PROJECTING THE TRANSMISSION DYNAMICS OF SARS-COV-2 [COVID19] THROUGH THE POST-PANDEMIC PERIOD – Kissler, Tedijanto, Goldstein, Grad, Lipsitch, Science Magazine, 14/04

For social distancing to have reversed the epidemic in China, the effective reproduction number must have declined by at least 50-60%, assuming a baseline R0 [taxa de transmissibilidade do vírus – per capita] between 2 and 2.5. Through intensive control measures, Shenzhen was able to reduce the effective reproduction number by an estimated 85%. However, it is unclear how well these declines in R0 might generalize to other settings: recent data from Seattle suggests that the basic reproduction number has only declined to about 1.4, or by about 30-45% assuming a baseline R0 between 2 and 2.5. Furthermore, social distancing measures may need to last for months to effectively control transmission and mitigate the possibility of resurgence.”

We used data from the United States to model betacoronavirus transmission in temperate regions and to project the possible dynamics of SARS-CoV-2 infection through the year 2025.”

According to the best-fit model parameters, the R0 for HCoV-OC43 and HCoV-HKU1 varies between 1.7 in the summer and 2.2 in the winter and peaks in the 2nd week of January, consistent with the seasonal spline estimated from the data. Also in agreement with the findings of the regression model, the duration of immunity for both strains in the best-fit SEIRS model is about 45 weeks, and each strain induces cross-immunity against the other, though the cross-immunity that HCoV-OC43 infection induces against HCoV-HKU1 is stronger than the reverse.”

Next, we incorporated a third betacoronavirus into the dynamic transmission model to represent SARS-CoV-2. We assumed a latent period of 4.6 days, and an infectious period of 5 days, informed by the best-fit values for the other betacoronaviruses. We allowed the cross immunities, duration of immunity, maximum R0, and degree of seasonal variation in R0 to vary. We assumed an establishment time of sustained transmission on 11 March 2020, when the World Health Organization declared the SARS-CoV-2 outbreak a pandemic and we varied the establishment time in a sensitivity analysis. For a representative set of parameter values, we measured annual SARS-CoV-2 infections and the peak annual SARS-CoV-2 prevalence through 2025. We summarized the post-pandemic SARS-CoV-2 dynamics into the categories of annual outbreaks, biennial outbreaks, sporadic outbreaks, or virtual elimination. Overall, shorter durations of immunity and smaller degrees of cross-immunity from the other betacoronaviruses were associated with greater total incidence of infection due to SARS-CoV-2, and autumn establishments and smaller seasonal fluctuations in transmissibility were associated with larger pandemic peak sizes.”

SARS-CoV-2 can proliferate at any time of year”

If immunity to SARS-CoV-2 is not permanent, it will likely enter into regular circulation

Much like pandemic influenza, many scenarios lead to SARS-CoV-2 entering into long-term circulation alongside the other human betacoronaviruses, possibly in annual, biennial, or sporadic patterns over the next five years.”

High seasonal variation in transmission leads to smaller peak incidence during the initial pandemic wave but larger recurrent wintertime outbreaks”

The R0 for influenza in New York declines in the summer by about 40%, while in Florida the decline is closer to 20%, which aligns with the estimated decline in R0 for HCoV-OC43 and HCoV-HKU1. A 40% summertime decline in R0 would reduce the unmitigated peak incidence of the initial SARS-CoV-2 pandemic wave. However, stronger seasonal forcing leads to a greater accumulation of susceptible individuals during periods of low transmission in the summer, leading to recurrent outbreaks with higher peaks in the post-pandemic period.”

If immunity to SARS-CoV-2 is permanent, the virus could disappear for five or more years after causing a major outbreak”

Low levels of cross immunity from the other betacoronaviruses against SARS-CoV-2 could make SARS-CoV-2 appear to die out, only to resurge after a few years”

Pharmaceutical treatments and vaccines may require months to years to develop and test, leaving non-pharmaceutical interventions (NPIs) as the only immediate means of curbing SARS-CoV-2 transmission. Social distancing measures have been adopted in many countries with widespread SARS-CoV-2 transmission. The necessary duration and intensity of these measures has yet to be characterized. To address this, we adapted the SEIRS transmission model to capture moderate/mild/asymptomatic infections (95.6% of infections), infections that lead to hospitalization but not critical care (3.08% of infections), and infections that require critical care (1.32% of infections). We assumed the worst-case scenario of no cross-immunity from HCoV-OC43 and HCoV-HKU1 against SARS-CoV-2, which makes the SARS-CoV-2 model unaffected by the transmission dynamics of those viruses. Informed by the transmission model fits, we assumed a latent period of 4.6 days and an infectious period of 5 days, in agreement with estimates from other studies. The mean duration of non-critical hospital stay was 8 days for those not requiring critical care and 6 days for those requiring critical care, and the mean duration of critical care was 10 days. We varied the peak (wintertime) R0 between 2.2 and 2.6 and allowed the summertime R0 to vary between 60% (i.e. relatively strong seasonality) and 100% (i.e. no seasonality) of the wintertime R0, guided by the inferred seasonal forcing for HCoV-OC43 and HCoV-HKU1.”

