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

Alfonso Vivanco-Lira|arXiv (Cornell University)|Mar 15, 2020

COVID-19 Clinical Research StudiesMedicine19 references18 citations

TL;DR

This study proposes a hybrid modeling approach combining a discrete, time-dependent Markov chain and a modified SIR model to predict the spatial and temporal distribution of COVID-19 cases across Mexican states. It estimates disease spread dynamics and provides actionable insights for public health planning during the early pandemic phase in Mexico.

ABSTRACT

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.

Motivation & Objective

• To model the stochastic progression of COVID-19 cases across Mexican states using a discrete, time-dependent Markov chain.
• To estimate the cumulative number of cases in Mexico through a modified SIR-type differential equation model.
• To integrate biological mechanisms of SARS-CoV-2 with epidemiological modeling for improved disease course prediction.
• To support policy makers and the public with data-driven, preparedness-oriented forecasts during the early pandemic phase.

Proposed method

• A discrete-time, state-dependent Markov chain models the probability distribution of infected cases across 32 Mexican states at each time step.
• Transition probabilities in the Markov model are derived from regional transmission dynamics and case data.
• A modified SIR model with time-varying transmission rates is used to simulate the overall epidemic curve in Mexico.
• The SIR model incorporates parameters such as infection rate, recovery rate, and population size per state.
• The models are calibrated using early reported case data from Mexico's national health authorities.
• The integration of biological mechanisms of SARS-CoV-2 (e.g., ACE2 receptor binding, NLRP3 inflammasome activation) informs model assumptions.

Experimental results

Research questions

• RQ1 How can a time-dependent Markov chain accurately represent the spatial distribution of COVID-19 cases across Mexican states?
• RQ2 What is the predicted cumulative number of cases in Mexico using a modified SIR model with time-varying transmission?
• RQ3 How do biological features of SARS-CoV-2 influence the structure and parameters of the epidemic models?
• RQ4 To what extent can the combined model support public health decision-making during the initial pandemic wave?

Key findings

• The Markov chain model successfully captures the evolving probability distribution of cases across Mexican states over time.
• The modified SIR model predicts a peak in cumulative cases in Mexico within a few months of the initial outbreak, consistent with early data trends.
• The model identifies high-risk states based on transition probabilities and early case clustering.
• The integration of viral pathophysiology enhances model realism and supports parameter justification.
• The combined approach provides a framework for real-time forecasting and preparedness planning in resource-limited settings.