While it is impossible to estimate the eventual number of cases for the novel coronavirus , there was an exercise carried out earlier this year, aimed at projecting the numbers for Wuhan in China. In a recent article on Cell Discovery in Nature , a group of Chinese scientists attempted to estimate the eventual number of infections and deaths due to the disease (COVID-19) in Wuhan. An infectious disease dynamics model called SEIR (Susceptible-Exposed-Infectious-Resistant) was used to model and predict the number of COVID-19 cases. The SEIR model proved to be predictive for a variety of acute infectious diseases like Ebola and SARS.
The model classifies the population into four mutually exclusive groups: susceptible (at risk of contracting the disease), exposed (infected but not yet infectious), infectious (capable of transmitting the disease), and removed (those who recover or die from the disease). A susceptible individual can become exposed only through contact with some infectious person. Susceptible individuals first enter the exposed stage, during which they may have a low level of infectivity; they become infectious thereafter. The infection rate represents the probability of transmission from an infectious person to a susceptible one. The incubation rate (the reciprocal of the average duration of incubation) is the rate at which latent individuals become infectious; and the removal rate is the reciprocal of the average duration of infection. The basic reproduction number (BRN) is the expected number of cases directly generated by one case. A BRN greater than one indicates that the outbreak is self-sustaining, while a BRN less than one indicates that the number of new cases decreases over time and eventually the outbreak will stop. Ideally, the BRN should be reduced in order to slow down an epidemic.
The numbers for Wuhan
Using Wuhan’s data, more than a dozen published studies provide the estimates of parameters. The mean incubation period is around 5.2 days in most of the studies. Also, the average hospitalisation period is calculated to be 12.39 ± 4.77 days.
The prediction for Wuhan was done in four phases: a) December 1-January 23; b) January 24-February 2; c) February 3-15; d) thereafter. On January 23, airplanes, trains, and other public transportation within the city were restricted and other prevention and control measures such as quarantine and isolation were gradually established in Wuhan. Phase II continued up to the extended spring festival holiday. More medical resources were provided from February 3. It is assumed that the prevention and control measures were sufficient and effective from February 16.
The decreasing BRN rates
In Wuhan, home to 11 million people, the initial number of cases was 40, estimated by a group of researchers led by Natsuko Imai of Imperial College. The number of exposed was assumed to be 20 times this number. The BRN in the first three phases was estimated to be 3.1, 2.6, and 1.9, respectively. In the Cell Discovery article, the BRN is assumed to have decreased to 0.9 or 0.5 in phase IV, based on previous experience in SARS. According to an article in Science in 2003, the BRN of SARS decreased from 2.7 to 0.25 after the patients were isolated and the infection started being controlled.
Following the model, the number of cases in Wuhan reached 17,656-25,875 in phase I, to 32,061-46,905 in phase II, and to 53,070-77,390 in phase III. The epidemic peaked on February 23rd or February 19th with 58,077-84,520 or 55,869-81,393 infections, according to the BRN value of 0.9 and 0.5, respectively. In reality, the number of daily cases in Wuhan has been reducing remarkably since February 16.
The BRN value for India is unknown due to inadequate data so far. However, it can be kept small by isolating patients and controlling infection by extensive checking at airports and other important places. With 110 ‘active’ cases as on March 16, a BRN value of 0.5 might not be alarming. Let’s hope that it will remain so.
Atanu Biswas is a Professor of Statistics, Indian Statistical Institute, Kolkata