zhao1

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Abstract
Mathematical models have been used to simulate HIV transmission and to study the use of preexposure prophylaxis (PrEP) for HIV prevention. Often a single intervention outcome over 10 years has been used to evaluate the effectiveness of PrEP interventions. However, different metrics express a wide variation over time and often disagree in their forecast on the success of the intervention. We develop a deterministic mathematical model of HIV transmission and use it to evaluate the public-health impact of oral PrEP interventions. We study PrEP effectiveness with respect to different evaluation methods and analyze its dynamics over time. We compare four traditional indicators, based on cumulative number or fractions of infections prevented, on reduction in HIV prevalence or incidence and propose two additional methods, which estimate the burden of the epidemic to the public-health system. We investigate the short and long term behavior of these indicators and the effects of key parameters on the expected benefits from PrEP use. Our findings suggest that public-health officials considering adopting PrEP in HIV prevention programs can make better informed decisions by employing a set of complementing quantitative metrics.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
default 1.0
Id Name Initial quantity Compartment Fixed
EXT EXT 1.0 default
I Infected 149400.0 default
Ip Infected on PrEP 16600.0 default
S Susceptible 667200.0 default
Sp Susceptible on PrEP 166800.0 default

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v_1 EXT = Sp

k*Lambda
v_10 I = EXT

d*I
v_2 Sp = Ip

((1-alphas)*beta*I/N+(1-alphas)*(1-alphai)*beta*Ip/N)*Sp
v_3 Sp = EXT

mu*Sp
v_4 EXT = S

(1-k)*Lambda
v_5 S = I

(beta*I/N+(1-alphai)*beta*Ip/N)*S
v_6 S = EXT

mu*S
v_7 Ip = EXT

mu*Ip
v_8 Ip = EXT

d*Ip
v_9 I = EXT

mu*I

Global parameters

Id Value
Lambda 38094.0
N 0.0
alphai 0.5
alphas 0.5
ba 0.003
beta 0.0
d 0.1302
k 0.2
mu 0.025
n 65.8494

Local parameters

Id Value Reaction

Assignment rules

Definition
N = Sp+S+Ip+I
beta = 1-(1-ba)^n

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments