When sex matters: a complete model of X-linked diseases

Abstract

X-linked recessive diseases are genetic disorders caused by gene's abnormalities placed on the X chromosome. Due to differences between males and females in sex chromosomes, the transmission mechanisms of these diseases vary in the two sexes. Other than the results of the well-known patterns of inheritance, the current spread of genetic disorders is influenced by spontaneous genetic mutations and individual's reduced reproduction capacities (fertility) conditioned by the disease severity. We developed a structured, continuous-time mathematical model describing how the disease spreads along time; the model accounts for a different fertility of affected individuals and for spontaneous mutations. Through Lyapunov analysis, we gained insights into system's asymptotic behaviour, that is how individual's fitness or spontaneous genetic mutations affect disease's diffusion. To the best of our knowledge, our model is the first one specifically designed to describe X-linked recessive diseases diffusion.

Keywords:

• Continuous-time nonlinear system
• equilibrium and stability
• epidemiology
• genetic diseases

Acknowledgments

Authors are grateful to Prof. Emanuele Durante Mangoni, MD PhD, from the Internal Medicine Unit, Second University of Naples, Italy, for helpful discussions and literature suggestions on X-linked diseases and their inheritance pattern and for his critical review of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

C. Del Vecchio

C. Del Vecchio received a five years degree in Manufacturing Engineering from the Università degli Studi Federico II, Naples, Italy, and PhD in Automatic Control Engineering from Università degli Studi del Sannio, Benvento, Italy, where she currently holds a position of assistant professor. Her research interests include modelling and control of manufacturing systems, smart energy systems, and biomedical systems.

F. Verrilli

F. Verrilli received the Laurea degree in electronic engineering for automation and telecommunication and the PhD degree in information engineering from the University of Sannio, Benevento, Italy, in 2016. She held a post-doctoral position with the University of Sannio. Her research interests included optimal control, model predictive control, and smart grid. She is currently solution building engineer at SopraSteria, Milan, Italy.

L. Glielmo

L. Glielmo was born in 1960; he holds a “laurea” degree in Electronic Engineering and a research doctorate in Automatic Control. He taught at the University of Palermo, at University of Naples Federico II, and then at University of Sannio at Benevento where he is now a professor of Automatic Control. His research interests over the years include singular perturbation methods, model predictive control methods, automotive controls, deep brain stimulation modeling and control, smart-grid control, systems biology. He co-authored more than 130 papers on international archival journals or proceedings of international conferences, co-edited two books, and holds three patents. He seated in the editorial boards of IEEE Transaction on Automatic Control and has been chair of the IEEE Control Systems Society Technical Committee on Automotive Controls; currently, he serves as Associate Editor for the online journal IEEE Control Systems Society Letter. He is General Co-Chair of the 2019 European Control Conference, to be held in Naples, Italy. He was head of the Department of Engineering of University of Sannio from 2001 to 2007 where he is currently Rector's delegate for technology transfer and coordinator of the PhD course on Information Technologies for Engineering.