A complete epidemiological model of a class of genetic diseases

Abstract

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 version presented in this paper completely captures the disease epidemiology as it includes the spread of affected women within a population that has not been considered in other works. Moreover the model allows for de novo mutations (i.e. affected sibling born to unaffected parents) and distinct reproduction rates of individuals depending on their health conditions. Among our contributions, we consider the analytical study of the properties 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 the Lyapunov method. Model sensitivity analysis has been carried out to quantify the influence of model parameters on system response.