Abstract

GUERRERO-FLORES, Shaday; OSUNA, Osvaldo  and  VILLAVICENCIO-PULIDO, Geiser. Different types of backward bifurcations on account of an improvement in treatment efficiency. Integración - UIS [online]. 2018, vol.36, n.1, pp.21-35. ISSN 0120-419X.  https://doi.org/10.18273/revint.v36n1-2018002.

Understanding why there are multiple equilibrium points when R 0 < 1 has been one of the main motivations to analyze existence of a backward bifurcation in epidemiological models. Existence of multiple endemic states is usually associated to branches of equilibrium points of the models, which could arise from either the disease-free equilibrium point if R 0 = 1 or from an endemic equilibrium point if R 0 > 1. In this work, an SIR model with a density-dependent treatment rate is analyzed. The nature of the point where backward bifurcation emerges is explained in function of the velocity of the per-capita treatment rate. Strategies for the control or eradication of the disease will be proposed in function of the efficiency of the treatment.

MSC2010: 34C23, 34C40, 34C55, 34C60, 92D30.

Keywords : Backward bifurcation; forward bifurcation; treatment; SIR model.

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