Chaotic model for COVID-19 growth factor
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Chaotic model for COVID-19 growth factor Thiago de Salazar e Fernandes 1 Received: 13 April 2020 / Accepted: 8 July 2020 # Sociedade Brasileira de Engenharia Biomedica 2020
Abstract Purpose The new COVID-19 pandemic caused by SARS-CoV-2 initiated in the world a large quarantine, due to the exponential capacity of the virus in spreading from human contact. In the present work, the dynamics of such spreading was evaluated by the analysis of the growth factor of the disease. Method It was applied the space phase of the time series, the detrended fluctuation analysis (DFA) of the series, and the fractal dimension of the space phase. Results It was possible to notice a strange attractor in the space phase of the growth factor indicating that the process is a deterministic chaos. The value of the alpha coefficient by DFA showed to be less than 0.5, characteristic of anti-persistent long-range memory, in which large events alternate with small events, and vice-versa. The fractal dimension of the phase space set was a fractal number, between 1 and 2, another indicator that the growth factor of the disease is not random. Conclusion This global analysis is pointing that the spread of COVID-19 is a deterministic chaos, with long-range memory. Understanding such dynamics may help the control of this disease. Keywords Fractal analysis . Deterministic chaos . Detrended fluctuation analysis . Coronavirus . COVID-19
Introduction Some processes in nature can be described as being nonlinear, which means that just small changes in the starting point can lead to enormous consequences. This is the case of the new infections by SARS-CoV-2 and the emergence of COVID-19 in the world. Just small changes in the genome of the first virus, SARS-CoV epidemics in 2002, resulted in a more severe spread and human infection of SARS-CoV-2, leading to the pandemic of COVID-19. Recently, many countries in the world started the suppression of the virus by quarantine, with social distance of healthy individuals and isolation of the elders or those with clinical symptoms such as fever. Schools, works, and shopping centers were closed. If the governments do not act in suppression, but only in mitigation, the number of deaths would reach thousands in some countries and millions in the world (Ferguson et al. 2020).
* Thiago de Salazar e Fernandes [email protected] 1
Departamento de Biofísica e Radiobiologia, Universidade Federal de Pernambuco, Avenida Moraes Rego, 1235, Cidade Universitária, Recife, PE 50670-901, Brazil
Understanding exponential growth is difficult for human minds that evolved in a world in which daily tasks need only the linearity of events. It is hard to figure out that when we reach 30 steps in an exponential manner, we do not reach something linear to that such as 30 “something,” but we are already in the scale of millions. Therefore, it is necessary to act early in prevention of SARS in order to avoid the collapse of the health system. But if the understanding of exponential growth is already diffi
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