Modelling changes in HIV prevalence among women attending antenatal clinics in Uganda

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Modelling changes in HIV prevalence among women
attending antenatal clinics in Uganda Brian
Williams
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b
N
d

I
l
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I
/
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I
S

m
I
m
S
? birth rate N S I ? rate at which new
infections occur ? mortality
The basic model
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R0 3.3
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b
N
d

I
l
S
I
/
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I
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m
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Normal (Weibull 2)
? birth rate N S I ? infection
rate ?I Weibull mortality
Exponential (Weibull 1)
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I
b
N

d
l

S
/
N

I
I

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m
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m
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? birth rate N population ? ?e?P ?I
Weibull mort.
?P
e

Heterogeneity in sexual behaviour
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C(t)
Including control
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aM

• ? birth rate
• N population
• ?e
• ?I mortality

e

aM

Mortality leads to behaviour change
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Nairobi
6 yr
Nunn P et al. Tuberculosis control in the era of
HIV. Nat Rev Immunol. 2005 Oct5(10)819-26.
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Corbett 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. 2003188 1156-63.
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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
(0.140.95) 0.48 (0.27-0.84) 1.15 (0.48-1.13)
DDR 0.13 (0.090.20)
Gold miners in South Africa
We define disease duration as prevalence divided
by incidence
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TB-HIV model
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.
Williams BG et al. The impact of HIV/AIDS on the
control of tuberculosis in India. PNAS 2005 102
9619-9624.
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Percent Percent
HIV positive HIV negative
Williams BG et al. HIV Infection, Antiretroviral
Therapy, and CD4 Cell Count Distributions in
African Populations. J Infect Dis, 2006 194
1450-8.
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?
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
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Spatial Epidemiology of HIV Doubling time 1
year Life expectancy 10 years Number 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.
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Questions for all of us

• Can we combine spatial/network models with our
  more conventional continuous time models of HIV?
• Can we get a better understanding of the
  host-viral interaction?
• What are the population level implications of 2?
• Do we have enough data to explore fully the joint
  dynamics of TB and HIV?

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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