A stochastic SIRS modeling of transport-related infection with three types of noises

Abstract

People’s ability to easily travel across cities is thought to play a major role in the spread of infectious diseases. This research develops and analyzes a new Susceptible-Infected-Recovered-Susceptible (SIRS) model that accounts for transport-related infection, media coverage, and three types of noise (white, telegraph, and Lévy) to examine the role of transport in disease transmission. Thus, several theoretical and numerical uses of the revised model are investigated. Using Lyapunov functions, we check whether or not the model has a positive global solution. The infection either dies out or stays put beyond that point. The researched analytical results are validated by developing and using a numerical scheme to analyze and simulate the effects of various factors on the model’s dynamics.

Keywords

• Stochastic SIRS epidemic model
• Extinction
• Persistence
• Lévy noise
• Markov chain process