1. Cholera in South Africa 2000/2001
Catalina Anghel
Andrea Borowski

2. Overview What is cholera? Cholera in South Africa Models Conclusions
Data
Models
SIR model
Modified SIR model according to Torres Codeco
Conclusions

3. 1. What is cholera? Acute intestinal infection caused by the bacterium
Vibrio cholerae
Infection results in a diarrhoea that can lead to dehydration and death
Infected people:
excrete bacteria between 7 and 14 days
<20% show typical symptoms of cholera
Rarely person to person transmission
History? Natural reservoir? Rarey transmitted through person to person contact, mainly desease of young children

4. 2. Cholera in South Africa in 2000/2001
Total number of infected:
Start in mid august 2000
Affected region: KwaZulu-Natal
population: 9.3 mi.
most people use rivers and wells as their water supply
Heavy rainfall starting in November 2000

5. 2.1. Data
total infected cases and deaths from October 13, 2000 to April 16, 2001

6. ratio of total deaths to total number of infected people decreased, then stabilized
2.1 Data

7. 3. Models

8. 3.1 SIR model
x 10 4
accumulative infectives c(t), fitted using SIR, first trial 9
raw data
fitted data 8 7 6
Fitted α and β numerically using a integration method embedded within a minimization routine
α = [1/day]
β = 2.2 x 10-7 [1/day] 5
number of infected 4 3
Person-person contact model 2 1 20 40 60 80
100
120
140
160
180
200
days
3.1 SIR model

9. Whole susceptible population becomes infected
Number of infected increases and decreases over time
3.1 SIR model

10. Fitted α, β and S0 using the same method α = - 0.025 [1/day]
β = 1.5 x 10-7 [1/day]
S0= 82,500
Un-physical results:
α < 0
S0< total infected. 20 40 60 80
100
120
140
160
180
200 1 2 3 4 5 6 7 8 9
x 10
accumulative infectives c(t), fitted using SIR, 2nd trial
days
number of infected
raw data
fitted data
3.1 SIR model

11. 3.2 Modified SIR model (Torres Codeco)
Infected
(I) r
Susceptible (S) a e
λ(B)
Environmental factors
Population growth during infection was not taken into account!
Aquatic toxigenic V. cholerae (B) m
3.2 Modified SIR model (Torres Codeco)

12. 3.2 Modified SIR model (Torres Codeco)
Symbol
Description λ
probability to catch cholera (cells/ml) B
concentration of toxigenic V. cholerae in water (cells/ml) a
rate of exposure to contaminated water (day-1) r
rate at which people recover from cholera (day-1) m
growth rate of V. cholerae in aquatic environment (day-1) e
contribution of each infected person to the population of V. cholerae in the aquatic environment (cells/ml day-1 person-1) K
concentration of V. cholerae in water that yields 50% chance of catching cholera (cells/ml)
3.2 Modified SIR model (Torres Codeco)

13. 3.2 Modified SIR model (Torres Codeco)
Fitted a, r and e:
a = (Codeco: a = 1)
r = (Codeco: r = 0.2)
Different definition for cholera cases
e =
(Codeco: e = 10)
Hospitalizing
Hospitalizing may lower contribution of sick people to bacteria population or they died this fast that they could not
fitted data look similar to SIR model, where only alpha and beta were fitted.
3.2 Modified SIR model (Torres Codeco)

14. 3.2 Modified SIR model (Torres Codeco)
S and I plots similar to SIR model
3.2 Modified SIR model (Torres Codeco)

15. 3.2 Modified SIR model (Torres Codeco)
‘Heavy rains and flooding have increased the risk of contaminating rivers and drinking wells.’
‘The risks are particularly high because many villages have no latrines, and human waste mixes with floodwaters.’
‘10 million households were cut off from water in 2001.’
3.2 Modified SIR model (Torres Codeco)

16. 3.2 Modified SIR model (Torres Codeco)
modified e over time to take rainy season into consideration:
3.2 Modified SIR model (Torres Codeco)

17. 3.2 Modified SIR model (Torres Codeco)
a = 0.110, r =
e =1.566* (1+sin(2*π/ ))
3.2 Modified SIR model (Torres Codeco)

18. 3.2 Modified SIR model (Torres Codeco)
Number of susceptibles decreases to 320,000 and stays constant
Infected population decreases at the beginning (start of the epidemic in august!)
3.2 Modified SIR model (Torres Codeco)

19. 3.2 Modified SIR model (Torres Codeco)
Control mechanisms
Hygienic disposal of human feces
Adequate supply of safe drinking water
Hygienic measures: washing hands, cooking food
Vaccination (long-term)
3.2 Modified SIR model (Torres Codeco)

20. How do control mechanisms influence the parameters?
Good sanitation reduces parameter e and water treatment reduces parameter a.
The smaller these parameters are, the larger must be the susceptible pool in order to a cholera outbreak to develop.
3.2 Modified SIR model (Torres Codeco)

21. 4. Conclusions
Simple SIR model does not consider transmission through water supply.
SIR model taking into account the aquatic reservoir corresponds to our data
Through changing parameter e over time, we included the onset of the rainy season in the model.
FUTURE:
Taking into account the onset of the epidemic (August-October)
Seasonal changes also in parameter a
Independent estimates for parameters to compare with fitted parameters
Using the model to fit data from other cholera outbreaks

22. References www.who.int www.textbookofbacteriology.net
Endemic and epidemic dynamics of cholera: the role of the aquatic reservoir, Claudia Torres Codeco, BMC Infectious Diseases, 2001