Modelling changes in HIV prevalence among women attending antenatal

clinics in Uganda

Brian Williams

0

5

10

15

20

1970 1990 2010 2030

Pre

vale

nce

(%)

ANC women

Behaviour change in Uganda

= birth rate

N = S + I

= rate at which new infections occur

= mortality

S I

I N SI /N I

S

The basic model

0

20

40

60

80

100

1970 1990 2010 2030

Pre

vale

nce

(%)

012345678910

Inci

denc

e/M

orta

lity

(%/y

r)

ANC women in Uganda

R0 = 3.3

0

0

-1=70%

R

R

= birth rate

N = S + I

= infection rate

I = Weibull mortality

S I

I N SI /N I

S

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30Time (years)

P(s

urv

ivin

g)

Normal (Weibull 2)

Exponential(Weibull 1)

0

20

40

60

80

1970 1990 2010 2030

Pre

vale

nce

(%)

0

2

4

6

8

10

12

Inci

denc

e/M

orta

lity

(%/y

r)

ANC women in Uganda

= birth rate

N = population = e–P

I = Weibull mort.

~

~

S I

I N S I /N I S

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30Prevalence (%)

Re

lativ

e t

ran

smis

sio

n

.

–Pe

Heterogeneity in sexual behaviour

0

5

10

15

1970 1990 2010 2030

Pre

vale

nce

(%)

0

1

2

Inci

denc

e/M

orta

lity

(%/y

r)

ANC women in Uganda

0.0

0.2

0.4

0.6

0.8

1.0

1985 1990 1995 2000Year

Re

lativ

e t

ran

smis

sio

n

.

~

S I

I N SI /N I

S ~

= birth rate

N = population = C(t)

I = mortality

~

~

C(t)

Including control

0

5

10

15

1970 1990 2010 2030

Pre

vale

nce

(%)

0

1

2

Inci

denc

e/M

orta

lity

(%/y

r)

ANC women in Uganda

~

S I

I N SI /N I

S *

= birth rate

N = population = e

I = mortality

~

* –M

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4Annual mortality (%)

Re

lativ

e t

ran

smis

sio

n

. –Me

Mortality leads to behaviour change

0

5

10

15

1970 1990 2010 2030

Pre

vale

nce

(%)

0

1

2

Inci

denc

e/M

orta

lity

(%/y

r)

ANC women in Uganda

Nairobi

6 yr

Nunn P et al. Tuberculosis control in the era of HIV. Nat Rev Immunol. 2005 Oct;5(10):819-26.

9.4

1.11.11.0

5.9

2.2

0

2

4

6

8

10

1991-1994 1995-1997 1998-1999

Ann

ual in

ciden

ce (

%)

.HI V- HI V+

TB incidence among gold miners in SACorbett EL Stable incidence rates of tuberculosis (TB) among human immunodeficiency virus (HIV)-negative South African gold miners during a decade of epidemic HIV-associated TB. J Infect Dis. 2003;188: 1156-63.

SS+ Tuberculosis

Prevalence Incidence Disease Duration

(%) (%/yr) (yr)

HIV+ 0.44 (0.02-1.05) 2.87 (1.94-4.25) 0.15 (0.05-0.48)

HIV- 0.55 (0.14–0.95) 0.48 (0.27-0.84) 1.15 (0.48-1.13) DDR = 0.13 (0.09–0.20)

Gold miners in South Africa

We define disease duration as prevalence divided by incidence

Repeat the model 4 times, once for each stage of HIV. Use time series of HIV prevalence to determine incidence. Incidence gives rate at which people enter first stage; overall (Weibull) survival determines rate at which people move to next stage.

TB-HIV model

Williams BG et al. The impact of HIV/AIDS on the control of tuberculosis in India. PNAS 2005 102: 9619-9624.

Impact of interventions on TB cases in KenyaT

B in

cide

nce/

100k

/yr

800

600

400

200

0

.Baseline

ARV 80%

TLTI (6 m)

TLTI (life)

ARV 100%

TB detect.

TB cure

HIV incid

Base line:CDR = 50%CR = 70%Interventions:1% increase

1980 2000 2020 2040 Year

Currie, C. et al. Cost, affordability and cost-effectiveness of strategies to control tuberculosis in countries with high HIV prevalence. BMC, 2005. 5: 130.

Per

cent

Per

cent

HIV

pos

itive

HIV

neg

ativ

e

Williams BG et al. HIV Infection, Antiretroviral Therapy, and CD4+ Cell Count Distributions in African Populations. J Infect Dis, 2006 194: 1450-8.

1,000

2,000

10 20

Time to death (yrs)

Initi

al C

D4/

L

Time to death (yrs)

1,000

2,000

10 20

Initi

al C

D4/

L

Model 1

CD4 decline independent of starting value

Survival determined by pre-infection CD4

Model 2

Survival independent of starting value

CD4 decline determine entirely by starting value and survival distribution

Spatial Epidemiology of HIV

Doubling time = 1 yearLife expectancy = 10 yearsNumber of partners = 4

Proportion of random partners chosen at random = 0 (left hand set) or 10% (right hand set) in the following slides.

Note that in this model migrants have exactly the same sexual behaviour and individual risk as non-migrants.

1. Can we combine spatial/network models with our more conventional continuous time models of HIV?

2. Can we get a better understanding of the host-viral interaction?

3. What are the population level implications of 2?

4. Do we have enough data to explore fully the joint dynamics of TB and HIV?

Questions for all of us

Advice to young epidemiologists

Never make a calculation until you know the answer. Make an estimate before every calculation,

try a simple biological argument (R0, generation time, selection, survival, control). Guess the answer to every puzzle. Courage: no one else needs to know what the guess is. Therefore, make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case, life as an epidemiologist, however long, is more fun.

Plagiarised from E.F. Taylor and J.A. Wheeler Space-time Physics 1963