Transmission rates and environmental reservoirs for COVID-19 - a modeling study

Abstract

The coronavirus disease 2019 (COVID-19) remains a global pandemic at present. Although the human-to-human transmission route for this disease has been well established, its transmission mechanism is not fully understood. In this paper, we propose a mathematical model for COVID-19 which incorporates multiple transmission pathways and which employs time-dependent transmission rates reflecting the impact of disease prevalence and outbreak control. Applying this model to a retrospective study based on publicly reported data in China, we argue that the environmental reservoirs play an important role in the transmission and spread of the coronavirus. This argument is supported by our data fitting and numerical simulation results for the city of Wuhan, for the provinces of Hubei and Guangdong, and for the entire country of China.

Keywords: 92D30; Disease transmission; compartmental modeling; data fitting.

Figure A1:

The relative sensitivities s(I, y) for the 9 parameters y ∈ P.

Figure 1:

Data fitting result for the cumulative confirmed cases in Wuhan city using both the direct and indirect transmission routes, for a period of 20 days from January 23, 2020 (day 1) to February 11, 2020 (day 20). The circles (in blue) denote the reported cases and the solid line (in red) denotes the fitting result.

Figure 2:

Simulation results for the cumulative confirmed cases in Wuhan city based on the data fitting result from Figure 1, for a period of 80 days from February 12, 2020 (day 1) to May 1, 2020 (day 80). The transmission rates are constants in this simulation. The circles (in blue) represent the reported data, and the solid and dashed lines (in red) represent the simulation results with and without incorporating the indirect transmission route, respectively.

Figure 3:

Data fitting and simulation results for Wuhan city without the indirect transmission route: (a) Data fitting for the cumulative confirmed cases from January 23, 2020 (day 1) to February 11, 2020 (day 20). (b) Simulation for the cumulative confirmed cases based on data fitting from part (a), for a period of 80 days from February 12, 2020 (day 1) to May 1, 2020 (day 80). The transmission rates are constants in the simulation.

Figure 4:

Data fitting and simulation results for Hubei province: (a) Data fitting for the cumulative confirmed cases using both the direct and indirect transmission routes, from January 23, 2020 (day 1) to February 11, 2020 (day 20). The circles denote the reported cases and the solid line denotes the fitting result. (b) Simulation for the cumulative confirmed cases based on data fitting from part (a), for a period of 80 days from February 12, 2020 (day 1) to May 1, 2020 (day 80). The transmission rates are constants in the simulation. (c) Data fitting for the cumulative confirmed cases using the direct transmission routes only, from January 23, 2020 (day 1) to February 11, 2020 (day 20). (d) Simulation for the cumulative confirmed cases based on data fitting from part (c), for a period of 80 days from February 12, 2020 (day 1) to May 1, 2020 (day 80). The transmission rates are constants in the simulation.

Figure 5:

Data fitting and simulation results for Guangdong province: (a) Data fitting for the cumulative confirmed cases using both the direct and indirect transmission routes, from January 23, 2020 (day 1) to February 11, 2020 (day 20). (b) Simulation for the cumulative confirmed cases based on data fitting from part (a), for a period of 80 days from February 12, 2020 (day 1) to May 1, 2020 (day 80). (c) Data fitting for the cumulative confirmed cases using the direct transmission routes only, from January 23, 2020 (day 1) to February 11, 2020 (day 20). (d) Simulation for the cumulative confirmed cases based on data fitting from part (c), for a period of 80 days from February 12, 2020 (day 1) to May 1, 2020 (day 80). The reported cases in Guangdong province increased significantly after March 15 (day 33) due to cases imported from abroad.

Figure 6:

Data fitting and simulation results for the entire country of China: (a) Data fitting for the cumulative confirmed cases using both the direct and indirect transmission routes, from January 23, 2020 (day 1) to February 11, 2020 (day 20). (b) Simulation for the cumulative confirmed cases based on data fitting from part (a), for a period of 80 days from February 12, 2020 (day 1) to May 1, 2020 (day 80). (c) Data fitting for the cumulative confirmed cases using the direct transmission routes only, from January 23, 2020 (day 1) to February 11, 2020 (day 20). (d) Simulation for the cumulative confirmed cases based on data fitting from part (c), for a period of 80 days from February 12, 2020 (day 1) to May 1, 2020 (day 80).

Figure 7:

Long-term simulation (200 days starting from February 12, 2020) for the numbers of infected individuals in two scenarios: with maximum disease control (where each transmission rate is fixed at its minimum), and with normal disease control (where each transmission rate varies with the infection level and time). (a) Wuhan city; (b) Hubei province; (c) Guangdong province; (d) the entire country of China. The simulation is based on model (2.1) with both the direct and indirect transmission routes.

Figure 8:

Data fitting and simulation results based on the modified reported data using the reporting rates estimated in [10]: (a)(b) Wuhan city; (c)(d) Hubei province; (e)(f) Guangdong province; (g)(h) the entire country of China. Left panel: fitting from Jan 23 to Feb 11, 2020; Right panel: simulation from Feb 12 to May 1, 2020.