When sex matters: a complete model of X-linked diseases

X-linked recessive diseases are genetic disorders caused by gene's abnormalities placed on the X chromosome. Due to differences between males and females in sex chromosomes, the transmission mechanisms of these diseases vary in the two sexes. Other than the results of the well-known patterns of inheritance, the current spread of genetic disorders is influenced by spontaneous genetic mutations and individual's reduced reproduction capacities (fertility) conditioned by the disease severity. We developed a structured, continuous-time mathematical model describing how the disease spreads along time; the model accounts for a different fertility of affected individuals and for spontaneous mutations. Through Lyapunov analysis, we gained insights into system's asymptotic behaviour, that is how individual's fitness or spontaneous genetic mutations affect disease's diffusion. To the best of our knowledge, our model is the first one specifically designed to describe X-linked recessive diseases diffusion.