  Measles is an infectious disease caused by the Morbilivirus Measles Virus
which has accompanied the human race since the 4th millennium BC, it is a
disease usually concerning the paediatric population and in the past, before
the advent of vaccination, almost all the population suffered from it, and in
some cases the complications derived from this disease, such as central nervous
involvement. Vaccination changed the course of the disease worldwide and
diminished the associated comorbidities and mortality; in Mexico the
vaccination program commenced in the decade of the 1970s and was successful in
preventing peaks of infection. Nevertheless, due to various factors, has the
world seen measles outbreaks once more, this commencing in the year 2019 and
extending towards the year 2020. Here we make account of the biology and the
pathophysiology of the viral infection, and present three models: one
concerning the dynamics of the cases by means of a continuous method and a
discrete stochastic model; one concerning the cellular compartmentalization
behaviour of the virus, that is the viral tropism towards certain cell types in
the host and the tendencies in extended or complicated infection; the last one
concerning geographic behaviour of the virus, regarding in particular the
tendencies in Mexico City, those involved at a global scale, and finally a
model providing a prediction of the viral genotypes' distribution worldwide.
