Analysis of vaccination on Markovian random walk model of epidemic proliferation

Abstract

The global outbreak of the new crown in the last two years has brought the issue of epidemic transmission to the forefront of everyone's mind. Epidemic transmission is closely related to the virus itself, epidemic prevention measures and population density. Therefore, the focus of our study is to investigate the effects of population density, migration rate, infection rate and recurrence rate on the transmission of infectious diseases using Markov random walk model which is developed based on traditional SIR and VSIR models. We will first present the history of the development of research epidemics and current advances in epidemic modeling. Secondly, we will build a random walk model (based on SIR) to obtain the basic simulated epidemic transmission charts, and then we will manipulate the variables of population density, mobility, infection rate, and recovery rate, to investigate how much some epidemic prevention measures can change the transmission rate of epidemic diseases. Finally, we introduce a vaccination process into the random walk model and analyze the effectiveness of the vaccine against the spreading of diseases.