Certain aspects of the SIS stochastic epidemic model

The SIS model is a fundamental tool in epidemiology for understanding the spread of infectious diseases. This article focuses on the stochastic SIS model, introducing randomness through the disease transmission parameter. The study investigates the behavior of the model, revealing the conditions for the recurrence or extinction of the disease. In particular, it addresses the calculation of the conditional expected time for the disease to exceed a certain threshold, using both Laplace transforms and numerical techniques for its specific application. Real-world phenomena are discussed, and a method for determining the most suitable stochastic parameter is proposed, with examples such as gonorrhea and pneumococcus.