Different types of backward bifurcations on account of an improvement in treatment efficiency

Abstract

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.

COVID-19 SIR model: Bifurcation analysis and optimal control

“…When the value of which is shown in the curve as the Limit Point (LP), then again endemic equilibrium state stable and increased the value , curves move forward and state stable. This phenomenon is known as bistability [37] as it is shown in Fig. 3(b) .…”