Selection and mutation effects on equilibrium and stability of X-linked recessive diseases

The epidemiology of X-linked recessive diseases, a class of genetic disorders, has been modeled through a discrete time, structured, non linear mathematical system. The model allows for de novo mutations (i.e. affected sibling born to unaffected parents) and selection (i.e., distinct fitness rates depending on individual’s health conditions). Applying Lyapunov direct method 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. Applications of the proposed model to the most common X-linked recessive diseases are described.