Reproduction number and herd immunity in COVID-19

A new modeling study published on the preprint server medRxiv* in May 2020 hypothesizes that the asymptomatic cases in the ongoing pandemic in Japan may far outnumber the symptomatic infections by several orders of magnitude. This has implications for future predictions and public health policies.

How it all began

The beginning of the ongoing COVID-19 pandemic was reported as a small, apparently local outbreak in Wuhan, China, in December 2019. This had shot up to about 50,000 cases by March 6, 2020. In Japan, meanwhile, the first case was reported on January 3, 2020, being a Wuhan returnee. By April 26, 2020, there were over 7,700 cases in Japan.

The outbreak peaked on February 12 in Wuhan, but at the end of March in Japan.

The COVID-19 outbreaks are characterized by a high reproduction number, R0, around 2, and low outbreak peaks, concerning the number of new cases and the total number of cases. The R0 should mean that the outbreak will peak when the virus infects half of the population.

At Wuhan’s peak, the total number of patients was 48,000, and in Japan, 7,700 cases. The population of Wuhan is 11 million, and of Japan, 120 million. This does not agree with the earlier characteristic. To reconcile this, the current study offers a new model.

Study: Asymptomatic infection and herd immunity of COVID−19 in Wuhan and Japan. Image Credit: TierneyMJ / Shutterstock

The SIR model is applied

The scientists used a SIR (susceptible–infected–recovery) model to study the Wuhan epidemic curve. The incubation period was taken from empirical data in Japan.

Asymptomatic and symptomatic cases were assumed to be equally infectious.

The number of symptomatic patients in Wuhan came from the published statistics from January 20 through March 5, and in Japan, from the figures published by the Ministry of Labour, Health and Welfare (MLHW) for January 14 – April 24. Where the onset date was unknown, it was estimated based on available data. In Wuhan, in the absence of any onset date, the same data was applied to estimate it.

The number of patients with unknown onset dates was estimated, accounting for underestimation due to reporting delays.

The investigators then modeled the epidemic in Wuhan, assuming only one initial case in the absence of daily reporting until January 20. After the model prediction reached the number of patients on this day, they compared the two sets of data – modeled predictions and observations.

The epidemic curve in Japan is marked into three periods, during which voluntary event cancellation and school closure (VECSC) from February 27 to March 19. The curve had been increasing gradually, but became almost entirely flat in this period of VECSC, after which it showed an exponential rise. After it peaked on April 2, it began to decline monotonically.

The scientists, therefore, concluded that each of these peaks had a different reproduction number, R0, Rv, and Ra.

The results

The total number of cases was over 68,000 in Wuhan from January 20 to March 5. In Japan, it was 13,000 from January 14 to April 26, considering only community-acquired cases and excluding asymptomatic cases.

The duration of onset to report was 30 days at most. The model shows that the first outbreak peak occurred in Japan on April 3, with the infections having occurred on March 29. The incubation periods among 91 cases with reported exposure dates and onset dates published by the MHLW shows an average of 6.6 days.

The estimated R0, Rv, and Ra were 3.19 with range of [3.08, 3.31], 147.7 [145.3, 157.0], and 2.048 [2.048, 2.024] in Wuhan. Also, q was estimated as 99.32 [99.31, 99.36]%.  

In Japan, R0, Rv, and Ra were estimated respectively as 2.16 [1.97, 2.20], 1.13 [1.00, 1.44], and 2.96 [2.81, 3.08]. Moreover, q in Japan was estimated as 99.9888% [99.9885, 99.9890]%.

The peak in Wuhan was observed on February 7 and was part of an epidemic curve that did not show any response to lockdown measures, which began on January 23.  This means that most of the patients infected at the peak of the epidemic acquired the virus after the lockdown, and the peak is probably not because of the lockdown.

In Japan, the first peak occurred on April 3, and the data used to estimate this peak includes almost all cases reported within 30 days. This shows that the first peak is over in Japan. At the peak, no lockdown was in place, with the VECSC period already being over on March 21. Japan declared a state of emergency on April 7.

Between these dates, therefore, the only countermeasure was a recommendation to avoid large mass gatherings, and therefore the peak is not due to strong countermeasures. However, the VECSC appeared to have been effective.

Climate and weather conditions also may not have contributed to the infectious nature of the virus since these remained relatively stable throughout March.

The scientists say, “This is the first model which can show a peak and declining phase without a change in the reproduction number for COVID-19 outbreak.”

The current estimated R0 was similar but slightly lower than previous estimates of 2.24–3.58 in Wuhan, but much higher than the earlier estimate of 0.06 in Japan. This means that contact tracing may be essential to detect clusters of transmission if over 60 million people are likely to be infected.

Huge numbers of asymptomatics in Japan

The proportion of asymptomatic cases in the infected population is 99.32 and 99.98%, respectively, in Wuhan and Japan. In other words, there are 150 and 9,000 asymptomatic patients for each confirmed symptomatic individual in these places, respectively. This is a massive departure from an earlier estimate of 3 asymptomatic among 23 infected individuals. The reason might be the use of PCR testing, which necessitates active infection at the time of testing but does not detect past infection. Large-scale antibody testing in the community may be the only way to confirm the current results.

A similar antibody testing trial in New York showed an antibody prevalence of 15% at a reported case prevalence of only 0.88% for an asymptomatic: infected ratio of 94%, comparable to the current study.

The researchers hypothesize that the asymptomatic proportion is so different in Wuhan and China because of underlying health conditions and behaviors like diabetes, smoking, and air pollution, leading to a higher state of health in Japan compared to Wuhan. This could lead to a higher chance of symptomatic disease in Wuhan.

Another reason might be differences in testing strategy since more asymptomatic cases might be diagnosed in Japan if PCR tests only severe cases. A third possibility is that of mutation of the virus to develop different characteristics in Japan.

Limitations of the study

Study limitations include the entirely hypothetical basis of the model, the need to assess the reasons for the success of VECSC, and the possible effects of under-ascertaining cases, in addition to differences in the testing and reporting systems.

The scientists also caution that future waves might occur in Japan, even higher than the first, especially since April marks the beginning of the school year and the financial year. This means a significant change in many population-level movements and activities in Japan. Thus, the Japanese outbreak cannot be concluded to be over.

The study concludes: “By introducing a very high proportion of asymptomatic cases, two inconsistent phenomena might be resolved as a result of this study: the high reproduction number and low peak. Nevertheless, it is currently only a hypothesis.”

*Important Notice

medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.

Journal reference:
Dr. Liji Thomas

Written by

Dr. Liji Thomas

Dr. Liji Thomas is an OB-GYN, who graduated from the Government Medical College, University of Calicut, Kerala, in 2001. Liji practiced as a full-time consultant in obstetrics/gynecology in a private hospital for a few years following her graduation. She has counseled hundreds of patients facing issues from pregnancy-related problems and infertility, and has been in charge of over 2,000 deliveries, striving always to achieve a normal delivery rather than operative.

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