Forecasting the Population-Level Impact of Reductions in HIV Antiretroviral Therapy in Papua New Guinea

Table 1

Definitions and value ranges for input and fitting parameters used in our HIV transmission model.

Parameter	Description	Value (Range)	Footnote/Reference
Demographic parameters
𝑁0	Initial size of sexually active population	2,317,648	(a)
𝜌	Population growth rate	4.8% (4.7–4.9%)
𝛼0	Initial proportion of population in urban areas	15%	(b)
𝜈𝑢	Migration rate from urban to rural settings	2.25% (2–2.5%)
𝜈𝑟	Migration rate from rural to urban settings	0.2% (0.18–0.23%)
1/𝜇	Average duration that a person remains in the sexually active population	45 years	Assumed
HIV Biological parameters
𝛽	Rate at which susceptible individuals with partners that are chronically infected become infected with HIV	fitted (±10%)	(c)
𝜃𝑎	Multiplicative increase in HIV transmission probability for partners with AIDS	5 (4–6)	[7, 8]
𝜃𝑡	Multiplicative decrease in HIV transmission probability for HIV-infected partners on effective ART	0.08 (0.05–0.13)	[9, 10]
𝛾	Disease progression rate at which individuals chronically infected with HIV progress to AIDS	0.075 (0.06–0.09)	[7, 9]
𝜇𝑐	Death rate per year for a person chronically infected with HIV	3%	[11, 12]
𝜇𝑎	Death rate per year for individuals with AIDS	30%	[11, 12]
𝜇𝑡	Death rate per year for HIV-infected individuals on ART	5%	[11, 12]
Clinical parameters
𝛿^𝑐𝑢	Diagnosis rate for urban individuals with chronic infection	fitted (±10%)	(e)
𝛿^𝑎𝑢	Diagnosis rate for urban individuals with AIDS	fitted (±10%)
𝛿^𝑐𝑟	Diagnosis rate for rural individuals with chronic infection	fitted (±10%)
𝛿^𝑎𝑟	Diagnosis rate for rural individuals with AIDS	fitted (±10%)
𝜏𝑢	Rate at which urban individuals diagnosed with AIDS begin treatment	fitted (±10%)	(f)
𝜏𝑟	Rate at which rural individuals diagnosed with AIDS begin treatment	fitted (±10%)
1/𝜔	Average duration at which individuals remain on ART	10 years (6.7–20 years)	(g)

(a)To calibrate the model to the HIV epidemic in PNG from 1990 to 2010, the sexually active population size was assumed to be equal to the 15–49-year-old adult population estimated by the World Bank [13]. From the initial 1990 population, the value of 𝜌 (which is assumed to be the same for urban and rural areas) is set to match the growth of the 15–49-year-old population seen in PNG from 1990 to 2008 [13].
(b)Data from the World Bank gives the proportion of the population that is living in urban areas to be approximately 15%. However, the proportion of the population in urban areas has been declining very slightly from 1990 to 2008 [13]. The migration rates between urban and rural areas are set to follow this trend after the urban proportion is set to be initially 15%.
(c)This rate incorporates the number of sexual partners, condom usage, effect of STIs, and other factors that affect HIV transmission. As we are focused on the impact of ART reductions, we group these factors into a single rate which is then fitted to the annual prevalence and incidence estimates for PNG. The value of 𝛽 is likely to be different for urban and rural areas; however, there is limited data available for these population categories so we have assumed the same value for fitting purposes.
(d)The value and range for 𝛾 have been used to match the estimates for the number of people who require ART in PNG. The disease progression rate we use corresponds to an average duration of being chronically infected equal to 11–16.6 years which is much longer than established durations for low resource settings [14]. Due to the simplicity of our HIV transmission model, which only has one infection stage prior to AIDS, a longer average time period is required to match the actual epidemiology.
(e)The rate at which infected people are diagnosed is fitted to match the overall number of diagnoses recorded in PNG [2].
(f)The rate at which individuals diagnosed with AIDS begin treatment is fitted to match the overall number of people who have started treatment since 2003, the estimated number of people who require treatment, and the ART coverage in PNG [2, 4].
(g)The average duration at which urban and rural people remain on ART is likely to be different due to supply and logistical issues. However, there is very little data on the length of time people remain on ART in PNG; hence, we have assumed the same value and range for urban and rural areas.