Parameter estimation of the COVID-19 transmission model using an improved quantum-behaved particle swarm optimization algorithm

Abstract

The outbreak of coronavirus disease (COVID-19) and its accompanying pandemic have created an unprecedented challenge worldwide. Parametric modeling and analyses of the COVID-19 play a critical role in providing vital information about the character and relevant guidance for controlling the pandemic. However, the epidemiological utility of the results obtained from the COVID-19 transmission model largely depends on accurately identifying parameters. This paper extends the susceptible-exposed-infectious-recovered (SEIR) model and proposes an improved quantum-behaved particle swarm optimization (QPSO) algorithm to estimate its parameters. A new strategy is developed to update the weighting factor of the mean best position by the reciprocal of multiplying the fitness of each best particle with the average fitness of all best particles, which can enhance the global search capacity. To increase the particle diversity, a probability function is designed to generate new particles in the updating iteration. When compared to the state-of-the-art estimation algorithms on the epidemic datasets of China, Italy and the US, the proposed method achieves good accuracy and convergence at a comparable computational complexity. The developed framework would be beneficial for experts to understand the characteristics of epidemic development and formulate epidemic prevention and control measures.

Keywords: COVID-19; Mathematical modeling; Parameter estimation; Quantum-behaved particle swarm optimization.

Fig. 1

The SEAIQRD model. Graphic scheme of interaction of different stages in mathematical model SEAIQRD: S, susceptible (uninfected); E, exposed; A, asymptomatic infectious (undetected); I, symptomatic infectious (undetected); Q, confirmed (under quarantine); R, recovered; D, dead.

Fig. 2

The overview of the proposed algorithm.

Algorithm 1

The QPSO method for identifying the SEAIQRD model parameters.

Algorithm 2

The proposed method for identifying the SEAIQRD model parameters.

Fig. 3

China: Graphical validation of the different methods. a, the proposed method. b, WQPSO. c, QPSO. d, PSO. e, GA. f, LS. g, the approach in . The colored solid line represents the model fitting results; the black dotted line represents the observed data. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

Fig. 4

Italy: Graphical validation of the different methods. a, the proposed method. b, WQPSO. c, QPSO. d, PSO. e, GA. f, LS. g, the approach in . The colored solid line represents the model fitting results; the black dotted line represents the observed data.

Fig. 5

The US: Graphical validation of the different methods. a, the proposed method. b, WQPSO. c, QPSO. d, PSO. e, GA. f, LS. g, the approach in . The colored solid represents the model fitting results; the black dotted line represents the observed data.

Fig. 6

Comparative analysis of the prediction results. The ordinate is the number of cumulative infection case, it consists of the active confirmed cases (Q), the recovered cases (R) and the deaths (D). The abscissa is the number of days. a. China epidemic dataset; b. Italy epidemic dataset; c. the US epidemic dataset.

Fig. 7

Comparison of the convergence.