Using Mathematical Models to understand TB Epidemics

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Using Mathematical Models to understand TB
Epidemics

• Dr Pieter Uys
• Prof John Hargrove
• Stephen Millen
• SACEMA

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TB 101

• TB agent mycobacterium tuberculosis

• Airborne droplets enter lungs

• Disease immediate or possibly latent

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The bacterium
Thin section transmission electron
micrograph Source http//www.wadsworth.org/databa
nk/hirez/mcdonp4.gif

• Bacteria revealed using acid-fast Ziehl-Neelsen
  stain Magnified 1000 X.
• Source CDC-PHIL ID 5789

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Extent of the problem

• Over one-third of the world's population carries
  the TB bacterium. Not everyone infected develops
  the full-blown disease, so asymptomatic, latent
  TB infection is most common. However, 10 of
  latent infections progress to active TB disease,
  which, if left untreated, kills more than half of
  its victims.

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• In 2004, mortality and morbidity statistics
  included 14.6 million chronic active TB cases,
  8.9 million new cases, and 1.6 million deaths,
  mostly in developing countries. Increasingly,
  people in the developed world are contracting
  tuberculosis because their immune systems are
  compromised by e.g. HIV/AIDS.

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• The rise in HIV infections and the neglect of TB
  control programs have enabled a resurgence of
  tuberculosis. The emergence of drug-resistant
  strains has also contributed to this new epidemic
  with, from 2000 to 2004, 20 of TB cases being
  resistant to standard treatments and 2 resistant
  to second-line drugs.

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TB Incidence per 100 000
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Mathematical modelling of a TB epidemic

• Based on the SEIR framework

Susceptible
infEcted
Infectious
Recovered
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Model for susceptible and resistant TB, with
reinfection
Model is represented by a system of differential
equations and investigated by computer simulations
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Annual costs of treating susceptible cases and
MDR cases
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The Impact of the Delay Time
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• To achieve control of a TB epidemic, at no time
  prior to diagnosis should the value of
  exceed

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So what can be done to reduce delay to diagnosis?

• What factors contribute to the delay?

Need to examine the various scenarios from onset
of symptoms to eventual diagnosis and start of
therapy
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• Delay in deciding to visit a health care provider.

May visit a health care provider who has no
facility for testing for TB
Delay in getting to a health care provider who
does test for TB
He may be treated for the cough, but not for TB,
and discharged. A CXR may be taken. A sputum
sample may be taken, and further samples
requested
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• The delay in the start of treatment, in the event
  that the patient tests positive.

The delay arising from the time it takes the
laboratory to examine the sputa.
The delay in the patient returning to get the
result, once all of the sputum samples have been
provided.
Although a patient may have TB, the test may,
nonetheless, return a negative result. The
result is a function of the sensitivity of the
test
Same considerations apply to CXRs