Table 1

Model parameters in the Murray-Salomon basic model
Symbol Definition HIV neg HIV pos
Birth rate g births/year/person 0.03c 0c,h
N population size 0.821i 0.179i
T births per year = birth rate×Nc
λg infection rate 1.81×10−3m 2.96×10−3m
Kk # respiratory contacts with infected/person/year
Lk probability that respir. contact with infectious source leads to infection
KL 5–15a
Yk # infectious cases in population
μg non-TB death rate 0.009c 0.05c
p proportion of new infections entering slow breakdown 0.9 (0.85–0.95)a 0.4 (0.3–0.5a)
βFg fast breakdown rate 2c 3
βSg slow breakdown rate 0.001 (5–15×10−4a) 0.075 (0.05–0.10a)
χg rate of application of INH to infected individuals 0.75 ()
ν protection from superinfection conferred by primary infection 0.75 (0.5–1a)
w short-term INH effectiveness 0.7
h long-term INH effectiveness 0.7
di,j proportion of pre-diagnosed cases in clinical category i entering diagnosis category j
d1,1 0.45 (0.4–0.5)j 0.35 (0.3–0.4)j, e
d2,1 0.55 (0.5–0.6) 0.65 (0.6–0.7) e
d3,1 e
di,2 di,2=1−di,1 f
si proportion of new cases in clinical category i
s1, s2 proportion of new cases in clinical category i 0.45 (0.4–0.5a)
s3 proportion of new cases in clinical category i s3=1−s1s2d
δjg diagnosis rate for category j 0.6 0.6
σg 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.

Decision variable.

mCan also be treated as a decision variable.

Ben-Haim et al.

Ben-Haim et al. BMC Public Health 2012 12:1091   doi:10.1186/1471-2458-12-1091

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