Scientists at the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory and the University of Illinois at Urbana-Champaign (UIUC) have developed a new mathematical model to predict the spread of COVID-19. This model takes into account not only the varying biological susceptibility of individuals to infection, but also their levels of social activity, which change naturally over time. Using their model, the team showed that a temporary state of herd immunity – what they called “transient herd immunity” – arose during the early, rapid stages of the epidemic. However, subsequent “waves”, or increases in the number of cases, continued to appear due to changing social behavior. Their results are published in the Proceedings of the National Academy of Sciences.
The COVID-19 epidemic reached the United States in early 2020, spreading rapidly to several states in March. To mitigate the spread of the disease, states have issued stay-at-home orders, closed schools and businesses, and put in place masked warrants. In big cities like New York (NYC) and Chicago, the first wave ended in June. In winter, a second wave erupted in both cities. Understanding why the initial waves end and subsequent waves begin is essential to being able to predict future epidemic dynamics.
Here’s where modeling can help. But classic epidemiological models were developed almost 100 years ago. Although these models are mathematically robust, they do not capture reality perfectly. One of their faults is that they ignore the structure of person-to-person contact networks, which serve as channels for the spread of infectious diseases.
“Classical epidemiological models tend to ignore whether a population is heterogeneous, or different, on many levels, including physiologically and socially,” said Alexei Tkachenko, a physicist in the Theory and Computation Group at the Center for Functional Nanomaterials (CFN ), a user installation of the DOE Office of Science at the Brookhaven Lab. “We do not all have the same susceptibility to infection due to factors such as age, pre-existing health problems and genetics. Likewise, we do not have the same level of activity in our social lives. We differ in the number of relatives. the contacts we have and how often we interact with them during the different seasons. The heterogeneity of the population – these individual differences in biological and social sensitivity – is particularly important because it lowers the threshold of immunity of the herd. “
Herd immunity is the percentage of the population that must gain immunity for an epidemic to end.
“Collective immunity is a controversial topic,” said Sergei Maslov, CFN user and professor and Bliss scholar at UIUC, with appointments in the departments of physics and bioengineering and at the Carl R. Woese for genomic biology. “Since the start of the COVID-19 pandemic, it has been suggested that collective immunity be achieved quickly, thereby ending local transmission of the virus. However, our study shows that the apparent collective immunity achieved in this way wouldn’t last. “
“What was lacking prior to this work is that people’s social activity increases and decreases, especially due to lockdowns or other mitigating measures,” added Nigel Goldenfeld, professor of physics at Swanlund and director. from the NASA Institute of Astrobiology for Universal Biology at UIUC. “So a wave of the epidemic may appear to go away due to mitigation measures when sensitive or more social groups collectively have been infected – what we call transient herd immunity. But once those measures are relaxed and as people’s social media will renew itself, another wave may begin, as we’ve seen with states and countries opening up too early, thinking the worst is behind them. “
Ahmed Elbanna, Donald Biggar Willett Faculty Fellow and UIUC Professor of Civil and Environmental Engineering, noted that transitional collective immunity has profound implications for public policy.
“Mitigation measures, such as wearing a mask and avoiding large gatherings, should continue until the true threshold of herd immunity is reached through vaccination,” said said Elbanna. “We cannot outsmart this virus by forcing our way to herd immunity through widespread infection because the number of people infected and the number of hospitalizations likely to die would be too high.”
The nuts and bolts of predictive modeling
Over the past year, the Brookhaven-UIUC team has led various projects related to a larger COVID-19 modeling effort. Previously, they modeled how the outbreak would spread across Illinois and the UIUC campus, and how mitigation efforts would impact that spread. Last May, they launched this project to calculate the effect of population heterogeneity on the spread of COVID-19.
Several approaches already exist to model the effect of heterogeneity on epidemic dynamics, but they generally assume that heterogeneity remains constant over time. So, for example, if you are not socially active today, you will not be socially active tomorrow or in the weeks and months to come.
“Basic epidemiological models only have a characteristic time, called the generation interval or incubation period,” Tkachenko said. “It refers to when you can infect another person after you’ve been infected yourself. For COVID-19, it’s about five days. But that’s just a timescale. other timescales during which people change their social behavior. “
In this work, the team incorporated temporal variations in individual social activity into existing epidemiological models. While a complex, multidimensional model is needed to describe each group of people with different susceptibilities to the disease, they compressed this model into just three equations, developing a single parameter to capture the biological and social sources of heterogeneity.
“We call this parameter the immunity factor, which tells you how much the reproduction number decreases as susceptible individuals are removed from the population,” Maslov explained.
The breeding number indicates how transmissible an infectious disease is. Specifically, quantity refers to the number of people an infected person will in turn infect. To estimate the social contribution to the immunity factor, the team drew on previous studies in which scientists actively monitor people’s social behavior. They also looked at actual epidemic dynamics, determining which immunity factor was most consistent with data on COVID-19-related hospitalizations, intensive care unit admissions, and daily deaths in New York and Chicago. For example, when the number of susceptible subjects fell by 10 percent during the early and rapid epidemic in New York and Chicago, the number of reproduction fell by 40 to 50 percent – which is a factor immunity estimated from four to five.
“It is a fairly important immunity factor, but it is not representative of lasting herd immunity,” Tkachenko said. “On a longer timescale, we estimate a much lower immunity factor of about two. Just because a single wave stops doesn’t mean you’re safe. It can come back.”
This state of temporary immunity arises because the heterogeneity of the population is not permanent; people change their social behavior over time. For example, people who isolated themselves during the first wave – staying home, not having visitors, ordering groceries online – subsequently begin to relax their behaviors. Any increase in social activity carries a risk of additional exposure.
“The epidemic has been with us for a year now,” Maslov said. “It’s important to understand why he’s been here for so long. The gradual change in the social behavior of individuals is part of the reason why plateaus and subsequent waves occur. For example, both cities avoided a summer wave but experienced a winter wave. We attribute the winter wave to two factors: the change of seasons and the decline in transient herd immunity. “
With vaccination becoming more widespread, the team is hoping we will be spared another wave. In their most recent work, they study the dynamics of epidemics in more detail. For example, they incorporate statistics from “super-diffuser” events – gatherings where a single infected person causes a large outbreak among the attendees into the model. They are also applying their model to different parts of the country to explain the overall epidemic dynamics from the end of the lockdown to early March 2021.
This work was supported by the DOE Office of Science; The University of Illinois System Office, Vice Chancellor’s Office for Research and Innovation, Grainer College of Engineering and UIUC’s Department of Physics; DOE Computer Science Graduate Scholarship; and the Career Development Program (CAREER) of the Faculty of the National Science Foundation. This research was carried out as part of a CFN user program. The Illinois Department of Public Health, through a data use agreement with Civis Analytics, provided data for the calculations. Calculations were performed on the Illinois Campus Cluster, a computing resource managed by the Illinois Campus Cluster Program in conjunction with the National Center for Supercomputing Applications, funded by UIUC funds.