The susceptible-unidentified infected-confirmed (SUC) epidemic model for estimating unidentified infected population for COVID-19

Abstract

In this article, we propose the Susceptible-Unidentified infected-Confirmed (SUC) epidemic model for estimating the unidentified infected population for coronavirus disease 2019 (COVID-19) in China. The unidentified infected population means the infected but not identified people. They are not yet hospitalized and still can spread the disease to the susceptible. To estimate the unidentified infected population, we find the optimal model parameters which best fit the confirmed case data in the least-squares sense. Here, we use the time series data of the confirmed cases in China reported by World Health Organization. In addition, we perform the practical identifiability analysis of the proposed model using the Monte Carlo simulation. The proposed model is simple but potentially useful in estimating the unidentified infected population to monitor the effectiveness of interventions and to prepare the quantity of protective masks or COVID-19 diagnostic kit to supply, hospital beds, medical staffs, and so on. Therefore, to control the spread of the infectious disease, it is essential to estimate the number of the unidentified infected population. The proposed SUC model can be used as a basic building block mathematical equation for estimating unidentified infected population.

Keywords: COVID-19; Epidemic model; Least-squares fitting.

Fig. 1

Epidemic curve of COVID-19 confirmed cases from 21 January to 24 February 2020.

Fig. 2

Flow chart of the SUC model: S is susceptible, U is infected but not confirmed (i.e., unidentified infected), and C is confirmed or removed. Here, the removed indicates the recovered or dead cases.

Fig. 3

Computational results: (a), (b), and (c) are results with $N={10}^9,{10}^8,{10}^7$and $p=22$; (d), (e), and (f) are results with $N={10}^9,{10}^8,{10}^7$and $p=14$; (g), (h), and (i) are results with $N={10}^9,{10}^8,{10}^7$and $p=7$.

Fig. 4

(a), (b), and (c) are results with $p=8$and $N={10}^9,{10}^8,$and 10⁷, respectively, from 17 February 2020.