In the case of a 20-week period of social distancing with 60% reduction in R0, for example, the resurgence peak size was nearly the same as the peak size of the uncontrolled epidemic: the social distancing was so effective that virtually no population immunity was built.”

Strong social distancing maintained a high proportion of susceptible individuals in the population, leading to an intense epidemic when R0 rises in the late autumn and winter. None of the one-time interventions was effective in maintaining the prevalence of critical cases below the critical care capacity.

Intermittent social distancing could prevent critical care capacity from being exceeded). Due to the natural history of infection, there is an approximately 3-week lag between the start of social distancing and the peak critical care demand. When transmission is seasonally forced, summertime social distancing can be less frequent than when R0 remains constant at its maximal wintertime value throughout the year. The length of time between distancing measures increases as the epidemic continues, as the accumulation of immunity in the population slows the resurgence of infection. Under current critical care capacities, however, the overall duration of the SARS-CoV-2 epidemic could last into 2022, requiring social distancing measures to be in place between 25% (for wintertime R0 = 2 and seasonality) and 75% (for wintertime R0= 2.6 and no seasonality) of that time. When the latent, infectious, and hospitalization periods are gamma-distributed [segundo uma constante, e não exponencialmente], incidence rises more quickly, requiring a lower threshold for implementing distancing measures (25 cases per 10,000 individuals for R0 = 2.2 in our model) and more frequent interventions.”

SERIAM NECESSÁRIOS MUITO MAIS DO QUE APENAS HOSPITAIS E LEITOS DE CAMPANHA: “Increasing critical care capacity allowed population immunity to be accumulated more rapidly, reducing the overall duration of the epidemic and the total length of social distancing measures.”

The observation that strong, temporary social distancing can lead to especially large resurgences agrees with data from the 1918 influenza pandemic in the United States, in which the size of the autumn 1918 peak of infection was inversely associated with that of a subsequent winter peak after interventions were no longer in place.”

Although disease dynamics may differ by age, we did not have sufficient data to parameterize an age-structured model. We also did not directly model any effect from the opening of schools, which could lead to an additional boost in transmission strength in the early autumn. The transmission model is deterministic, so it cannot capture the possibility of SARS-CoV-2 extinction. It also does not incorporate geographic structure, so the possibility of spatially heterogeneous transmission cannot be assessed. The construction of spatially explicit models will become more feasible as more data on SARS-CoV-2 incidence becomes available; these will help determine whether there are differences in seasonal forcing between geographic locations, as for influenza, and will also help to assess the possibility of epidemic extinction while accounting for re-introductions.”

In a recent study, an estimated 4% of individuals with coronavirus sought medical care, and only a fraction of these were tested.”

Our findings generalize only to temperate regions, comprising 60% of the world’s population, and the size and intensity of outbreaks could be further modulated by differences in average interpersonal contact rates by location and the timing and effectiveness of non-pharmaceutical and pharmaceutical interventions. The transmission dynamics of respiratory illnesses in tropical regions can be much more complex. However, we expect that if post-pandemic transmission of SARS-CoV-2 does take hold in temperate regions, there will also be continued transmission in tropical regions seeded by the seasonal outbreaks to the north and south. With such reseeding, long-term disappearance of any strain becomes less likely, but according to our model the effective reproductive number of SARS-CoV-2 remains below 1 during most of each period when that strain disappears, meaning that reseeding would shorten these disappearances only modestly.”

While long-lasting immunity would lead to lower overall incidence of infection, it would also complicate vaccine efficacy trials by contributing to low case numbers when those trials are conducted, as occurred with Zika virus. In our assessment of control measures in the initial pandemic period, we assumed that SARS-CoV-2 infection induces immunity that lasts for at least 2 years, but social distancing measures may need to be extended if SARS-CoV-2 immunity wanes more rapidly. In addition, if serological data reveals the existence of many undocumented asymptomatic infections that lead to immunity, less social distancing may be required. Serology could also indicate whether cross-immunity exists between SARS-CoV-2, HCoV-OC43, and HCoV-HKU1, which could affect the post-pandemic transmission of SARS-CoV-2. We anticipate that such cross-immunity would lessen the intensity of SARS-CoV-2 outbreaks, though some speculate that antibody-dependent enhancement (ADE) induced by prior coronavirus infection may increase susceptibility to SARS-CoV-2 and exacerbate the severity of infection.”

A vaccine would accelerate the accumulation of immunity in the population, reducing the overall length of the epidemic and averting infections that might have resulted in a need for critical care. Furthermore, if there have been many undocumented immunizing infections, the herd immunity threshold may be reached sooner than our models suggest. Still, SARS-CoV-2 has demonstrated an ability to challenge robust healthcare systems, and the development and widespread adoption of pharmaceutical interventions will take months at best, so a period of sustained or intermittent social distancing will almost certainly be necessary.”

Less effective one-time distancing efforts may result in a prolonged single-peak epidemic, with the extent of strain on the healthcare system and the required duration of distancing depending on the effectiveness. Intermittent distancing may be required into 2022 unless critical care capacity is increased substantially or a treatment or vaccine becomes available.”

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