A double epidemic model for the SARS propagation

Abstract

Background: An epidemic of a Severe Acute Respiratory Syndrome (SARS) caused by a new coronavirus has spread from the Guangdong province to the rest of China and to the world, with a puzzling contagion behavior. It is important both for predicting the future of the present outbreak and for implementing effective prophylactic measures, to identify the causes of this behavior.

Results: In this report, we show first that the standard Susceptible-Infected-Removed (SIR) model cannot account for the patterns observed in various regions where the disease spread. We develop a model involving two superimposed epidemics to study the recent spread of the SARS in Hong Kong and in the region. We explore the situation where these epidemics may be caused either by a virus and one or several mutants that changed its tropism, or by two unrelated viruses. This has important consequences for the future: the innocuous epidemic might still be there and generate, from time to time, variants that would have properties similar to those of SARS.

Conclusion: We find that, in order to reconcile the existing data and the spread of the disease, it is convenient to suggest that a first milder outbreak protected against the SARS. Regions that had not seen the first epidemic, or that were affected simultaneously with the SARS suffered much more, with a very high percentage of persons affected. We also find regions where the data appear to be inconsistent, suggesting that they are incomplete or do not reflect an appropriate identification of SARS patients. Finally, we could, within the framework of the model, fix limits to the future development of the epidemic, allowing us to identify landmarks that may be useful to set up a monitoring system to follow the evolution of the epidemic. The model also suggests that there might exist a SARS precursor in a large reservoir, prompting for implementation of precautionary measures when the weather cools down.

Figure 1

Typical dynamics for the SIR model.

Figure 2

Daily new number of confirmed SARS cases from Hong Kong: hospital, community and the Amoy Gardens.

Figure 3

Comparison of the SEIR (red) and SIR (green) models with the same parameters "r" and "a". SEIR model evolution (in red) is much slower (and thus may seam less severe) but reaches the same final size of epidemic.

Figure 4

The cumulative number of SARS cases in Hong Kong community (and the simulated case "a").

Figure 5

Number of SARS cases in Hong Kong community (and the simulated case "a") per three days.

Figure 6

The cumulative number of SARS cases in Hong Kong community (and the simulated case "b").

Figure 7

Number of SARS cases in Hong-Kong community (and the simulated case "b") per three days.

Figure 8

Cumulative number of SARS cases in Beijing.

Figure 9

Number of SARS cases per day in Beijing.

Figure 10

Cumulative number of SARS cases in Inner Mongolia.

Figure 11

Number of SARS cases per day in Inner Mongolia.