The application of Markov random walk model on the epidemic spread of Covid-19 via SEIR and SEIRS model

Abstract

Since the outbreak of the Covid-19 pandemic in 2020, most countries are still suffering from the virus, and human society has been greatly changed. As the new virus is highly contagious, many people are still infected with the virus every day, and even face death in serious cases. However, there are still a lot of people who do not realize the harm of the virus, in order to make people more intuitive feel the spread of the virus in a certain period, this paper will use two classic epidemiological mathematical models based on the Markov chain called SEIR and SEIRS model for simulating the virus spread in New York City in 180 days. In both models, there are four states: Susceptible, Exposed, Infected, and Recovered. At first, Markov chain was used to randomly generate a populous population, and only one person in the population was infected, and then the changes in the number of people in these four states were observed over time. In addition, by incorporating certain coefficients in the models into a formula, an index for measuring infectious diseases called Reproduction number (R₀) will be obtained. The R₀ of Covid-19 in New York City is about 5.93, much greater than 1. Indicating that on average one person can infect about six people, which is highly contagious, so measures need to be taken to reduce this number. Finally, the SEIRS model is more suitable by comparing these two models since people do get re-infected over time.