All over the world, epidemiologists have tried to understand the dynamics of COVID-19. A study from Indian Institute of Technology, Madras, may offer a different perspective to modelling COVID-19 dynamics.
Since December 2019, several waves of COVID-19 have washed over populations across the world, in different countries. It is important to understand their dynamics, so that governments can plan mitigation strategies at every level. With this aim in mind, researchers study disease dynamics models, many of which build on the idea that the growth of infections is exponential in nature. An example of exponential growth is the series 2, 4, 8, 16… which doubles at constant rate.
Fast growth
A recent work from IIT Madras suggests that the growth rate of infections is hyperexponential, that is, faster than exponential, in the initial stages of extreme (severe) waves of COVID-19. This is based on their study of 12 representative waves of COVID-19 across nine countries (India, the U.S., U.K., South Africa, Germany, Italy, Japan, Brazil and Mexico). They also study two cases of such waves in Indian cities (Chennai and Delhi).
The researchers observed faster-than-exponential growth in extreme (severe) waves in each of the studied countries. “The growth rate is not constant; it is increasing. The rate of change of infections per day is not proportional to the current number of infections,” says R.I. Sujith, who is D. Srinivasan Chair Professor, Department of Aerospace Engineering, IIT Madras, and an author of the paper published in Chaos.
Oscillations not noise
Further, the researchers find that the average per week of acquired infections oscillates about a mean value before reaching a saturation. “The mean is not constant here. It is growing as a power law, so the correct phrase is ‘mean power law growth’,” explains Induja Pavithran, a post-doctoral fellow from the Aerospace Engineering Department of IIT Madras and the first author of the paper. These are known as “log periodic oscillations.”
“Log-periodic oscillations are not noise, but they are there as a consequence of the discrete nature of the spreading process,” she says.
The hyperexponential growth of COVID-19 waves implies that the growth rate varies continuously during the transmission. New variants of the virus can have higher growth rates,” says Prof. Sujith explaining one reason for the pattern they observe.
Problems with data
There is, however, a question as to whether this nonlinearity may stem from inhomogeneities in the data. “There is no discussion of other possible reasons for the deviation from exponential growth,” says R. Shankar, Chennai-based condensed matter physicist, who has analysed COVID-19 data.
He refers to, for example, the inhomogeneous nature of the population in a country, variation in the level of detection of cases due to testing levels, changing human behaviour during the growth period (masking and physical distancing levels), and so on, which can also cause deviations from exponential growth within the standard compartmental models.
“The discrepancy between reported and actual cases is always a problem. Therefore, we should not compare the data between different countries…,” says Prof. Sujith.
“A weekly average will remove such fluctuations arising due to the inconsistency in the number of tests per day,” he says. “We can expect different types spread over large countries. To avoid this, we choose to demonstrate the log-periodicity for densely populated cities or small countries,” he adds, explaining that the limitations of the study have been pointed out in the paper.
Warning sign
Next, the researchers are thinking of getting more information from data such as secondary infection rate and the spreading pattern itself. “Also, by identifying the correct growth pattern at the start of an epidemic wave helps us to be prepared for future outbreaks or pandemics. Log-periodic can warn us of impending catastrophic waves,” says Dr. Induja Pavithran.
