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

Stochastic and nonstochastic descriptions of the 2019-2020 measles outbreak worldwide with an emphasis in Mexico