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Studying COVID-19 Using the Markov Process

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October 08, 2020

Studying COVID-19 Using the Markov Process

Jennifer Morency

picture Studying COVID-19 Using the Markov Process

The coronavirus was first introduced to the world at the very beginning of 2020. What was, at the time, progressively newsworthy, is now a devastating global pandemic that has killed over 1M people around the world.

Experts have been studying this viral disease, trying to develop a vaccine and figuring out how to protect the world against its devastating nature before then. Findings have concluded that COVID-19 is more contagious than influenza and therefore has a higher frequency of cluster outbreaks.

In addition, perhaps the biggest problem with the coronavirus is that many are asymptomatic, showing no signs of having the disease and more likely to spread it. Furthermore, most of the patients that do present symptoms of COVID-19 report symptoms that are similar to other common illnesses, making it more difficult to discern and contain its virality.

In an attempt to identify COVID-19 symptoms early and distinguish them from other illnesses, researchers in California and Japan published a research article on Modeling the Onset of Symptoms of COVID-19 in the Frontiers in Public Health. Below are the findings of this research.

The Markov Process Applied to Coronavirus Patients

In order to understand the difference between the coronavirus and other respiratory diseases such as influenza, Severe Acute Respiratory Syndrome (SARS) and the Middle East Respiratory Syndrome (MERS), the progression of symptoms was evaluated. Seeing as the order of symptom occurrence wasn’t largely available in terms of information and statistics for any of the diseases, the experts of the study applied the Markov Process.

This process was applied to a graded partially ordered set (poset) that was established according to clinical observations of patients who were tested positive for COVID-19. In doing so, the order of discernible symptoms could be determined. These symptoms include:

  • Fever
  • Cough
  • Nausea/vomiting
  • Diarrhea

The Markov Process is a stochastic sequence of events that determines the possibility of the next state based on the current state and not past or future states. It allowed the researchers to treat symptoms (states) as independent variables and build a model that closely calculates the probability of symptoms developing in definitive orders with the help of available, non-ordered patient data. Here are the probabilities developed:

  • State probability of a node = the frequency of a specific combination of symptoms in a patient, divided by the total number of patients who experience the same number of symptoms.
  • Transition probability between two symptoms (states) = the probability of getting a single definitive symptom, divided by the probability of getting all possible next symptoms.
  • Greedy algorithmic approach = use of transition probabilities to evaluate probability of all possible orders and concluding the most and least likely orders of symptoms.

By applying the Markov Process, the researchers were able to grade the poset, which in this case, represents all possible combinations of symptoms and the orders of their occurrence. Grading the poset allows them to rank the symptoms by the number each one represents. The combination of fever and cough, for example, has the same rank as cough and diarrhea.

In doing this study, researchers found that for the symptomatic COVID-19 patients, the order of appearance of the symptoms did not have a link to the severity of the admitted case. This also permitted to study the order of symptoms in SARS, MERS and influenza, and compare them to the coronavirus.

The model predicts the following symptom progressions:

  • Influenza begins with a cough
  • COVID-19 begins with a fever
  • MERS begins with a fever
  • SARS begins with a fever

The model also finds that although COVID-19, MERS and SARS all begin with a fever, COVID-19 differs from the two other respiratory diseases in the order of gastrointestinal symptoms. The researchers believe that fever screening remains the best way to identify possible coronavirus cases and should be used when people attempt to enter facilities.

The full article and its findings can be found in this website.