Table 2.

Table of notation.

Notation	Description	Source
Rv	The calibrated country- and population-specific rate of transmission from HIV-infected members of the primary cohort in viral load stratum v ∈ V to any susceptible cohort of interest. V is the set of viral load strata (see Methods).	Derived
NHIV−	The number of HIV-uninfected persons in the primary cohort at risk of infection at index year (simulation time 0).	Literature
PSQ,0	Monthly incidence probability at time 0 in the primary cohort in the status quo strategy.	Literature
Pup	Proportion of the primary cohort members who participate in the intervention.	Literature
Peff	The relative incidence reduction of a prevention intervention for individuals who participate. For PrEP, this can be viewed as a combined adherence/efficacy parameter, and for ART and testing, this can be assumed to be 0. This parameter accounts for the instantaneous incidence reduction at the time the person initiates the prevention intervention.	Literature
PINT,0	Monthly incidence probability at time 0 in the primary cohort in the intervention strategy. This value should be lower than PSQ,0 if both Pup and Peff> 0.	Derived
ISQ,agg (IINT,agg)	Aggregate incidence rate in the status quo (intervention) strategy, including inside- and outside-attributable incidence.	Literature (Derived)
ISQ,in (IINT,in)	Incidence rate in the status quo (intervention) attributable to those inside the primary cohort (inside-attributable incidence).	Literature (Derived)
ISQ,out (IINT,out)	Incidence rate in the status quo (intervention) attributable to those not in the primary cohort (outside-attributable incidence)	Derived
t	Duration of the intervention (in months).	User-defined
PSQ,0:t (PINT,0:t)	Cumulative incidence probability within the primary cohort in the status quo strategy (intervention strategy).	Derived
ISQ,0:t, agg	Aggregate infections within the primary cohort in the status quo strategy from time 0 to t.	Derived
TSQ,0:t,in (TINT,0:t,in)	The number of inside transmissions in the status quo (intervention) from time 0 to t.	Model output
ISQ,0:t, in (IINT,0:t, in)	The number of inside-attributable infections in the status quo (intervention) from time 0 to t.	Model output
ISQ,0:t,out (IINT,0:t,out)	Cumulative infections within the primary cohort from time 0 to t in the status quo (intervention) strategy attributable to those outside the primary cohort.	Derived
IINT,0:t,agg	Aggregate infections within the primary cohort in the intervention strategy from time 0 to t.	Derived
(PSQ,0:t,out (PINT,0:t,out)	The cumulative probability of acquiring HIV between time 0 and t in the status quo (intervention) strategy due to transmissions attributable to outside the primary cohort.	Derived
${\overline{\mathit{P}}}_{\mathit{INT}}$	The average monthly incidence probability (from time 0 to t) within the primary cohort in the intervention strategy.	Derived
PINT,t	The monthly incidence probability at time t in the intervention strategy.	Derived
y	The year (since model start) in which a hypothetical transmission is averted due to the intervention. We assume y ∈ (1,2,…,Y}. Y is an arbitrary user-defined horizon and may correspond to either the duration of the intervention, the lifetime of the primary cohort, or another relevant horizon.	User-defined
TSQ,y,out (TINT,y,out)	Total transmissions to outside the primary cohort (“outside transmissions”) in the status quo (intervention) in year y.	Model output
TAy	Transmissions averted in year y due to the intervention.	Derived
LHIV+,y	Average life-years of a susceptible cohort that starts off with acute HIV infection (for a transmission in year y).	Model output
LHIV−,y	Average life-years of a susceptible cohort that starts off HIV-uninfected but is subject to an HIV incidence (for a transmission in year y).	Model output
CHIV+,y	Average HIV cost of a susceptible cohort that starts off with acute HIV infection (for a transmission in year y).	Model output
CHIV−,y	Average cost of a susceptible cohort that starts off HIV-uninfected but is subject to an HIV incidence (for a transmission in year y).	Model output
tilde (~)	Denotes that life years/costs have been further discounted based on the year the transmission was averted and thus have been brought back to time 0 of the primary cohort (index year). For instance, for a transmission that is averted in year y, L is the discounted average life-years in year y (automatically discounted in the model), whereas $\tilde{\mathit{L}}$ is the corresponding value further discounted and brought back to time 0 of the primary cohort (this is done manually outside the model via Eq.’s 6-10).
${\tilde{\mathit{L}}}_{\mathit{TA}}$	Total life-years gained via all the transmissions averted over Y years.	Derived
${\tilde{\mathit{C}}}_{\mathit{TA}}$	Total change in HIV-related costs due to all the transmissions averted over Y years. Note that this number is expected to be negative, as averting transmissions is likely to reduce costs (but does not have to for the method to work).	Derived
d	Model discount rate (often set to 3%, per convention [16]).	User-defined
$\Delta \tilde{\mathit{L}}$	The average life-years difference between the status quo and intervention for the primary cohort, discounted at d (often 3%).	Model output
$\Delta \tilde{\mathit{C}}$	The average cost difference between the status quo and intervention for the primary cohort, discounted at d (often 3%).	Model output
N	The size of the primary cohort.	Literature or model run size
ICER	Incremental cost-effectiveness ratio (change in cost divided by change in life expectancy), including the benefits of averting HIV transmissions.	Derived

ART: antiretroviral therapy; HIV: human immunodeficiency virus; PrEP: pre-exposure prophylaxis.