A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action

Abstract

The ongoing coronavirus disease 2019 (COVID-19) outbreak, emerged in Wuhan, China in the end of 2019, has claimed more than 2600 lives as of 24 February 2020 and posed a huge threat to global public health. The Chinese government has implemented control measures including setting up special hospitals and travel restriction to mitigate the spread. We propose conceptual models for the COVID-19 outbreak in Wuhan with the consideration of individual behavioural reaction and governmental actions, e.g., holiday extension, travel restriction, hospitalisation and quarantine. We employe the estimates of these two key components from the 1918 influenza pandemic in London, United Kingdom, incorporated zoonotic introductions and the emigration, and then compute future trends and the reporting ratio. The model is concise in structure, and it successfully captures the course of the COVID-19 outbreak, and thus sheds light on understanding the trends of the outbreak.

Keywords: COVID-19; City lockdown; Epidemic; Governmental action; Individual reaction; Mathematical modelling.

Figure 1

The timeline of the facts of COVID-19 and control measures implemented in Wuhan, China from December 2019 to February 2020. The red dots are the events in the COVID-19 outbreak, and the blue dots are the control measures.

Figure 2

The daily number of (a) cases or (b) deaths, cumulative number of (c) cases or (d) deaths, and the percentage of (e) cases or (f) deaths, of COVID-19 in Wuhan, China. In panel (f), the 100% represents the count of deaths or cured cases.

Figure 3

Comparison between different sources of reported cases: official released data (NHCPRC, 2020) in red, data from Li et al. (denoted as NEJM) (Li et al., 2020) in green, from Liu et al. (denoted as GDCDC) (Liu et al., 2020) in blue, and from P. Wu et al. (denoted as Eurosurv) (P. Wu et al., 2020) in purple.

Figure 4

(a) Daily new cases with a reporting delay of 14 days under three scenarios: naive (i.e., no action taken) as grey dotted curve, individual reaction regarding to the outbreak as red dashed curve, and individual reaction plus governmental action as green solid curve and reported cases (from official release and (Li et al., 2020) as grey curve with dotes. (b) The reporting ratio between reported cases and estimates when individual reaction and governmental action are involved.

Figure 5

Sensitivity analyses on α and κ. We simulate the base model with both individual reaction and governmental action while varying α and κ. We show model outcome when (a) α = 0.5 (black solid), 0.6 (red dashed), 0.7 (green dotted), 0.8 (blue dash-dotted) and 0.9 (cyan long dashed curve), while κ = 1117.3, when (b) κ = 100 (black solid), 500 (red dashed), 900 (green dotted), 1300 (blue dash-dotted) and 1700 (cyan long dashed curve), while α = 0.8478. Grey dots show the reported cases.