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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| Language: | English |
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AIMS Press
2008-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.585 |
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| author | Christine K. Yang Fred Brauer |
| author_facet | Christine K. Yang Fred Brauer |
| author_sort | Christine K. Yang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9dc659548ea649aaaf512e425fdff60b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9dc659548ea649aaaf512e425fdff60b2025-01-24T01:58:24ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-05-015358559910.3934/mbe.2008.5.585Calculation of $R_0$ for age-of-infection modelsChristine K. Yang0Fred Brauer1Harvard Graduate School of Education, Harvard University, Cambridge, MA 02138Harvard Graduate School of Education, Harvard University, Cambridge, MA 02138We 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.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.585basic reproduction numberepidemic modelsage-of-infection modelstreatment models. |
| spellingShingle | Christine K. Yang Fred Brauer Calculation of $R_0$ for age-of-infection models Mathematical Biosciences and Engineering basic reproduction number epidemic models age-of-infection models treatment models. |
| title | Calculation of $R_0$ for age-of-infection models |
| title_full | Calculation of $R_0$ for age-of-infection models |
| title_fullStr | Calculation of $R_0$ for age-of-infection models |
| title_full_unstemmed | Calculation of $R_0$ for age-of-infection models |
| title_short | Calculation of $R_0$ for age-of-infection models |
| title_sort | calculation of r 0 for age of infection models |
| topic | basic reproduction number epidemic models age-of-infection models treatment models. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.585 |
| work_keys_str_mv | AT christinekyang calculationofr0forageofinfectionmodels AT fredbrauer calculationofr0forageofinfectionmodels |