Stability and sensitivity analysis of an epidemiological model of genetic diseases

The epidemiology of X-linked recessive diseases, a class of genetic disorders, has been modeled through a discrete time, structured, mathematical system. The model accounts for both de novo mutations and distinct reproduction rates of procreating couples depending on their health conditions. Relying on Lyapunov´s and LaSalle method, asymptotic stability properties of model equilibrium points have been proved. Model´ sensitivity analysis has also been carried out to quantify the influence of model´s parameters on system´s response. The model allows to predict the spread over time in the population of any recessive genetic disorder transmitted through the X Chromosome.