possible once the virus started spreading widely.
The situation that prevailed in the United States during the early stages of the COVID-19 epidemic is not unusual for a virus with the characteristics of SARS-CoV-2. Viruses that have high numbers of asymptomatic infections and that can spread before the onset of symptoms are very challenging for public health officials to control. Because asymptomatic patients don’t realize that they are infected, they can be identified only by extensive random testing and tracing all contacts of infected individuals. A long infectious period before the onset of symptoms is also challenging for contact tracing because of the limitations of human memory. It is difficult for people who test positive to remember every person they came in contact with some days ago. Some countries like Israel and Taiwan are using cell phone tracking technology to monitor movements and contacts. This is a potentially powerful approach for contact tracing, but with obvious privacy concerns.
When extensive testing, quarantine, and contact tracing are no longer possible because the virus is spreading rapidly, what other public health measures can be put in place to mitigate the spread of an epidemic caused by a highly infectious virus? The biggest concern at such a time is that the healthcare system may be overwhelmed leading to many unnecessary deaths. For various scenarios regarding hospital capacity, Reff, and other variables, mathematical models can be used to compare the effects of different public health measures. Let us first consider the effects of social distancing, a strategy that was employed by many countries during the COVID-19 pandemic.
Social Distancing Can “Flatten the Curve”
The idea of keeping your distance from a potential infected person is likely as old as humanity. In biblical times, leper colonies were created to isolate lepers from coming in contact with healthy members of the community. As we mentioned earlier, during the bubonic plague in the fourteenth century, without even knowing that microbes caused disease, people fled from Florence to the countryside to wait for the disease to pass. Modern social distancing policies have their origins in the regulations put in place in St. Louis during the 1918 influenza pandemic.
In the summer of 1918, Dr. Max Starkloff, the health commissioner of St. Louis, was monitoring the growing influenza epidemic in Boston and its spread across the continent. In early October, the first cases identified in St. Louis were in a family of seven. The next day, when 50 more cases were identified, Starkloff sprang into action. He urged the mayor of St. Louis to forbid gatherings of large numbers of people and to close movie theaters, churches, pool halls, and concert halls. He also closed the public schools. As the number of cases grew, Starkloff began to restrict business activities. By early November, even though the number of new cases was beginning to stabilize, he moved to close all nonessential businesses, in spite of the emotional objections of the business owners. He may have done this to prevent a massive public gathering for the celebrations planned for November 11 to commemorate the end of World War I. An experiment to ease restrictions in mid-November resulted in a new outbreak of cases in children, and he reimposed strict closures of schools and businesses. As cases declined at the end of December, he gradually eased restrictions and allowed normal life to resume.
The concept of using social distancing as a public health measure was strongly supported by the St. Louis experience, which resulted in a lower fatality rate there compared with other cities during the months of September
1918 to February 1919. An oft-made comparison is with what transpired in Philadelphia. Officials in Philadelphia allowed a parade to be held in September 1918, and imposed strict social distancing measures 17 days after the first cases were reported. Philadelphia’s healthcare system was quickly overwhelmed, and the number of deaths far exceeded that in St. Louis. In general, data across US cities showed that during the 1918 influenza pandemic, US cities that imposed social distancing policies sooner had smaller peak death rates and smaller overall death rates during the first wave of infections. This is because social distancing reduces human contact, thus making Reff smaller. So, the number of infections and deaths is smaller. This is what epidemiologists mean when they say that social distancing is necessary to “flatten the curve.”
The data from the 1918 influenza pandemic showed that imposing social distancing measures early in an epidemic can mitigate the possibility of overwhelming the healthcare system and reduce the number of deaths during the first wave of the epidemic. Many of the measures that were implemented around the world during the COVID-19 pandemic were similar to those that Starkloff put in place in St. Louis in 1918. These measures, which did succeed in flattening the curve in most places, included the following:
1.Encouraging distancing between people, with and without masks
2.Banning of large public gatherings, such as sporting events and concerts
Viruses, Pandemics, and Immunity Page 10