Calculation of $R_0$ for age-of-infection models
We consider age-of-infection epidemic models to describe multiple-stage epidemic models, including treatment. We derive an expression for thebasic reproduction number $R_0$ in terms of the distributions of periods of stayin the various compartments. We find that, in the model without treatment,$R_0$...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2008-05-01
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| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.585 |
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| Summary: | We consider age-of-infection epidemic models to describe multiple-stage epidemic models, including treatment. We derive an expression for thebasic reproduction number $R_0$ in terms of the distributions of periods of stayin the various compartments. We find that, in the model without treatment,$R_0$ depends only on the mean periods in compartments, and not on the formof the distributions. In treatment models, $R_0$ depends on the form of the dis-tributions of stay in infective compartments from which members are removedfor treatment, but the dependence for treatment compartments is only on themean stay in the compartments. The results give a considerable simplificationin the calculation of the basic reproduction number. |
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| ISSN: | 1551-0018 |