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 stabil- ity 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.