Fig 5 - uploaded by Khagendra Adhikari
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Bifurcation diagram and model solutions with í µí»¿ ℎ = 0. (a) Backward bifurcations showing the intervals of í µí± for the existence of lower-level stable endemic equilibrium, bi-stability, and the existence of higher-level stable endemic equilibrium. The lower green section represents one stable endemic equilibrium, with a complex pair representing the lower level of stable endemic equilibrium of malaria in the home country that exists when í µí± < 72.39. The upper green section (one endemic equilibrium with a complex pair) and the magenta section (one endemic equilibrium with two negative solutions), respectively, represent the higher level stable endemic equilibrium of malaria in the home country that exists when í µí± > 80. The three endemic equilibria in bistability region (72.39 < í µí± < 80) are represented by the blue, dotted red, and black lines. (b) Model solutions verifying the backward bifurcation (a), where the model solution converges to a higher level stable endemic equilibrium when í µí± = 100(í µí± > 80) (end of the magenta curve) and converges to a lower level stable endemic equilibrium when í µí± = 50(í µí± < í µí± * ) (end of the green curve), regardless of the initial conditions. For 72.39 < í µí± < 80, bi-stability (ends of the black and blue curves) occurs, i.e., the solution converges to a higher endemic level or lower endemic level depending on the prevalence above or below the breakpoint density, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Source publication
The existence of backward bifurcation indicates an obstacle to disease eradication even when the basic reproduction number falls below unity. Bifurcation analysis allows us to identify causes for backward bifurcation, thereby helping to design a strategy to avoid such phenomena for disease eradication. In this study, we perform an in-depth bifurcat...
Context in source publication
Context 1
... endemic equilibria to be mathematically untractable. Thus, we numerically demonstrated the possibility of one and three endemic equilibria and their stability. We also estimated the approximate threshold value of the mosquito biting rate (í µí±) for the low endemic level, bi-stability, and high malaria endemic level in the home country of Nepal (Fig. ...
