Investigating the ARSIRI Model: An Extended SIR Model with Reinfection for Modelling Addiction-Related Phenomena

This paper investigates the ARSIRI model, a modified SIR model that considers the possibility of reinfection from the recovered compartment to the infected compartment. This modification is motivated by representing an addiction-related phenomenon in which recovered individuals can become reinfected. The paper examines disease-free and endemic equilibrium points. The stability conditions of the equilibrium points are investigated using a reproductive number that cannot be computed using the regular next-generation matrix. The most important parameter in the model, namely the reinfection rate, is then analyzed from a bifurcation point of view. Finally, the ARSIRI model is applied to simulated data as well as real data related to alcohol addiction, demonstrating its superiority over the regular SIR model.