Effects of selection and mutation on epidemiology of X-linked genetic diseases

Francesca Verrilli; Hamed Kebriaei; Luigi Glielmo; Martin Corless; Carmen Del Vecchio; Francesca Verrilli; Hamed Kebriaei; Luigi Glielmo; Martin Corless; Carmen Del Vecchio

doi:10.3934/mbe.2017042

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 3: 755-775. doi: 10.3934/mbe.2017042

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Effects of selection and mutation on epidemiology of X-linked genetic diseases

1.
Dipartimento di Ingegneria, Università degli Studi del Sannio, Benevento (Italy), Piazza Roma, 21, Benevento 82022, Italy
2.
School of Electrical and Computer Engineering, College of Engineering, University of Tehran, Tehran, Iran
3.
School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana, USA

Received: 02 March 2016 Accepted: 11 November 2016 Published: 01 June 2017
MSC : Primary: 58F15, 58F17; Secondary: 53C35

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.
- Genetic epidemiology,
- nonlinear system,
- global and local stability,
- domain of attraction,
- X-linked recessive diseases
Citation: Francesca Verrilli, Hamed Kebriaei, Luigi Glielmo, Martin Corless, Carmen Del Vecchio. Effects of selection and mutation on epidemiology of X-linked genetic diseases[J]. Mathematical Biosciences and Engineering, 2017, 14(3): 755-775. doi: 10.3934/mbe.2017042

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Abstract

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.

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