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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The cumulative number of SARS cases in Hong Kong community (and the simulated case "b").
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Figure 6: The cumulative number of SARS cases in Hong Kong community (and the simulated case "b").

Mentions: We consider here the extreme case that IP(0) = 10, that is only 10 Hong Kong people are infected by disease B. S(0) is assumed to be 6.8 million and we still assume that E(0) = 100 and I(0) = 50. The parameters obtained by the gradient-based optimization algorithm are as follows: r = 10.08 × 10-8, rP = 7.94 × 10-8, a = 0.52, aP = 0.12 and b = 0.105. The resulting curve for R fits well with the observed total number of confirmed cases of SARS from the community from 17 March, 2003 to 10 May, 2003 (totally 55 days). Figure 6 is the curve for R, while Figure 7 shows the expected and observed daily new cases. The limiting value of the curve R is 1033. Note that a = 0.52 and b = 0.105 and therefore 1/a + 1/b = 11.44 which is close to the observed figure 10.12. Both the parameters rP and a are greater than the corresponding parameters in case a. This is reasonable as the initial population IP(0) = 10 is much smaller than the previous case. Therefore disease B needs to spread much faster in order to "protect" people from being infected by SARS.


A double epidemic model for the SARS propagation.

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

The cumulative number of SARS cases in Hong Kong community (and the simulated case "b").
© Copyright Policy
Related In: Results  -  Collection

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

Figure 6: The cumulative number of SARS cases in Hong Kong community (and the simulated case "b").
Mentions: We consider here the extreme case that IP(0) = 10, that is only 10 Hong Kong people are infected by disease B. S(0) is assumed to be 6.8 million and we still assume that E(0) = 100 and I(0) = 50. The parameters obtained by the gradient-based optimization algorithm are as follows: r = 10.08 × 10-8, rP = 7.94 × 10-8, a = 0.52, aP = 0.12 and b = 0.105. The resulting curve for R fits well with the observed total number of confirmed cases of SARS from the community from 17 March, 2003 to 10 May, 2003 (totally 55 days). Figure 6 is the curve for R, while Figure 7 shows the expected and observed daily new cases. The limiting value of the curve R is 1033. Note that a = 0.52 and b = 0.105 and therefore 1/a + 1/b = 11.44 which is close to the observed figure 10.12. Both the parameters rP and a are greater than the corresponding parameters in case a. This is reasonable as the initial population IP(0) = 10 is much smaller than the previous case. Therefore disease B needs to spread much faster in order to "protect" people from being infected by SARS.

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