Covid-19 growth rate analysis: application of a low-complexity tool for understanding and comparing epidemic curves

The acceleration of new cases is important for the characterization and comparison of epidemic curves. The objective of this study was to quantify the acceleration of daily confirmed cases and death curves using the polynomial interpolation method.

METHODS:

Covid-19 epidemic curves from Brazil, Germany, the United States, and Russia were obtained. We calculated the instantaneous acceleration of the curve using the first derivative of the representative polynomial.

RESULTS:

The acceleration for all curves was obtained.

CONCLUSIONS:

Incorporating acceleration into an analysis of the Covid-19 time series may enable a better understanding of the epidemiological situation.

Keywords:
Covid-19; SARS-CoV-2; Polynomial interpolation

Authorship

Airandes de Sousa Pinto

Universidade Estadual de Feira de Santana, Departamento de Saúde, Feira de Santana, BA, Brasil. Universidade Estadual de Feira de SantanaBrasilFeira de Santana, BA, Brasil Universidade Estadual de Feira de Santana, Departamento de Saúde, Feira de Santana, BA, Brasil.

http://orcid.org/0000-0003-3526-5263

Edval Gomes dos Santos Júnior

Carlos Alberto Rodrigues

Universidade Estadual de Feira de Santana, Departamento de Ciências Exatas, Feira de Santana, BA, Brasil.Universidade Estadual de Feira de SantanaBrasilFeira de Santana, BA, Brasil Universidade Estadual de Feira de Santana, Departamento de Ciências Exatas, Feira de Santana, BA, Brasil.

Paulo Cesar Mendes Nunes

Livia Almeida da Cruz

Grupo Baiano de Oncologia, Feira de Santana, BA, Brasil. Grupo Baiano de OncologiaBrasilFeira de Santana, BA, Brasil Grupo Baiano de Oncologia, Feira de Santana, BA, Brasil.

Matheus Gomes Reis Costa

Manoel Otávio da Costa Rocha

Universidade Federal de Minas Gerais, Faculdade de Medicina, Programa de Pós-Graduação em Infectologia e Medicina Tropical, Belo Horizonte, MG, Brasil. Universidade Federal de Minas GeraisBrasilBelo Horizonte, MG, Brasil Universidade Federal de Minas Gerais, Faculdade de Medicina, Programa de Pós-Graduação em Infectologia e Medicina Tropical, Belo Horizonte, MG, Brasil.

Corresponding author: Airandes de Sousa Pinto. e-mail:airandes@uefs.br

Authors’ contribution:ASP: Study design, Data Collection, Data analysis, Article drafting, Critical revision, Final approval of submission; EGSJ: Study design, Article drafting, Final approval of submission; CAR: Study design; Data analysis, Article drafting, Critical revision, Final approval of submission; PCMN: Data Collection; LAC: Study design, Article drafting, Final approval of submission; MGRC: Data Collection; MOCR: Study design, Data analysis, Article drafting, Critical revision, Final approval of submission.

Conflict of interest: The authors declare that there is no conflict of interest.

SCIMAGO INSTITUTIONS RANKINGS

Grupo Baiano de Oncologia, Feira de Santana, BA, Brasil. Grupo Baiano de OncologiaBrasilFeira de Santana, BA, Brasil Grupo Baiano de Oncologia, Feira de Santana, BA, Brasil.

Figures | Tables | Formulas

Figures (2)
Tables (1)
Formulas (1)

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FIGURE 1:
1A: Polynomial x curve of new cases in Brazil. 1B: Polynomial x curves of new cases in Germany. 1C: Instantaneous acceleration curve in Brazil. 1D: Instantaneous acceleration curve in Germany. A - Maximum acceleration limit between A1 and A2 intervals. P - Peak of new cases, limit between the acceleration (A1 + A2) and deceleration phases of reports (D1 + D2). D - Maximum deceleration (absolute value), limit between D1 and D2 intervals. Intervals: A1 - First stage of curve acceleration phase, increase in new cases. A2 - Second stage of curve acceleration phase, increase in new cases and decrease in acceleration to zero over time. Acceleration value decreases and remains positive until reaching zero. D1 - First stage of deceleration phase, decrease in new cases, and acceleration becomes increasingly negative until reaching D. D2 - Second stage of deceleration phase, decrease in new cases, and acceleration returns to zero over time. New cases in Brazil = 3.8 x 10 ^-11 day⁸ - 1.4 x 10 ^-8 day⁷ + 1.5 x 10 ^-6 day⁶ + 2.3 x 10 ^-5 day⁵ - 1.4 x 10 ^-2 day⁴ + 9.8 x 10 ^-1 day³ - 2.9 x 10 day² + 3.9 x 10 ² day - 1.9 x 10 ³. New cases in Germany= 2.4 x 10 ^-9 day ⁸ - 8.7 x 10 ^-7 day ⁷ + 1.3 x 10 ^-4 day⁶ - 9.2 x 10 ^-3 day⁵ + 3.5 x 10^-1 day⁴ - 6.5 x day³ + 5.4 x 10 day² -1.5 x 10² day + 5.6 x 10.

