. 2019 Jul 16;9:10264. doi: 10.1038/s41598-019-46706-7

Table 5.

Equations’ parameters, specifications, assumptions, and data sources used for the optimization models where we analyze the transport of surplus excreta towards municipalities with a nutrient deficit to meet crop needs.

Eq.	Param.	Definition/Variables represent (Specifications, assumptions and data sources)
5	$W_{i}$	Total weight of excreta in municipality $i \in S$
	g_l	Weight of excreta per individual and year from source l, human sludge or manure. We obtained the coefficient (m3) of slurry and solid manure production of livestock from[58] and human excreta production (as dry mass) per year from⁵⁷. A m3 of solid manure weighs 0.5 tons, and a m3 of slurry weighs 1 ton[58]
	E_li	Number of individuals of source l in municipality i
6	$k_{i}^{n}$	Concentration, the amount of nutrient n in each ton of excreta at each surplus municipality i which is used in constraint 8.2
6	$Q_{i}^{n}$	Total quantity of nutrientn in excreta in municipality i, where n represents nutrient (N, P or K), (Eq. 1)
7	$T^{n}$	Total amount of nutrient n transported along with a surplus of P
	$B_{i}^{n}$	Balance of nutrient n in municipalities i, where n represent nutrient N, P, or K (Eq. 3)
	$Q_{i}^{n}$	Total quantity of nutrient n in excreta in municipality i (Eq. 1)