Malaysian Journal of Mathematical Sciences, March 2025, Vol. 19, No. 1
Investigating the ARSIRI Model: An Extended SIR Model with Reinfection for Modelling Addiction-Related Phenomena
N. Susyanto
Corresponding Email: [email protected]
Received date: 23 January 2024
Accepted date: 4 November 2024
Abstract:
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.
Keywords: ARSIRI model; equilibrium points; reproductive number; bifurcation analysis; alcohol addiction model
