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Figure 3 | BMC Biology

Figure 3

From: A multistage theory of age-specific acceleration in human mortality

Figure 3

Predicted patterns of mortality from a multistage model. I calculated the curves based on the mathematical analyses and assumptions described in the Methods section (see Midlife rise in acceleration caused by increasing transition rates). The plots show that a multistage model can generate mortality patterns similar to those observed for various causes of death. There are not enough data on stages in disease progression to attempt a fit between observations and the model. Instead, the plots illustrate how various assumptions affect acceleration in a multistage model. I chose parameters for panels A and B to provide a rough match to the observations for heart disease in Figures 1D and 1F: the parameters are n = 4, u = 0.02, F = 20, a = 8.5, b = 1.5, T = 100, where n is the number of stages, u is the baseline transition rate between stages, F is the upper bound on transition rates, a and b set the shape of the function that determines how transition rates rise with age, and T is maximum age. I chose parameters for panels C and D to provide a rough match to the observations for cancer in Figures 1G and I: the parameters are n = 4, u = 0.012, F = 5, a = 5, b = 5, T = 100. I did not attempt to fine-tune the fit to the data; about ten trial and error choices for parameters gave the rough matches shown. The model is sufficiently flexible to generate a wide variety of shapes for different values of n. Therefore, the rough matches here mean little with regard to whether a multistage model is a good explanation for the observations. Tests of the model will require better understanding of stages in disease progression and rates of transition between stages.

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