COVID-19 The Evolution of a Pandemic
Lockdowns, quarantines, and measures of social distancing have become the new normal as the world makes a concerted effort to stop the spread of COVID-19. How did a virus originating in Wuhan, China evolve from a local outbreak, into a regional epidemic, and finally into a global pandemic? Furthermore, how can we expect the pattern of infections to continue to develop?
To understand the initial acceleration of the outbreak and how it will progressively evolve over time, it is first necessary to understand some important epidemiologic concepts. The reproductive rate, represented by R0 and pronounced as R-naught or R-zero, describes the speed in which an unmitigated infection spreads throughout a community. R0 is measured by the number of person-to-person transmissions that occur from each infected individual. For example, if an infectious agent has an R0 of 2, it means that every infected person will transmit the infection to 2 other people, these 2 newly infected people will each transmit to 2 more, and this pattern of spread will continue. Based on this definition, it becomes clear that R0 describes the speed of the infections and the higher the R0, the faster the transmission rate. Figure 1 displays two different patterns of person-to-person infection spreads.
Figure 1. Comparing reproductive rates: The person-to-person spread of an infection.
COVID-19 is thought to have an R0 of about 2.5. For comparison, the H1N1 swine flu virus had an R0 of about 1.5. Figure 2 illustrates the impact of R0 with respect to a community-based infection spread. The difference between the two cases is dramatic. With only a 1-point higher R0, the COVID-like infection can affect an entire community of thousands of people, while the H1N1-like disease affects far fewer within the same span of days.
Figure 2. Comparing reproductive rates: The community spread of an infection.
It is important to note that the R0 of an infection typically does not remain constant. That is, R0 will evolve over time due to various factors such as weather, available vaccinations, and social distancing. In the early stages of a pandemic, an infection’s R0 will be at its peak. This means that infections will spread most rapidly because the aforementioned factors have not yet played a role. Because of COVID-19’s high unmitigated R0, the number of new infections began rising at an exponential pace.
As community methods of control are implemented, R0 will begin to decline and this will affect the pattern of new infections. When R0 is lowered to 1, meaning that, on average, each person transmits the virus to 1 other person, the number of new daily infections will become constant. This will change the pattern of new infections and cause the number to rise linearly instead of exponentially. A sign that the spread of the pandemic is slowing is the straightening of the curve of the number of new daily infections. The inflection point is the time in which the curve turns from a convex (upward) to a concave (downward) curvature.
To ultimately contain a pandemic, R0 must be brought down to less than 1. Without an available vaccine, this can be done by other methods such as physical separation and sanitation. Communities that strictly practice these methods of control can reduce the speed of the pandemic as was proven in various countries (e.g. China and South Korea) when COVID-19 initially began to surface. Figure 3 illustrates the general pattern of outbreak data.
Figure 3. The evolution of daily infection rates.
The number of new daily infections, as reported, is most likely inaccurate. There are several reasons for that, most notably, it reflects only those who were tested because they may have passed the criteria required for testing. Another reason is the lag between the time of the transmission and the time that the test returned a positive result. These reasons all suggest that in the early phase of a pandemic, the number of new daily infections markedly under-estimates the true rate, especially when the pandemic is like COVID-19 and has a high unmitigated R0. On the other hand, when the rate of infections is slowing down, the number of new daily infections tends to overestimate the true rate. This is important to understand because it means that when an inflection point is observed, the actual inflection may have already occurred.
The inflection point can be estimated to help predict when the number of new cases will begin to decline. Because the inflection point indicates a change in the pattern (the number of cases is still rising, but not as dramatically), the knowledge of when it occurs can translate into the knowledge that a decrease in cases should follow shortly. Our strategy for estimating the inflection point is based on a statistical model to eliminate the variability in the reported numbers. We estimate the slope of the curve of new infections with a statistical regression that models a group of 5 daily points at a time. We compare these slopes sequentially until several successive slopes show a reduction in trend. Once an inflection point has been identified, we then develop a statistical model to incorporate the day-to-day variability and project the future number of new daily infections.
Italy: A Case Study
Throughout March, Italy had been the epicenter of the Covid-19 pandemic in Europe. After exhibiting an explosion of new cases, the country has implemented various containment methods which are helping to curb the growth of new infections. Analysis of the data suggests that an inflection point has occurred in Italy in mid-March. On March 21, our model projected that within 10 to 15 days, the number of new daily inflections will peak. On March 28, a flattening of the number of new infections was noticeable.
Figure 4. The evolution and prediction of daily infection rates in Italy.
USA: Infection Rates
Towards the end of March, the USA became the worldwide epicenter of the pandemic. While the number of daily infections grew exponentially during that period, at the time of writing this article, some states and cities show a slowing in the number of daily infections as a result of social distancing, 'stay at home' orders, more testing, and other measures. Assuming the trend follows the Italian trajectory, the number of daily inflections is projected to fall between the middle and late April.
Figure 5. The evolution and prediction of daily infection rates in the United States.
USA: Death Rates
The death rates in various countries that exhibit a large number of infections vary widely, ranging from 1% to >10% of those patients with positive test results. In the USA, death rates are 2-4% of those testing positive. The variability is due to regional demographics of the population, other background illnesses, and the availability and quality of medical care. It is also apparent that the deaths lag behind the onset of the infections. We are using a statistical model to correlate the death rate as a function of the infection rate. Our model suggests that there is a strong correlation between daily deaths and infections occurring up to 10 days prior to death. From our model, we can project future death rates with good accuracy up to 30 days. As shown in Figure 6, our model for the number of daily deaths suggests a sharp drop in the second part of April, although it will be variable across the USA.
Figure 6. The evolution and prediction of death rates in the United States.
The Covid-19 pandemic will continue to evolve over time, and new outbreaks are expected. We continue to monitor this evolution and continuously update our projections as more data becomes available.
All illustrations and graphics are with permission from Logecal Data Analytics.
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