The chaotic behavior of SARS-CoV-2 infection

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was first identified in China in 2019, leading to the coronavirus disease 2019 (COVID-19) pandemic. Despite strict actions to mitigate the spread of the SARS-CoV-2 virus, COVID-19 resulted in a significant loss of human life in 2020 and early 2021. Therefore, it is important to have a sound understanding of the dynamics of the virus so that effective policies can be devised.

Now, a new study published in the journal IEEE Access seeks to better understand the dynamics of the spread of COVID-19 and evaluates the evidence of its chaotic behavior in the US and globally using a compartmental model.

Chaotic Systems

Many aspects of the pandemic (e.g., mechanisms and infection transmission rate) have been investigated, but it isn't easy to assess its dynamics accurately. Looking at the trajectory of transmission from China to all over the world, scientists opine that the dynamics must be a complex phenomenon, of which chaotic behavior is the main factor.

In chaotic behavior, elements of the system align and compete for survival. Chaotic systems are rendered unpredictable owing to their sensitivity to initial conditions, although they can be characterized by a few variables and equations.

A New Study

Researchers analyzed data from a total of 214 counties and territories worldwide. The data were collected from Johns Hopkins University (JHU) Center for Systems Science and Engineering (CSSE).

The studies’ compartmental model investigated the dynamics of one class of susceptible populations and three classes of infected populations. A fractional-order counterpart of the model was considered to improve the degree of freedom and accuracy of the model.

A variety of numerical tools were used to study the complex dynamics of the system, including Lyapunov exponents (LEs), Lyapunov spectrums, and bifurcation diagrams. Calculating the divergence rate of trajectories in phase space can be used to assess chaotic behavior; positive LE may indicate chaos while negative LE is not generally indicative of stability.

The key aim was to verify that the COVID-19 epidemic displays chaotic behavior. To this end, time-series data of reported daily infections were analyzed. Firstly, the spread of infection in different US states was investigated, followed by its behavior in other countries around the world.

In the study, a 0-1 test was used that is not computationally intensive and does not require a phase space reconstruction of the system under study. When the test results are close to 1, chaos is present, while chaos is absent when they are closer to 0.

K-Median Values From the 0–1 Test for Confirmed Daily COVID-19 Cases in the US.
K-Median Values From the 0–1 Test for Confirmed Daily COVID-19 Cases in the US.

Main Findings

In the context of the United States, the K-median values from the 0–1 test were used to determine whether the time-series infection data exhibited deterministic chaos (K-median values ≥ 0.9 were classified as chaotic). The results showed that the spread of COVID-19 infection in 19 out of 50 states was chaotic (39.2%). After having determined the chaotic spread of SARS-CoV-2 in the USA, scientists analyzed the transmission globally.

Examples of confirmed daily COVID-19 cases for states showing chaotic behavior.
Examples of confirmed daily COVID-19 cases for states showing chaotic behavior.

Overall, 118 countries (out of 213 countries/territories) exhibited chaotic behavior of the spread of COVID-19 infections, i.e., roughly 55%.

All countries and territories have been categorized under three broad headings, namely, developed economies, economies in transition, and developing economies, based on various econometric measures. The Department of Economic and Social Affairs of the United Nations Secretariat (UN/DESA) is responsible for this classification.

Examples of confirmed daily COVID-19 cases for states showing non-chaotic behavior.
Examples of confirmed daily COVID-19 cases for states showing non-chaotic behavior.

68.3% (110 out of 161) of developing countries or territories reported chaotic time series of daily confirmed COVID-19 cases. In comparison, the same proportion was 13.9% (5 out 36) and 18.8% (3 out of 16) for the developed and in-transition countries, respectively. In Europe, 11 out of 32 (34.4%) countries showed a chaotic spread. The figures were alarming 86% for Sub-Sharan Africa and 70% for Latin America and the Caribbean. In Asia, 46.4% (13 out of 28) of the countries showed chaotic transmission.

In the current study, only confirmed daily COVID-19 cases were subjected to nonlinear dynamics analysis. One limitation of the study was that the data on the number of hospitalizations, the daily number of deaths, and a number of recoveries were not considered.

Other factors, such as income, education, employment, the proportion of people under the poverty line, total population, government regulations, etc., could also aid in our better understanding of COVID-19 transmission dynamics.

Scientists stated that future research should assess the most prominent Lyapunov exponent of each time-series data for daily infections to confirm the current results.


Researchers analyzed time-series data representing the spread of confirmed COVID-19 infections from 1/22/2020 to 12/13/2020 and investigated the presence of chaos.

Most countries (irrespective of the continent) were found to demonstrate a chaotic behavior, making it difficult to predict the dynamics of the pandemic in the long term.

To overcome some of the limitations of this study, other data regarding the relevant sociopolitical factors, government regulations, and public health policies should be considered.

Journal reference:
  • N. Sapkota et al. (2021) The Chaotic Behavior of the Spread of Infection During the COVID-19 Pandemic in the United States and Globally. IEEE. 9.  pp. 80692-80702, 2021, doi: 10.1109/ACCESS.2021.3085240,
Dr. Priyom Bose

Written by

Dr. Priyom Bose

Priyom holds a Ph.D. in Plant Biology and Biotechnology from the University of Madras, India. She is an active researcher and an experienced science writer. Priyom has also co-authored several original research articles that have been published in reputed peer-reviewed journals. She is also an avid reader and an amateur photographer.


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