Table 3. Household level model of observation, initial infestation, treatment, and residual infestation during treatment phase of a Chagas disease vector campaign, Arequipa, Peru, 2003–2011*.

Treatment received	Observed infestation	Estimated initial prevalence	Estimated residual prevalence
I and II		pI/II = nI/II/TI//II	rI/II = pI/II × (1 – c)2
I only	OI+IIØ = nI × s	pI = nI/TI	rI = pI × (1 – c)
II only	OIØII+ = nII × s	pII = nII/TII	rII = pII × (1 – c)
None	Not observed	pØ = pII	rØ = pØ

*Upper case letters refer to observed quantities. Lower case letters refer to estimated quantities. O_IxIIy, number of infested households observed in the first (Ix) and second (IIy) step of the treatment phase, with x and y taking the following values: ∅, no treatment and infestation could not be observed; +, treated and observed infested; –, treated and observed noninfested. For n_z, p_z, T_z, and r_z, the subscript z corresponds to the participation in treatments: I, only first; II, only second; I/II, both; n_z, estimated number of infested households; p_z, estimated initial prevalence of infestation; T_z, total number of households; r_z, estimated residual prevalence of infestation post treatment phase; s, sensitivity of technicians performing treatment to household infestation; c, probability of clearing infestation when treated. Further details and the solved system of equations have been provided by the authors (http://www.spatcontrol.net/articles/Barbu2014/suppMet.pdf).