When Will All This End? New Modeling Looks at Control Measure Duration and Resurgent Infections of COVID-19

In their study, the authors considered a variety of factors that together will determine the extent and trajectory of the COVID-19 pandemic, and used mathematical modeling to present a variety of possible scenarios for the United States, some extending into 2022 or even 2024. Key factors that the group considered included the following:

• The degree of seasonal variation in transmission of the SARS-CoV-2 virus.
• The duration of the immunity conferred by infection with the virus.
• The degree of cross-immunity between SARS-CoV-2 and human coronaviruses such as HCoV-OC43 and HCoV-HKU1, which are reportedly the second-most common cause of the common cold (after rhinoviruses).
• The intensity and timing of control measures such as social distancing.
• The effect of the value of R0 (the average number of additional cases an infected person will cause during their infectious period).

Seasonal Variation

Infection by the human coronaviruses during the “cold season”, as represented by the value of R0, typically reaches a maximum value of 2.2 in winter, peaking in the second week in January, and a low of 1.7 in summer. While it is currently unknown whether SARS-CoV-2 might follow a similar pattern, the degree of its seasonal variation could differ between northern and southern geographical locations, as is seen with influenza. Thus, R0 for influenza in New York declines in summer by about 40%, but in Florida the decline is only about 20% (similar to that for the human coronaviruses). While a 40% summertime decline in R0 for SARS-CoV-2 during the current pandemic wave would result in a lower peak incidence (flatter curve) and be immediately beneficial, it could lead to higher peaks in future recurrent outbreaks, such as next fall/winter.

Duration of Immunity, and Cross-Immunity Between Coronavirus Strains

Immunity acquired as the result of infection by seasonal human coronavirus has been reported to wane appreciably within one year, and modeling shows its duration to be only about 45 weeks. Significantly, infection by either strain (HCoV-OC43 and HCoV-HKU1) also induces cross-immunity against the other strain, although the immunity induced by OC43 against HKU1 is stronger than vice versa. In contrast, the original SARS virus (SARS-CoV-1) is known to induce significantly longer-lasting immunity. In addition, it can generate antibodies against HCoV-OC43, and the reverse is also true: HCoV-OC43 can generate cross-reactive antibodies against SARS-CoV-1.

Currently, the length of the immunity conferred by SARS-CoV-2 infection is not known, and neither is the extent of any cross-immunity between SARS-CoV-2 and the human coronaviruses. If immunity to SARS-CoV-2 is effectively permanent or at least long-lasting, it could virtually disappear for several years after a major outbreak, or even become eliminated. If it could also induce cross-immunity against the seasonal human coronaviruses to the same extent as HCoV-OC43 against HCoV-HKU1 (70%), these too could be eliminated.

If immunity to SARS-CoV-2 is not permanent, it could enter into long-term circulation along with the human coronaviruses, in regular or sporadic outbreaks. Modeling shows annual outbreaks if immunity is short-term like that of the human coronaviruses, or outbreaks every two years if immunity is longer-term (two years). Modest cross-immunity (30%) from the human coronaviruses could extend that for up to three years, leading to a possible new outbreak around 2024.

Control Measures, and Their Effect On R0

The authors evaluated the impact of a single round of social distancing of various durations (weeks) and effectiveness (% reductions in R0) on the peak and timing of the pandemic, with and without seasonality as a factor. Although one-time social distancing reduced the predicted epidemic peak size, there was a resurgence of infection under all scenarios of duration and effectiveness once the social distancing measures were lifted. In one scenario, with a long period of social distancing (20 weeks) and a large reduction in R0 (60%), the resurgence peak was almost as great as if there had been no controls in the first place; the controls were so effective that no population immunity was accumulated. When potential seasonal effects were factored in, the resurgence in the fall and winter months showed a peak size possibly even greater than that resulting from an initial uncontrolled pandemic.

The authors suggested that intermittent social distancing, rather than a single period of such controls, could at least prevent critical care capacity from being exceeded. The length of time between periods of social distancing could then increase as the pandemic progressed and increasing immunity in the population slowed subsequent resurgences. However, they warned that under current critical care capacities, the current pandemic could last into 2022. If the value for R0 is assumed to be between 2.0 and 2.6 as recent studies indicate, this would require social distancing measures to be in place somewhere between (i) 25% of the time (using wintertime R0 = 2 and seasonality, i.e., with even lower values in the summertime); and (ii) 75% of the time (with R0 = 2.6 year-round, i.e., no seasonality).

Other Factors

In a model in which critical care capacity is doubled, thus allowing for faster development of population immunity, the authors estimate that the pandemic could end by July 2022, and social distancing measures could be relaxed by early to mid-2021, depending on whether seasonality was a factor. However, much depends on the duration of acquired immunity to SARS-CoV-2, and to a lesser extent, on possible cross-immunity from the human coronaviruses HCoV-OC43 and HCoV-HKU1. If the immunity conferred by infection with SARS-CoV-2 does not last for at least two years but wanes in less than a year as it does with the human coronaviruses, recurrent wintertime outbreaks are likely to occur through at least 2025.

Several caveats pertain to this study, most of which are noted by the authors. First, the modeling represents possible scenarios in the absence of successful pharmaceutical intervention, specifically safe and effective treatments and vaccines that should, of course, hasten the end of the pandemic. Second, it applies only to temperate regions, covering just 60% of the global population; the situation in tropical regions could be much more complex. Third, it does not take into account the possibility that significant immunity may exist as a result of undocumented asymptomatic infections, thus reducing the extent of social distancing required; without widespread serological testing, the extent of such immunity is impossible to estimate.

The fourth caveat applies to the value of R0. The authors of this study assumed a baseline value of about 2.0 to 2.5 or 2.6, based on other recently published studies. However, an early-release paper by Sanche et al. from the Los Alamos National Laboratory entitled “High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2” and just published by the CDC re-examines data from the initial Wuhan outbreak and calculates a median R0 value of 5.7, more than double the currently accepted value and one that would indicate a significantly more serious situation than that predicted by the new modeling study from Harvard.

Overall, the Harvard modeling study clearly indicates that the peaking of the curve for different regions of the country will not necessarily mean that the worst is over. Resurgence of infection is highly likely, several critical factors must still be considered, and accurate information about those factors is still lacking.