Exponential coronavirus

Similar to SARS, the current Chinese Coronavirus, known as 2019-nCoV, is transmitted from person to person by close personal contact, and also believed to be readily transmitted by respiratory droplets and aerosols produced when an infected person coughs or sneezes. The CDC informs us that the Chinese epidemic “reportedly had some link to a large seafood and animal market, suggesting animal-to-person spread,” but some believe 2019-nCoV might be a Chinese bioweapon which leaked out of their Wuhan BSL-4 microbiology research laboratory.

 

2019-nCOV virus (photo courtesy of European Commission)

Exponential expansion of an infectious disease occurs when the rate of growth is proportional to the number of people currently infected. The mathematical formula for exponential growth is:

“xt” refers to the total number of cases, “xo” the number of index cases or the number of cases at the time of mathematical calculation, “r” the rate of disease transmission (the number of people infected by each prior case), and “t” the number of incubation time intervals during the course of an epidemic.

In the current 2019-nCoV epidemic “r” has been estimated by an international team of university researchers to be 3.8, and the best estimate for incubation time is 4-5 days, which occurred in earlier Coronavirus epidemics known as SARS and MERS. Read et al. have estimated that only 5% of Chinese cases have been detected and reported, but if we assume that 3 out of 4 cases remain in the incubation period, unsymptomatic, but still contagious toward the end of incubation, we can estimate the current number of cases to be ~8,000 rather than the ~2,000 currently acknowledged by the Chinese government.

Read et al. have mathematically predicted about 200,000 cases in China by February 4 using an estimate of 11,341 cases on January 21 and an “r” of 3.8. Using a more conservative “r” of 3.0, an incubation time of 5 days, and a current number of 8,000 cases (6,000 undetected and unreported) there would be 97,000 cases by February 4 and about 100 million cases by the first of March. Assuming the 10% fatality rate seen in SARS, there would be 10 million deaths by March. These numbers are extremely disturbing, but of course depend upon the accuracy of current estimates for disease transmission, incubation time, mortality rate, and an accurate appraisal of unreported cases. The case numbers could be reduced to some degree with strict quarantines and travel restrictions; of course the numbers might even be higher if the Chinese government is underreporting its cases, or if the mortality rate is closer to 35% as seen in MERS. If these estimates are accurate, or even in the right ballpark, it would be wise to place strict limits on, or ban, flights arriving from China.

Ronald R. Cherry, MD is author of Restoring the American Mind

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