Effects of selection and mutation on epidemiology of X-linked genetic diseases
The epidemiology of X-linked recessive diseases, a class of genetic disorders, is modeled with a discrete-time, structured, non linear mathematical system. The model accounts for both de novo mutations (i.e., affected sibling born to unaffected parents) and selection (i.e., distinct fitness rates de...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017042 |
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| author | Francesca Verrilli Hamed Kebriaei Luigi Glielmo Martin Corless Carmen Del Vecchio |
| author_facet | Francesca Verrilli Hamed Kebriaei Luigi Glielmo Martin Corless Carmen Del Vecchio |
| author_sort | Francesca Verrilli |
| collection | DOAJ |
| description | The epidemiology of X-linked recessive diseases, a class of genetic disorders, is modeled with a discrete-time, structured, non linear mathematical system. The model accounts for both de novo mutations (i.e., affected sibling born to unaffected parents) and selection (i.e., distinct fitness rates depending on individual's health conditions). Assuming that the population is constant over generations and relying on Lyapunov theory we found the domain of attraction of model's equilibrium point and studied the convergence properties of the degenerate equilibrium where only affected individuals survive. Examples of applications of the proposed model to two among the most common X-linked recessive diseases (namely the red and green color blindness and the Hemophilia A) are described. |
| format | Article |
| id | doaj-art-60f89cf6fa6f4b1c994066d7b3ac6452 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-60f89cf6fa6f4b1c994066d7b3ac64522025-01-24T02:39:47ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-05-0114375577510.3934/mbe.2017042Effects of selection and mutation on epidemiology of X-linked genetic diseasesFrancesca Verrilli0Hamed Kebriaei1Luigi Glielmo2Martin Corless3Carmen Del Vecchio4Dipartimento di Ingegneria, Università degli Studi del Sannio, Benevento (Italy), Piazza Roma, 21, Benevento 82022, ItalySchool of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, IranDipartimento di Ingegneria, Università degli Studi del Sannio, Benevento (Italy), Piazza Roma, 21, Benevento 82022, ItalySchool of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana, USADipartimento di Ingegneria, Università degli Studi del Sannio, Benevento (Italy), Piazza Roma, 21, Benevento 82022, ItalyThe epidemiology of X-linked recessive diseases, a class of genetic disorders, is modeled with a discrete-time, structured, non linear mathematical system. The model accounts for both de novo mutations (i.e., affected sibling born to unaffected parents) and selection (i.e., distinct fitness rates depending on individual's health conditions). Assuming that the population is constant over generations and relying on Lyapunov theory we found the domain of attraction of model's equilibrium point and studied the convergence properties of the degenerate equilibrium where only affected individuals survive. Examples of applications of the proposed model to two among the most common X-linked recessive diseases (namely the red and green color blindness and the Hemophilia A) are described.https://www.aimspress.com/article/doi/10.3934/mbe.2017042genetic epidemiologynonlinear systemglobal and local stabilitydomain of attractionx-linked recessive diseases |
| spellingShingle | Francesca Verrilli Hamed Kebriaei Luigi Glielmo Martin Corless Carmen Del Vecchio Effects of selection and mutation on epidemiology of X-linked genetic diseases Mathematical Biosciences and Engineering genetic epidemiology nonlinear system global and local stability domain of attraction x-linked recessive diseases |
| title | Effects of selection and mutation on epidemiology of X-linked genetic diseases |
| title_full | Effects of selection and mutation on epidemiology of X-linked genetic diseases |
| title_fullStr | Effects of selection and mutation on epidemiology of X-linked genetic diseases |
| title_full_unstemmed | Effects of selection and mutation on epidemiology of X-linked genetic diseases |
| title_short | Effects of selection and mutation on epidemiology of X-linked genetic diseases |
| title_sort | effects of selection and mutation on epidemiology of x linked genetic diseases |
| topic | genetic epidemiology nonlinear system global and local stability domain of attraction x-linked recessive diseases |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017042 |
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