How to follow Covid-19 epidemics intensity in real time?

People around the world are tracking how the COVID-19 spreads in different parts of the world using several well-known web sites and dashboards. These portals primarily report either the number of daily incidences or cumulative totals for each country, showing how disease progresses via creative animations and graphics. However, the most fundamental way to understand the epidemic and anticipate its future spreading is based the Rt, the basic reproductive number, which indicates how contagious is a virus during any given time period. When a person becomes infected, he or she will infect, on average, Rt number of other people. If the Rt is greater than 1, then the disease grows exponentially, until some large fraction of the population becomes infected and the society develops herd immunity. However, with fast COVID-19’s spreading speed, hospital systems in many countries are becoming overwhelmed, leading to severe shortages of hospital beds, ICU units and ventilators, which, in turn, may lead to many-fold increase in an overall death rate. Reducing the Rt via various government measures, such as tracing of infected individuals, and societal actions, such as school closures and lockdowns, can have a profound effect on epidemic’s dynamics, with an ultimate goal of flattening the growth curve such that a health care system will not be overrun by numerous very sick patients, hence, saving many lives. The reproductive number that is changed because of social distancing, lockdowns and other measures, is called, the Rt, where "t" indicates that it varies with time.

Despite the profound importance of the Rt, it is a difficult quantity to estimate in real-time. The needed information is particularly scarce for COVID-19, which is a fast moving pandemic that is overwhelming various health care systems. If complete epidemiological data are available about who-infected-whom, then the Rt can be simply calculated by counting the average number of persons who became infected by one individual. However, such data for COVID-19 currently rarely exist or might be unavailable due to medical privacy issues. Furthermore, a significant fraction of COVID-19 patients are asymptomatic and would not be tallied in most statistics.

Under these circumstances, statistical modeling can play an important role in estimating the Rt in any particular country in real time. In particular, in references (1-3) below, a Bayesian inference algorithms were developed, which consider all possible infection scenarios, choosing the most likely ways how the infection proceeded from person to person given the country’s data on daily positive tests of COVID-19. It turns out that because of significant time delays in disease onset and progression and also between symptoms and testing, the last three weeks of an Rt estimated curve would be severely underestimated (1-3). However, that is the most critical data section that could inform a population or country’s government about whether to intensify or relax the existing control measures. We have relied on some prior and also novel algorithms to correct the most recent Rt estimates, leading to very small errors when Rt is less than or equal to 1.5 and in the range of 0.1-0.5 underestimation when Rt is around 2 and larger. We are working on further algorithm improvements to reduce these later errors to 0.1 or less.

In the beginning of an epidemic, the Rt is a static quantity only if the disease spreads unchecked. However, governments and people can profoundly reduce Rt, by strictly following basic hygiene measures, such was washing wands and wearing masks, reducing their contacts, and governments actively tracing and quarantining the contacts of positively tested individuals. A number of countries found a way to keep their Rt around or below 1 by following these measures, in some cases not even necessarily by imposing harsh lockdowns. We believe that learning about an estimation of near-real-time Rt for various countries can help both ordinary people and governments to rationally respond by changing their behaviors accordingly. Our daily estimation of Rt curves and recent values for various countries, which is denoted Rt because of time-tracking, provides thus another important metric, presented visually on the world map, that complements in an important way the already existing trends’ data that are commonly followed on the web.


  • [1] Wallinga, J. and Teunis, P., 2004. Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. American Journal of epidemiology, 160(6), pp.509-516.
  • [2] Cauchemez, S., Boëlle, P.Y., Donnelly, C.A., Ferguson, N.M., Thomas, G., Leung, G.M., Hedley, A.J., Anderson, R.M. and Valleron, A.J., 2006. Real-time estimates in early detection of SARS. Emerging infectious diseases, 12(1), p.110.
  • [3] Chen, D. and Zhou, T., 2020. Control efficacy on COVID-19. arXiv preprint arXiv:2003.00305.