Limits...
A double epidemic model for the SARS propagation.

Ng TW, Turinici G, Danchin A - BMC Infect. Dis. (2003)

Bottom Line: 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.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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Mathematics, The University of Hong Kong, Hong Kong, China. ntw@maths.hku.hk

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.

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Number of SARS cases per day in Beijing.
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Figure 9: Number of SARS cases per day in Beijing.

Mentions: We have also applied the SEIRP model to study the outbreak of SARS in Beijing. The statistics on the numbers of SARS cases in Beijing are obtained from . The initial population S(0) was set to be 13.82 millions; the other parameters (including the initial conditions) that characterise the model were optimised to obtain the best fit; we obtained thus E(0) = 400; IP(0) = 35000; I(0) = 340; R(0) = 0; RP(0) = 0; r = 7.69 × 10-8; rP = 10.79 × 10-8; a = 0.488; aP = 0.618; b = 0.103. Figure 8 and 9 show that the model fit well with the observation in both the numbers cumulative cases and the daily new cases. The total number of people infected with the protective virus is RP = 12 millions. If the values of the parameters defining the model remain the same this simulation results in a final value of the total people infected with the SARS virus (that is R∞) at the level of 2700.


A double epidemic model for the SARS propagation.

Ng TW, Turinici G, Danchin A - BMC Infect. Dis. (2003)

Number of SARS cases per day in Beijing.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC222908&req=5

Figure 9: Number of SARS cases per day in Beijing.
Mentions: We have also applied the SEIRP model to study the outbreak of SARS in Beijing. The statistics on the numbers of SARS cases in Beijing are obtained from . The initial population S(0) was set to be 13.82 millions; the other parameters (including the initial conditions) that characterise the model were optimised to obtain the best fit; we obtained thus E(0) = 400; IP(0) = 35000; I(0) = 340; R(0) = 0; RP(0) = 0; r = 7.69 × 10-8; rP = 10.79 × 10-8; a = 0.488; aP = 0.618; b = 0.103. Figure 8 and 9 show that the model fit well with the observation in both the numbers cumulative cases and the daily new cases. The total number of people infected with the protective virus is RP = 12 millions. If the values of the parameters defining the model remain the same this simulation results in a final value of the total people infected with the SARS virus (that is R∞) at the level of 2700.

Bottom Line: 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.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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Mathematics, The University of Hong Kong, Hong Kong, China. ntw@maths.hku.hk

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.

Show MeSH
Related in: MedlinePlus