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Mortality Transition for Low-Income Countries

As described in the discussion of distal driver coefficients for low-income countries we use Global Burden of Disease (GBD) regression coefficients developed separately for low and high income countries.  However, given the long forecast horizon of IFs, we recognize that many low-income countries eventually will reach high levels of income and thus should follow a similar pattern of mortality.  Therefore, we allow low-income countries to transition gradually by computing two mortality rates for low-income countries˗one using the low-income beta coefficients and the other using the high-income model. We start the transition when countries reach GDPPCP of $3,000, and finish the transition when countries reach $15,000. The transition is computed finding target mortality in between the two, interpolating depending on the current level of GDPPCP. 

Given the target mortality, we compute how much change we need from current mortality (low-income based), and slowly adjust using a moving average of 20 percent of current required change and 80 percent of change used in previous years:

Change = Target Mortality – Low Income Mortality

Smooth Change = 0.2 * Change + 0.8 * Last Year Change

Final Mortality = Low Income Mortality + Maximum(Smooth Change, Change)

where Last Year Change = Maximum(Smooth Change(yr-1), Change(yr-1)).

Note that most of the time target mortality is lower than low income mortality, and thus change is negative.  Thus, when we find the maximum we are finding the smaller absolute number and smoothing change.