Forecasting of COVID-19 time series for countries in the world based on a hybrid approach combining the fractal dimension and fuzzy logic

Abstract

We describe in this paper a hybrid intelligent approach for forecasting COVID-19 time series combining fractal theory and fuzzy logic. The mathematical concept of the fractal dimension is used to measure the complexity of the dynamics in the time series of the countries in the world. Fuzzy Logic is used to represent the uncertainty in the process of making a forecast. The hybrid approach consists on a fuzzy model formed by a set of fuzzy rules that use as input values the linear and nonlinear fractal dimensions of the time series and as outputs the forecast for the countries based on the COVID-19 time series of confirmed cases and deaths. The main contribution is the proposed hybrid approach combining the fractal dimension and fuzzy logic for enabling an efficient and accurate forecasting of COVID-19 time series. Publicly available data sets of 10 countries in the world have been used to build the fuzzy model with time series in a fixed period. After that, other periods of time were used to verify the effectiveness of the proposed approach for the forecasted values of the 10 countries. Forecasting windows of 10 and 30 days ahead were used to test the proposed approach. Forecasting average accuracy is 98%, which can be considered good considering the complexity of the COVID problem. The proposed approach can help people in charge of decision making to fight the pandemic can use the information of a short window to decide immediate actions and also the longer window (like 30 days) can be beneficial in long term decisions.

Keywords: COVID-19; Forecasting; Fractal dimension; Fuzzy logic; Time series.

Fig. 1

Box counting algorithm for an arbitrary curve.

Fig. 2

Structure of the proposed method for fuzzy fractal time series forecasting.

Fig. 3

Structure of the fuzzy fractal model for forecasting the Countries based on COVID-19 data.

Fig. 4

Fuzzy rules expressing the forecasting knowledge in the fuzzy model.

Fig. 5

Output membership functions of the forecasting fuzzy system of the Countries.

Fig. 6

Input membership functions for the LFDD linguistic variable.

Fig. 7

Plot of confirmed cases for Belgium.

Fig. 8

Plot of confirmed cases for Italy.

Fig. 9

Plot of death cases for Belgium.

Fig. 10

Plot of death cases for China.

Fig. 11

Forecasting the confirmed cases of Covid-19 in Belgium.

Fig. 12

Forecasting the confirmed cases of Covid-19 in Germany.

Fig. 13

Forecasting the confirmed cases of Covid-19 in United States.

Fig. 14

Forecasting the confirmed cases of Covid-19 in Spain.

Fig. 15

Forecasting the confirmed cases of Covid-19 in Italy.

Fig. 16

Forecasting Confirmed cases of Covid-19 in 10 countries, 1 Belgium, 2 China, 3 France, 4 Germany, 5 Iran, 6 Italy, 7 Spain, 8 Turkey, 9 United Kingdom, 10 United States (April 16 of 2020 to April 25 of 2020).

Fig. 17

Forecasting errors in 10 countries, 1 Belgium, 2 China, 3 France, 4 Germany, 5 Iran, 6 Italy, 7 Spain, 8 Turkey, 9 United Kingdom, 10 United States.

Fig. 18

Forecasting the confirmed cases of Belgium from 22 Jul to 1 August.

Fig. 19

Forecasting France confirmed cases from 22 Jul to 1 August.

Fig. 20

Forecasting Germany confirmed cases from 22 Jul to 1 August.

Fig. 21

Forecasting Italy confirmed cases from 22 Jul to 1 August.

Fig. 22

Forecasting Spain confirmed cases from 22 July to 1 August.

Fig. 23

Forecasting United States from 22 July to 1 August.

Fig. 24

Forecasting the confirmed cases of Covid-19 in Mexico from 22 July to 1 August.

Fig. 25

Forecasting errors in 10 countries: 1) Belgium, 2) France, 3) Germany, 4) Iran, 5) Italy, 6) Mexico, 7) Spain, 8) Turkey, 9) United Kingdom, 10) United States for the period of July 22 to 1 August 2020.

Fig. 26

Forecasting Belgium Covid-19 confirmed cases from 8 July to 7 August 2020.

Fig. 27

Forecasting Spain Covid-19 confirmed cases from 8 July to 7 August 2020.

Fig. 28

Forecasting USA Covid-19 confirmed cases from 8 July to 7 August 2020.

Fig. 29

Forecasting Mexico Covid-19 confirmed cases from 8 July to 7 August 2020.