Incidence and consequences of damage to insecticide-treated mosquito nets in Kenya

Smith, Thomas; Denz, Adrian; Ombok, Maurice; Bayoh, Nabie; Koenker, Hannah; Chitnis, Nakul; Briet, Olivier; Yukich, Joshua; Gimnig, John E.

doi:10.1186/s12936-021-03978-7

Malaria Journal

Table 3 Estimates of derived quantities (analysis A1, with 95% credible intervals)

From: Incidence and consequences of damage to insecticide-treated mosquito nets in Kenya

Quantity			Estimate (95% credible interval)
Median life of LLIN (years)	\({\mathrm{L}}_{50}\)		2.86 (2.68, 3.08)
Proportion of lifetime of LLIN for which it is in use^a	\({\mathrm{P}}_{\mathrm{U}1}\)	\(\left({\int }_{\mathrm{t}=0}^{\infty }{\mathrm{S}}_{3}\left(\mathrm{t}\right)+ {\mathrm{S}}_{4}\left(\mathrm{t}\right)\mathrm{ dt}\right)/\left({\int }_{\mathrm{t}=0}^{\infty }1-\mathrm{A}\left(\mathrm{t}\right)\mathrm{ dt}\right)\)	0.60 (0.58, 0.62)
Proportion of lifetime of LLIN for which it is damaged	\({\mathrm{P}}_{\mathrm{H}}\)	\(\left({\int }_{\mathrm{t}=0}^{\infty }{\mathrm{S}}_{2}\left(\mathrm{t}\right)+ {\mathrm{S}}_{4}\left(\mathrm{t}\right)\mathrm{ dt}\right)/\left({\int }_{\mathrm{t}=0}^{\infty }1-\mathrm{A}\left(\mathrm{t}\right)\mathrm{ dt}\right)\)	0.78 (0.75, 0.81)
Proportion of lifetime of LLIN for which it is in use^b	\({\mathrm{P}}_{\mathrm{U}2}\)	\(\left({\int }_{\mathrm{t}=0}^{\infty }{{\mathrm{U}}_{\mathrm{I}}\mathrm{S}}_{3}\left(\mathrm{t}\right)+ {\mathrm{U}}_{\mathrm{H}}{\mathrm{S}}_{4}\left(\mathrm{t}\right)\mathrm{ dt}\right)/\left({\int }_{\mathrm{t}=0}^{\infty }1-\mathrm{A}\left(\mathrm{t}\right)\mathrm{ dt}\right)\)	0.56 (0.54, 0.58)
Reduction in net lifetime attributable to holes (years)	\({\mathrm{L}}_{\mathrm{H}}\)	\({\mathrm{L}}_{50}^{(\mathrm{H}=0)}-{\mathrm{L}}_{50}\)	2.88 (1.77, 4.34)
Proportion loss in net lifetime attributable to holes	\({\mathrm{P}}_{\mathrm{H}}\)	\(1-{\int }_{\mathrm{t}=0}^{\infty }1-\mathrm{A}\left(\mathrm{t}\right)\mathrm{ dt}/{\int }_{\mathrm{t}=0}^{\infty }1-{\mathrm{A}}^{(\mathrm{H}=0)}\left(\mathrm{t}\right)\mathrm{ dt}\)	0.49 (0.38, 0.58)
Proportion of attrition in damaged nets	\({\mathrm{P}}_{\mathrm{AH}}\)	\({\int }_{\mathrm{t}=0}^{\infty } {\mathrm{a}}_{2}{\mathrm{S}}_{2}\left(\mathrm{t}\right)+ {\mathrm{a}}_{4}{\mathrm{S}}_{4}\left(\mathrm{t}\right)\mathrm{ dt}/{\int }_{\mathrm{t}=0}^{\infty }{\mathrm{a}}_{1}{\mathrm{S}}_{1}\left(\mathrm{t}\right)+ {\mathrm{a}}_{2}{\mathrm{S}}_{2}\left(\mathrm{t}\right)+{\mathrm{a}}_{3}{\mathrm{S}}_{3}\left(\mathrm{t}\right)+ {\mathrm{a}}_{4}{\mathrm{S}}_{4}\left(\mathrm{t}\right)\mathrm{ dt}\)	0.91 (0.88, 0.93)
