The total expected number of transmission acquired HIV cases is
= BLOOD x T x (A + B + C + D)
Where A is the number of infected donors, who donate despite knowing they are HIV+
A = POP x PREV x INFDON x (1-(1-((1-SNAT) x (1-SEIA))))
Where B is the number of infected donors during the windows period where neither the Nucleic Acid Test nor ELISA test can detect HIV.
B = PSC x WNAT/(365.25 x YRSPS)
PSC = POP x INC x YRSPS x DON
Where C is the number of infected donors, who were asymptomatic and were not detected due to false-negative screening results resulting from the period where only the Nucleic Acid Test (but not the ELISA) can detect HIV (C1) and the period where both NAT and ELISA can detect HIV (C2).
C = C1 + C2
C1 = PSC x (1-SNAT) *(WNAT-WEIA)/(365.25 x YRSPS))
C2 = PSC x (YRSPS-WEIA/365.25)/YRSPS x (1-SNAT) x (1-SEIA)
Where D is the number of infected donors who are correctly detected but whose blood nevertheless is allowed to be donated due to laboratory misclassification errors.
D = (PSC + (POP x PREV x INFDON)- 2 (A + B + C)) x LAB
BLOOD = the average number of persons who become infected via transfusions from a single infected donor
T = Probability that recipient of infected blood donation will become infected (%)
POP = numbers aged 18–69 in group.
DON = Percentage of people in group who donate blood (%)
INFDON = Percentage of people who know they are HIV+ but nevertheless donate.
PREV = Prevalence rate
INC = Incidence rate per annum
YRSPS = Pre-symptomatic period: average length of time from infection to symptoms (years) based on weighted average of first-time to repeat donors over the 10 year period
PSC = Number of pre-symptomatic donors
B1 = number of infected donors during the window period of the Nucleic Acid Test.
B2 = number of infected donors during period when the Nucleic Acid Test is working but EIS is still in window period
SNAT = Sensitivity of the Nucleic Acid Test
WNAT = Duration of the Nucleic Acid Test window period (days)
SEIA = Sensitivity of the anti-HIV test
WEIA = Duration of the anti-HIV window period (days)
LAB = Laboratory misclassification error rate (%)