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Equations: Diarrhea, Malaria, and Respiratory Infections

IFs added three additional communicable diseases, namely diarrhea, malaria, and respiratory infection, after it had developed the modelling approach for distal drivers discussed above.  The model uses the more general Group I (communicable disease and maternal mortality excluding AIDS) forecast to project mortality related to all three additions:

diarrhea equation

M is mortality rate in deaths per 100,000 for a given region r, age category c, sex p, general (Group 1) cause dg=1 and specific disease d within general cause group dg=1. Here dg=1 refers to all communicable diseases (other than HIV/AIDS because Mathers and Loncar 2006 did not use the same approach to that particular communicable disease) and d refers to diarrhea, malaria or respiratory infections.

The constants and beta coefficients for the above equation for the three diseases come from Mathers and Loncar (2005 and 2006c). [1] For diarrhea and malaria we used their coefficients for infectious and parasitic diseases (Mathers and Loncar 2005: Table A-6 on page 115); for respiratory infections we used their coefficients for respiratory infections specifically (Mathers and Loncar 2006c, Table S5).

The results for these three subtypes are then subtracted from the mortality for the total Group I category (except HIV/AIDS). The reason for this is to make sure that the sum of all them does not exceed the total of Group 1 (excluding HIV/AIDS), which is a result the equation could theoretically produce.  In fact, we want to be sure that there is room for the Other Group 1 cause of death, so IFs limits the sum for diarrhea, malaria, and respiratory infection to 95 percent of the total of Group 1 (excluding HIV/AIDS).   If necessary, all three subcategories are reduced proportionally by a factor of 0.95/(SUM(3 subtypes)/Tot(big type)). Note that, if this restraint needs to be imposed, the denominator will always be higher than 0.95 and then the multiplicative adjustment factor will always be lower than 1.


[1] The extended process for using those is described in 2 working notes for the IFs project by Dale Rothman, Dealing with Diarrhoeal Diseases Including the Effects of Unsafe Water & Sanitation and Undernutrition (March 25, 2009) and Dealing with Effects of Indoor Air Pollution (October 8 2009).  Titles of the files are Incorporating Diarrhoea 25 March 2009 and Incorporating Indoor Air Pollution 9 October 2009, respectively.