A QUASI-BIRTH-DEATH PERSPECTIVE OF SUSCEPTIBLE-INFECTIOUS-RECOVERED TYPE MODEL

This research focuses on the development of a Susceptible-Infectious-Recovered (SIR) model to study the spread of the disease using stochastic approaches. Specifically, the emphasis is on the stochastic perspective, employing a Discrete Markov Chain as the stochastic model for the SIR model. Furthermore, the quasi-birth-death (QBD) process is used to formulate the stochastic model for the SIR model. The SIR model consists of three compartments representing susceptible (S), infected (I), and recovered (R) individuals. Initially formulated as a set of differential equations, the SIR model is then transformed into a probabilistic model. To proceed with the QBD process, the transition matrix and state space are constructed, forming the P matrix. Within the QBD process, a P matrix is prepared containing submatrices derived from the transition matrix. Furthermore, steady-state analysis is performed on the P matrix using the QBD process. This approach enables a probabilistic perspective for studying disease spread through the SIR model, allowing for a deeper understanding of the dynamics and potential outcomes