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FIGURE 2:
2A: Polynomial x daily death curve in Brazil. 2B: Polynomial x daily death curve in Germany. 2C: Curve of instantaneous acceleration of daily deaths in Brazil. 2D: Curve of instantaneous acceleration of daily deaths in Germany. A - Maximum acceleration, limit between A1 and A2 intervals. P - Peak daily deaths, limit between acceleration (A1 + A2) and deceleration phases of reports (D1 + D2). D - Maximum deceleration (absolute value) in historical series, limit between D1 and D2 intervals. Intervals: A1- First stage of death curve acceleration phase, increase in deaths, and increased acceleration over time. A2- Second stage of curve acceleration phase, growth in death numbers, and decrease in acceleration to zero over time. Acceleration value decreases and remains positive until reaching zero. D1- First stage of deceleration phase, decrease in new deaths, and acceleration becomes increasingly negative until reaching D. D2- Second stage of deceleration phase, decrease in deaths, and acceleration returns to zero over time. Daily deaths in Brazil = -1.1 x 10 ^-10 day ⁸ + 4.1 x 10 ^-8.day ⁷ - 6.5 x 10 ^-6 day ⁶ + 5.6 x 10 ^-4 Day⁵ -2.8 x 10 ^-2 day ⁴ + 8.5 x 10 ^-1 Day³ - 1.5 x 10 day² + 1.4 x 10 ² day - 5.3 x 10². Daily deaths in Germany = -2.6 x 10^-12 day⁸ - 1.7 x 10^-9 day⁷ + 7.4 x 10^-7day⁶ - 9.9 x 10^-5. day⁵ + 6.2 x 10 ^-3 day⁴ - 1.9 x 10 ^-1 day³ + 2.7 day² - 1.6 x 10 day + 2.3.x 10.

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TABLE 1:
Characteristics of curves for new case and new death for the countries under study.

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FIGURE 1: 1A: Polynomial x curve of new cases in Brazil. 1B: Polynomial x curves of new cases in Germany. 1C: Instantaneous acceleration curve in Brazil. 1D: Instantaneous acceleration curve in Germany. A - Maximum acceleration limit between A1 and A2 intervals. P - Peak of new cases, limit between the acceleration (A1 + A2) and deceleration phases of reports (D1 + D2). D - Maximum deceleration (absolute value), limit between D1 and D2 intervals. Intervals: A1 - First stage of curve acceleration phase, increase in new cases. A2 - Second stage of curve acceleration phase, increase in new cases and decrease in acceleration to zero over time. Acceleration value decreases and remains positive until reaching zero. D1 - First stage of deceleration phase, decrease in new cases, and acceleration becomes increasingly negative until reaching D. D2 - Second stage of deceleration phase, decrease in new cases, and acceleration returns to zero over time. New cases in Brazil = 3.8 x 10 ^-11 day⁸ - 1.4 x 10 ^-8 day⁷ + 1.5 x 10 ^-6 day⁶ + 2.3 x 10 ^-5 day⁵ - 1.4 x 10 ^-2 day⁴ + 9.8 x 10 ^-1 day³ - 2.9 x 10 day² + 3.9 x 10 ² day - 1.9 x 10 ³. New cases in Germany= 2.4 x 10 ^-9 day ⁸ - 8.7 x 10 ^-7 day ⁷ + 1.3 x 10 ^-4 day⁶ - 9.2 x 10 ^-3 day⁵ + 3.5 x 10^-1 day⁴ - 6.5 x day³ + 5.4 x 10 day² -1.5 x 10² day + 5.6 x 10.

FIGURE 2: 2A: Polynomial x daily death curve in Brazil. 2B: Polynomial x daily death curve in Germany. 2C: Curve of instantaneous acceleration of daily deaths in Brazil. 2D: Curve of instantaneous acceleration of daily deaths in Germany. A - Maximum acceleration, limit between A1 and A2 intervals. P - Peak daily deaths, limit between acceleration (A1 + A2) and deceleration phases of reports (D1 + D2). D - Maximum deceleration (absolute value) in historical series, limit between D1 and D2 intervals. Intervals: A1- First stage of death curve acceleration phase, increase in deaths, and increased acceleration over time. A2- Second stage of curve acceleration phase, growth in death numbers, and decrease in acceleration to zero over time. Acceleration value decreases and remains positive until reaching zero. D1- First stage of deceleration phase, decrease in new deaths, and acceleration becomes increasingly negative until reaching D. D2- Second stage of deceleration phase, decrease in deaths, and acceleration returns to zero over time. Daily deaths in Brazil = -1.1 x 10 ^-10 day ⁸ + 4.1 x 10 ^-8.day ⁷ - 6.5 x 10 ^-6 day ⁶ + 5.6 x 10 ^-4 Day⁵ -2.8 x 10 ^-2 day ⁴ + 8.5 x 10 ^-1 Day³ - 1.5 x 10 day² + 1.4 x 10 ² day - 5.3 x 10². Daily deaths in Germany = -2.6 x 10^-12 day⁸ - 1.7 x 10^-9 day⁷ + 7.4 x 10^-7day⁶ - 9.9 x 10^-5. day⁵ + 6.2 x 10 ^-3 day⁴ - 1.9 x 10 ^-1 day³ + 2.7 day² - 1.6 x 10 day + 2.3.x 10.

TABLE 1: Characteristics of curves for new case and new death for the countries under study.

		Brazil		USA		Russia		Germany
		day	number	day	number	day	number	day	number
Daily new cases	Maximum acceleration (new cases/day²)	89	466.0	40	1,690.6	75	379.0	33	320.7
	Peak (new cases/day)			50	34,517.0	87	11,656.0	42	6,933
	Maximum deceleration (new cases/day²)							59	-261.9
Daily new deaths	Maximum acceleration (new deaths/day²)	83	30.4	47	107.9	66	3.2	45	11.5
	Peak (new deaths/day)			67	2,683.0	92	119.0	54	333
	Maximum deceleration (new deaths/day²)			73	-46.1			73	-9.0

a_{n .} {d a y}^{n} + a_{n - 1 .} {d a y}^{n - 1} +_{\dots} + a_{1 .} d a y + a_{0;} n \in N

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Métricas

Covid-19 growth rate analysis: application of a low-complexity tool for understanding and comparing epidemic curves

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Mensagem

[1] Corresponding author: Airandes de Sousa Pinto. e-mail:airandes@uefs.br