A mathematical model for the novel coronavirus epidemic in Wuhan, China

Abstract

We propose a mathematical model to investigate the current outbreak of the coronavirus disease 2019 (COVID-19) in Wuhan, China. Our model describes the multiple transmission pathways in the infection dynamics, and emphasizes the role of the environmental reservoir in the transmission and spread of this disease. Our model also employs non-constant transmission rates which change with the epidemiological status and environmental conditions and which reflect the impact of the on-going disease control measures. We conduct a detailed analysis of this model, and demonstrate its application using publicly reported data. Among other findings, our analytical and numerical results indicate that the coronavirus infection would remain endemic, which necessitates long-term disease prevention and intervention programs.

Keywords: COVID-19; basic reproduction number; compartmental modeling.

Figure 1.

Cumulative confirmed cases for the city of Wuhan from January 23, 2020 to February 10, 2020. Circles (in blue) denote the reported cases and solid line (in red) denotes the simulation result. The basic reproduction number is ${\mathcal{R}}_0=4.25$ based on the parameters from Table 1 and the result of data fitting.

Figure 2.

A simulation result for the outbreak size in Wuhan using the transmission rates formulated in Eq (3.1), the parameters from Table 1, and the result of data fitting.

Figure 3.

A typical phase portrait for I vs. E with ${\mathcal{R}}_0=4.25$. Every orbit starts with a different initial point and converges to the endemic equilibrium where (E_*, I_*) = (1353, 2735).

Figure 4.

A simulation result for the outbreak size in Wuhan using the constant transmission rates given in Eq (3.2), the parameters from Table 1, and the result of data fitting.