The distribution of the number of the infected individuals in a stochastic SIR model on regular rooted trees

In this paper, we define and study a stochastic SIR model on the class of regular rooted trees, in order to describe the spread of an epidemic on a closed population. A generalized geometric random variable is defined, which is essential for our study in this stochastic process. The main objective of this paper is to obtain the distribution of random variable the number of infected individuals at the stopping time that a diagnosis occurs. The analyses, simulations, and figures created with the software MATLAB certify the validity of the obtained results.