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Predicting COVID-19 distribution in Mexico through a discrete and time-dependent Markov chain and an SIR-like model

COVID-19 is an emergent viral infection which rose in December 2019 in a city in the Chinese province of Hubei, Wuhan; the viral aetiology of this infection is now known as COVID-19 virus, which belongs to the Betacoronavirus genus. This virus produces the syndrome of acute respiratory stress that h as been witnessed in other coronaviruses, such as that MERS-CoV in Middle East countries or SARS-CoV which was seen in 2002 and 2003 in China. This virus mediates its entry through its spike (S) proteins interacting with ACE2 receptors in lung epithelial cells, and may promote an inflammatory response by means of inflammasome NLRP3 activation and unfolded protein response (these are possibly consequence of the envelope E protein of COVID-19 virus). Efforts have been made worldwide to prevent further spread of the disease, but in March 2020 the WHO declared it a pandemic emergency and Mexico started to report its first cases. In this paper we attempt to summarize the biological features of the virus and the possible pathophysiological mechanisms of its disease, as well as a stochastic model characterizing the probability distribution of cases in Mexico by states and the estimated number of cases in Mexico through a differential equation model (modified SIR model), thus will we be able to characterize the disease and its course in Mexico in order to display more preparedness and promote more logical actions by both the policy makers as well as the general population.

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