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

Abstract

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.