COVID-19 epidemic: Power law spread and flattening of the curve

Mahendra K. Verma; Ali Asad; Soumyadeep Chatterjee

and France require two exponential functions for the fits. For example, Germany's data requires two functions, exp(0.34t) and exp(0.25t). Note that the growth rate β varies for different countries, which is because β depends on various factors such as immunity level of the population, climate, local policy decisions (lockdown, social distancing), etc. Larger the β, larger the growth rate for the infection. Also, the inverse of the constant β yields the growth time scale. In fact, in the exponential phase, the number of cases double in time T = (log 2)/β. For South Korea, β = 0.67, hence, T ≈ 1; that is, I(t) for South Korea doubled every day in the early phase (18 February to 23 February). The doubling time for India in the exponential phase was log(2)/0.16 ≈ 4.3 days. Note that for the exponential regime,İ ≈ βI.