Info-gap management of public health Policy for TB with HIV-prevalence and epidemiological uncertainty

BMC Public Health

Table 1 Model parameters in the Murray-Salomon basic model

Symbol	Definition	HIV neg	HIV pos
Birth rate ^g	births/year/person	0.03^c	0^c,h
N	population size	0.821ⁱ	0.179ⁱ
T	births per year = birth rate×N ^c
λ ^g	infection rate	1.81×10⁻³ ^m	2.96×10⁻³ ^m
K ^k	# respiratory contacts with infected/person/year
L ^k	probability that respir. contact with infectious source leads to infection
KL		5–15^a
Y ^k	# infectious cases in population
μ ^g	non-TB death rate	0.009^c	0.05^c
p	proportion of new infections entering slow breakdown	0.9 (0.85–0.95)^a	0.4 (0.3–0.5^a)
β _F ^g	fast breakdown rate	2^c	3
β _S ^g	slow breakdown rate	0.001 (5–15×10⁻⁴ ^a)	0.075 (0.05–0.10^a)
χ ^g	rate of application of INH to infected individuals	0.75 (^ℓ)
ν	protection from superinfection conferred by primary infection	0.75 (0.5–1^a)
w	short-term INH effectiveness	0.7
h	long-term INH effectiveness	0.7
d ^i,j	proportion of pre-diagnosed cases in clinical category i entering diagnosis category j
d ^1,1		0.45 (0.4–0.5)^j	0.35 (0.3–0.4)^j, ^e
d ^2,1		0.55 (0.5–0.6)	0.65 (0.6–0.7) ^e
d ^3,1			^e
d ^i,2		d ^i,2=1−d ^i,1	^f
s ⁱ	proportion of new cases in clinical category i
s ¹, s ²	proportion of new cases in clinical category i	0.45 (0.4–0.5^a)
s ³	proportion of new cases in clinical category i	s ³=1−s ¹−s ² ^d
δ ^j ^g	diagnosis rate for category j	0.6 ^ℓ	0.6 ^ℓ
σ ^g	smear conversion rate	0.03 ^c

Model parameters in the Murray-Salomon basic model, Table Two, p.42, in ref. [18], except for K, L, Y and N which are defined in footnote 2 on p.21 of [18]. Where a value is specified only for HIV-negative, the same value is used for HIV-positive.
^aFootnote 8, p.24, [18].
^bFootnote e, Table A5, p.63, [18].
^cTable A5, p.63, [18].
^dFootnote c, Table A5, p.63, [18].
^eFootnote †, Table A5, p.63, and Figure A5, p.57 [18].
^fFootnote b, Table A5, p.63,[18].
^gRate: per person per year. In Botswana the average is 477 cases per year per 100,000 people. 62% of them are HIV infected.
^hDepends on HIV prevalence. In areas with HIV and without preventive treatment, 25% of babies born from HIV mothers are infected.
ⁱIn Botswana.
^j[Dye C, Scheele S, Dolin P, Pathania V, Raviglione MC. Consensus statement. Global burden of tuberculosis: estimated incidence, prevalence, and mortality by country. WHO Global Surveillance and Monitoring Project. JAMA. 1999 Aug 18;282(7):677–86.].
^kNot needed since λis a primary datum.
^ℓDecision variable.
^mCan also be treated as a decision variable.

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