This study addresses problems that have arisen in the literature when calculating backward bifurcations, especially in the context of epidemic modeling. Backward bifurcations are generally studied by varying a bifurcation parameter which in epidemiological models is usually the so-called basic reproduction number R-0. However, it is often overlooked that R-0 is an aggregate of parameters in the model. One cannot simply vary the aggregate R-0 while leaving all model parameters constant as has happened many times in the literature. We investigate two scenarios. For the incorrect approach we fix all parameters in the aggregate R-0 to constant values, but R-0 is nevertheless varied as a bifurcation parameter. In the correct approach, a key parameter in R-0 is allowed to vary, and hence R-0 itself varies and acts as a natural bifurcation parameter. We explore how the outcomes of these two approaches are substantially different.
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