Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment
Evolution problem is now a hot topic in the mathematical biology field. This paper investigates the adaptive evolution of pathogen virulence in a susceptible-infected (SI) model under drug treatment. We explore the evolution of a continuous trait, virulence of a pathogen, and consider virulence-depe...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/891401 |
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| _version_ | 1849683116275269632 |
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| author | Xinzhu Meng Yang Yang Shengnan Zhao |
| author_facet | Xinzhu Meng Yang Yang Shengnan Zhao |
| author_sort | Xinzhu Meng |
| collection | DOAJ |
| description | Evolution problem is now a hot topic in the mathematical biology field. This paper investigates the adaptive evolution of pathogen virulence in a susceptible-infected (SI) model under drug treatment. We explore the evolution of a continuous trait, virulence of a pathogen, and consider virulence-dependent cure rate (recovery rate) that dramatically affects the outcome of evolution. With the methods of critical function analysis and adaptive dynamics, we identify the evolutionary conditions for continuously stable strategies, evolutionary repellers, and evolutionary branching points. First, the results show that a high-intensity strength drug treatment can result in evolutionary branching and the evolution of pathogen strains will tend towards a higher virulence with the increase of the strength of the treatment. Second, we use the critical function analysis to investigate the evolution of virulence-related traits and show that evolutionary outcomes strongly depend on the shape of the trade-off between virulence and transmission. Third, after evolutionary branching, the two infective species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist, and no further branching is possible, which is independent of the cure rate function. |
| format | Article |
| id | doaj-art-d1b48cfc327e40dbbc811cec810476bb |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d1b48cfc327e40dbbc811cec810476bb2025-08-20T03:23:59ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/891401891401Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with TreatmentXinzhu Meng0Yang Yang1Shengnan Zhao2College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaEvolution problem is now a hot topic in the mathematical biology field. This paper investigates the adaptive evolution of pathogen virulence in a susceptible-infected (SI) model under drug treatment. We explore the evolution of a continuous trait, virulence of a pathogen, and consider virulence-dependent cure rate (recovery rate) that dramatically affects the outcome of evolution. With the methods of critical function analysis and adaptive dynamics, we identify the evolutionary conditions for continuously stable strategies, evolutionary repellers, and evolutionary branching points. First, the results show that a high-intensity strength drug treatment can result in evolutionary branching and the evolution of pathogen strains will tend towards a higher virulence with the increase of the strength of the treatment. Second, we use the critical function analysis to investigate the evolution of virulence-related traits and show that evolutionary outcomes strongly depend on the shape of the trade-off between virulence and transmission. Third, after evolutionary branching, the two infective species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist, and no further branching is possible, which is independent of the cure rate function.http://dx.doi.org/10.1155/2014/891401 |
| spellingShingle | Xinzhu Meng Yang Yang Shengnan Zhao Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment Abstract and Applied Analysis |
| title | Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment |
| title_full | Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment |
| title_fullStr | Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment |
| title_full_unstemmed | Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment |
| title_short | Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment |
| title_sort | adaptive evolution of virulence related traits in a susceptible infected model with treatment |
| url | http://dx.doi.org/10.1155/2014/891401 |
| work_keys_str_mv | AT xinzhumeng adaptiveevolutionofvirulencerelatedtraitsinasusceptibleinfectedmodelwithtreatment AT yangyang adaptiveevolutionofvirulencerelatedtraitsinasusceptibleinfectedmodelwithtreatment AT shengnanzhao adaptiveevolutionofvirulencerelatedtraitsinasusceptibleinfectedmodelwithtreatment |