Disease Spread Model in Structurally Complex Spaces: An Open Markov Chain Approach

Understanding the dynamical behavior of infectious disease propagation within enclosed spaces is crucial for effectively establishing control measures. In this article, we present a modeling approach to analyze the dynamics of individuals in enclosed spaces, where such spaces are comprised of different chambers. Our focus is on capturing the movement of individuals and their infection status using an open Markov chain framework. Unlike ordinary Markov chains, an open Markov chain accounts for individuals entering and leaving the system. We categorize individuals within the system into three different groups: susceptible, carrier, and infected. A discrete-time process is employed to model the behavior of individuals throughout the system. To quantify the risk of infection, we derive a probability function that takes into account the total number of individuals inside the system and the distribution among the different groups. Furthermore, we calculate mathematical expressions for the average number of susceptible, carrier, and infected individuals at each time step. Additionally, we determine mathematical expressions for the mean number and stationary mean populations of these groups. To validate our modeling approach, we compare the theoretical and numerical models proposed in this work.