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Stability and sensitivity analysis of SEIRZ model on smoking addiction in South Sulawesi
Syata I.
Aip Conference Proceedings
Abstract
In this paper, we construct and analyze a new smoking addiction model with compartments of susceptible, addicted, occasional, permanent quitting, and not interested in smoking. Susceptible individuals can become addicted to cigarette smoking using the Holling type incident rate function. The existence of addicted and non-addicted fixed points are considered, and their local stability is analyzed using linearization, eigenvalues methods, and Routh-Hurwitz criteria. The basic reproduction number (R0) is also considered using the next generation matrix. Based on the sensitivity analysis, transmission rate as a parameter has the most positive effect on R0. An inhibiting factor, as well as a parameter, has the most negative effect on R0. Furthermore, if R0 < 1 then the stability of the non-addicted fixed point is locally asymptotically stable, while if R0 > 1 then the stability of the addicted fixed point is locally asymptotically stable. Based on data from South Sulawesi Province, Indonesia, we carry out numerical simulations to visualize the dynamics of the number of individuals in each compartment. For R0 < 1, at the end of the simulation the number of E, I, and R decreased and went to 0, the number of S decreased but still remained, and the number of Z increased. When R0 > 1, at the end of the simulation the number of S, E, I, and R have decreased but are still present while the number of Z has increased.