Subthreshold coexistence of strains: the impact of vaccination and mutation
We consider a model for a disease withtwo competing strains and vaccination.The vaccine provides complete protection against one of the strains(strain 2) but onlypartial protection against the other (strain 1). The partial protection leads toexistence of subthreshold equilibria of strain 1. If the...
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| Format: | Article |
| Language: | English |
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AIMS Press
2007-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.287 |
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| _version_ | 1832590235859419136 |
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| author | Maia Martcheva Mimmo Iannelli Xue-Zhi Li |
| author_facet | Maia Martcheva Mimmo Iannelli Xue-Zhi Li |
| author_sort | Maia Martcheva |
| collection | DOAJ |
| description | We consider a model for a disease withtwo competing strains and vaccination.The vaccine provides complete protection against one of the strains(strain 2) but onlypartial protection against the other (strain 1). The partial protection leads toexistence of subthreshold equilibria of strain 1. If the first strain mutates into the second, there are subthreshold coexistence equilibriawhen both vaccine-dependent reproduction numbers are below one.Thus, a vaccine that is specific toward the second strainand that, in absence of other strains, should be able to eliminatethe second strainby reducing its reproduction number below one,cannot do so because it provides onlypartial protection to another strain that mutates into the second strain. |
| format | Article |
| id | doaj-art-14fd2dbb5ff74ef1906e859fa4597d31 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-14fd2dbb5ff74ef1906e859fa4597d312025-01-24T01:53:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-01-014228731710.3934/mbe.2007.4.287Subthreshold coexistence of strains: the impact of vaccination and mutationMaia Martcheva0Mimmo Iannelli1Xue-Zhi Li2Department of Mathematics, University of Florida, Gainesville, FL 32611-8105Department of Mathematics, University of Florida, Gainesville, FL 32611-8105Department of Mathematics, University of Florida, Gainesville, FL 32611-8105We consider a model for a disease withtwo competing strains and vaccination.The vaccine provides complete protection against one of the strains(strain 2) but onlypartial protection against the other (strain 1). The partial protection leads toexistence of subthreshold equilibria of strain 1. If the first strain mutates into the second, there are subthreshold coexistence equilibriawhen both vaccine-dependent reproduction numbers are below one.Thus, a vaccine that is specific toward the second strainand that, in absence of other strains, should be able to eliminatethe second strainby reducing its reproduction number below one,cannot do so because it provides onlypartial protection to another strain that mutates into the second strain.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.287latent stagecoexistencestronglysubthreshold coexistencevaccine enhanced pathogen polymorphism.multiple coexistence equilibriamultiple endemic equilibriamutationbackward bifurcationlatent-stage progression age structurealternating stabilityvaccination |
| spellingShingle | Maia Martcheva Mimmo Iannelli Xue-Zhi Li Subthreshold coexistence of strains: the impact of vaccination and mutation Mathematical Biosciences and Engineering latent stage coexistence stronglysubthreshold coexistence vaccine enhanced pathogen polymorphism. multiple coexistence equilibria multiple endemic equilibria mutation backward bifurcation latent-stage progression age structure alternating stability vaccination |
| title | Subthreshold coexistence of strains: the impact of vaccination and mutation |
| title_full | Subthreshold coexistence of strains: the impact of vaccination and mutation |
| title_fullStr | Subthreshold coexistence of strains: the impact of vaccination and mutation |
| title_full_unstemmed | Subthreshold coexistence of strains: the impact of vaccination and mutation |
| title_short | Subthreshold coexistence of strains: the impact of vaccination and mutation |
| title_sort | subthreshold coexistence of strains the impact of vaccination and mutation |
| topic | latent stage coexistence stronglysubthreshold coexistence vaccine enhanced pathogen polymorphism. multiple coexistence equilibria multiple endemic equilibria mutation backward bifurcation latent-stage progression age structure alternating stability vaccination |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.287 |
| work_keys_str_mv | AT maiamartcheva subthresholdcoexistenceofstrainstheimpactofvaccinationandmutation AT mimmoiannelli subthresholdcoexistenceofstrainstheimpactofvaccinationandmutation AT xuezhili subthresholdcoexistenceofstrainstheimpactofvaccinationandmutation |