COVID-19 Spread: SIR Platform Of COVID-19 Transmission Now Complemented By New Fractal Nature Model
: Brazilian researchers have developed a new model that predicts spatial and temporal evolution of epidemic diseases and can help plan more effective social isolation programs with less socio-economic impact. The new research study proposes an epidemiological model that provides a more detailed description of how the SARS-CoV-2 coronavirus that causes the COVID-19 disease is spreading in different countries and regions.
The study team shows that COVID-19 virus contamination follows a similar pattern in different regions of the world. The superlinear power-law behavior for the number of contamination cases as a function of the city population, with exponent β
of the order of 1.15 is always obtained. Due to the strong indication that scaling is a determinant feature of covid-19 spread, we propose an epidemiological model that embodies a fractal structure, allowing a more detailed description of the observed data about the virus spread in different countries and regions. The hypothesis that fractal structures can be formed in cities as well as in larger networks is tested, indicating that indeed self-similarity may be found in networks connecting several cities.
The research findings are published in the peer reviewed journal by Elsevier called Chaos, Solitons & Fractals
The new model is based on the idea of fractals, which are never-ending patterns that create self-similar across different scales. Fractals, often seen in nature, appear in the spread of the SARS-CoV-2 virus that has wreaked havoc on the world in the currently, say the researchers.
For example, with transmission, an infected person initially passes the virus to relatively small group or people within direct contact. Then there is a break in transmission, soon after which we see the initial pattern repeated with the infected group transmits the virus to a larger group. This pattern continues consistently, explain the researchers.
This model aims to complement models typical of pandemic transmission tracing, like the SIR. The SIR, which stands for susceptible (S), infected (I), and removed (R), is based on the idea that a susceptible person can be infected, and an infected person will eventually be removed (either via immunization or death): the sum of this total number of individual remains constant throughout the evolution of the epidemic even as the numbers of individuals in each category shifts.
Typically in a SIR model, we see a model where the curve representing the number of COVID-19 infected people rises sharply during the initial phase when the pathogen is spreading rapidly, peaks at maximum contamination, and slopes down more gently as contagion slows until there are no longer any infectious people. T
The study team behind this research thought that this type of model was missing a key piece of the COVID-19 story.
Research author Airton Deppman, a Professor in the University of São Paulo’s Physics Institute (IF-USP) told Thailand Medical News, “Although this model is a very useful tool to investiga
te the temporal evolution of the pandemic, it provides few insights into how contagion progresses spatially, which is key to the planning of social distancing programs that effectively protect people and at the same time reduce the socio-economic impact of the disease.”
The new fractal-based model aims to address that gap. In developing the model, the research team used data for China, the United States, and the state of São Paulo, testing their findings on data for São Paulo and Europe in order to explore spatial distribution.
Deppman explained, “When you construct a graph crossing the number of infected people with the population and quantify the variables on a logarithmic scale on the x and y axes, the result is a straight line. This is typical of a fractal phenomenon, in which the same pattern is repeated at various scales. The model successfully described in great detail the temporal evolution of contagion. As a rule of thumb, the curve rises steeply at first, and this is followed by smaller peaks and troughs as the virus are transmitted from one area to the next.”
The study team says their model can be used to determine when social-distancing and quarantine measures should begin and end. They say, based on the data, these decisions should be made on a region by region case, instead of for an entire state or country.
In team concluded, “We investigated the existence of signatures of fractality in the spread of COVID-19 in China, USA, the state of So Paulo and Europe. We obtain the characteristic power-law behavior, indicative of scaling properties in the epidemic process. A model based on fractal structure of cities is proposed, and with this model we can describe not only the contamination rates for different populations, but also the time evolution of the contamination in each region. One important characteristic of the model is the definition of a probability of contamination that follows the q-exponential function common in Tsallis statistics.” https://link.springer.com/article/10.1007/BF01016429
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