Proportion of reduced use^a attributable to holes	\({\mathrm{P}}_{\mathrm{UH}1}\)	\(\frac{{\int }_{\mathrm{t}=0}^{\infty }{{\mathrm{S}}_{3}\left(\mathrm{t}\right)+ {\mathrm{S}}_{4}\left(\mathrm{t}\right)-\mathrm{S}}_{3}^{(\mathrm{H}=0)}\left(\mathrm{t}\right)- {\mathrm{S}}_{4}^{(\mathrm{H}=0)}\left(\mathrm{t}\right)\mathrm{ dt}}{1-{\int }_{\mathrm{t}=0}^{\infty }{\mathrm{S}}_{3}^{(\mathrm{H}=0)}\left(\mathrm{t}\right)+ {\mathrm{S}}_{4}^{(\mathrm{H}=0)}\left(\mathrm{t}\right)\mathrm{ dt}}\)	0.13 (− 0.08, 0.30)
Proportion of reduced use^b attributable to holes	\({\mathrm{P}}_{\mathrm{UH}2}\)	\(\frac{{\int }_{\mathrm{t}=0}^{\infty }{\mathrm{U}}_{\mathrm{I}}\left({\mathrm{S}}_{3}\left(\mathrm{t}\right)-{\mathrm{S}}_{3}^{(\mathrm{H}=0)}\left(\mathrm{t}\right)\right)+ {\mathrm{U}}_{\mathrm{H}}\left({\mathrm{S}}_{4}\left(\mathrm{t}\right)- {\mathrm{S}}_{4}^{(\mathrm{H}=0)}\left(\mathrm{t}\right)\right)\mathrm{ dt}}{1-{\int }_{\mathrm{t}=0}^{\infty }{{\mathrm{U}}_{\mathrm{I}}\mathrm{S}}_{3}^{(\mathrm{H}=0)}\left(\mathrm{t}\right)+ {{\mathrm{U}}_{\mathrm{H}}\mathrm{S}}_{4}^{(\mathrm{H}=0)}\left(\mathrm{t}\right)\mathrm{ dt}}\)	0.09 (− 0.13, 0.27)
Total nights in use^b	\({\mathrm{L}}_{\mathrm{U}}\)	\(365 {\mathrm{L}}_{50}{\mathrm{P}}_{\mathrm{U}2}\)	581 (529, 639)
Total nights use of a net resistant to damage	\({\mathrm{L}}_{\mathrm{U}}^{(\mathrm{H}=0)}\)	\(365 {\mathrm{L}}_{50}^{(\mathrm{H}=0)}{\mathrm{P}}_{\mathrm{U}2}\)	654 (530, 823)
Proportion of the theoretical maximal use, lost because of damage	\({\mathrm{X}}_{\mathrm{H}}\)	\(1-\frac{{\mathrm{L}}_{\mathrm{U}}}{{\mathrm{L}}_{\mathrm{U}}^{(\mathrm{H}=0)}}\)	0.10 (− 0.12, 0.32)
Proportion of impact on vectorial capacity lost because of damage^c,d	\({\mathrm{X}}_{\mathrm{V}}\)	\(1-\frac{\left(1-{\mathrm{P}}_{\mathrm{V}}\right){\mathrm{L}}_{\mathrm{U}}}{{\mathrm{L}}_{\mathrm{U}}^{(\mathrm{H}=0)}}\)	0.18 (− 0.03, 0.38)

^aAs defined by ‘net in use’
^bAs defined by ‘net in use last night’
^cIncluding the reduction in available nets due to attrition via its effect on \({\mathrm{L}}_{\mathrm{U}}\)
^dWhere \({\mathrm{P}}_{\mathrm{V}}=0.08\) is the estimate of the proportion of impact on vectorial capacity lost because of the direct effect of holes in nets

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ISSN: 1475-2875

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