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.