Equilibrium and stability analysis of X-chromosome linked recessive diseases model

We present a mathematical model describing the population distribution of genetic diseases related to X chromosomes. The model captures the disease spread within a population according to the relevant inheritance mechanisms; moreover it allows to include de novo mutations (i.e., affected siblings born to unaffected parents). The resulting dynamic system is nonlinear, discrete time and positive. Among our contributions, we consider the analytical study of model's equilibrium point, that is the distribution of the population among healthy, carrier and affected subjects, and the proof of the stability properties of the equilibrium point through Lyapunov second method. In particular global exponential stability was demonstrated in the presence of significant mutation rates and global asymptotic stability for negligible mutation rates.