Modeling the 20001 Cholera Epidemic in South Africa

1
Modeling the 2000/1 Cholera Epidemic in South
Africa

• Ignacio Ramis Conde
• Martin Krkosek
• Subramanian Ramamoorthy
• Amber Smith

2
What is Cholera?

• Acute intestinal infection caused by
• Vibrio Cholerae
• Produces enterotoxin, causes diarrhea death by
  dehydration
• Endemic in India Bangladesh and has spread
  globally
• No epidemics in West Africa for 100 years prior
  to 1970
• long term dynamics of this disease is of interest
• In highly endemic areas, mainly a disease of the
  young
• population flux (birth, death, etc.) is of
  interest
• Outbreaks usually occur before and after monsoon
  rains
• effect of seasonal forcing may be of interest

3
Characteristics of Cholera

• Transmitted by contaminated water and food
• Multiple reservoirs aquatic, human
• Incubation period 1-5 days
• 90 of infections are sub-clinical but result in
  excretion of bacteria for up to 2 weeks
• Immunity
• acquired by sub-clinical exposure to bacteria
• not life-long, lt 3 years

4
Model of Cholera Dynamics with Aquatic Reservoir
Susceptible S
Infected I
Recovered R
r
e
Aquatic Cholera B
k
5
Equations Parameters

6
Alternate Functional Forms of

• Linear
• Saturating
• Sigmoidal

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Model Fitting
Fixed parameters S01.4M r10-1 (days)-1
I0900 ?0.12 (days)-1 k-?-0.33
(days)-1 Fitted parameters ?2.91x10-4
Lday-1 e1.99x10-4 Lday-1
Sources of data WHO, Codeco (2001)
8
R0 Calculation
Assume intrinsic growth rate of the free-swimming
stage is always negative so ?-kgt0 Pseudo steady
state approximation for B
Rate of encounter with bacteria
To calculate R0 introduce 1 infective individual
in a completely susceptible population
Aquatic concentration of bacteria produced by
one infective
Lifetime of infective
9
Control Strategies

• e - sewage treatment
• - drinking water treatment - food
  preparation hygiene - personal hygiene
• ? - treating infected individuals

Note if treat infectives with rehydration
therapy and not address sanitation ? gt
R0
10
Long-term Dynamics
Susceptible S
Infected I
Recovered R
r
d
d
d
e
bN
Aquatic Cholera B
k
k
11
Long-term Dynamics, Cont.

12
Long Term Dynamics
S
R
I
B
13
Other Factors to Consider Seasonality

• KwaZulu-Natal seasons
• Summer Sept. - April (Jan is hottest wettest)
• Winter May - August
• V. Cholerae
• Vibrios grow rapidly in warm temps
• Have symbiotic relationship with zooplankton
• More zooplankton in warm temps

14
Seasonality cont.

• Contamination Issues
• Heavy rains/flooding increase water contamination
• i.e., Contact with contaminated water oscillates
• i.e., Contribution to contaminated water
  oscillates

15
Conclusions Future Work

• Simple SIR-B model corresponds to data
• Ro1.12
• Long-term dynamics damped oscillations
• Preliminary results show damped oscillations
• Can we make better predictions, build better
  models?
• Effect of Control Mechanisms
• Water sanitation
• Hand washing food prep
• Further explore
• seasonality effects
• long-term control mechanisms
• vaccination strategies

16
Acknowledgements

• Park City Mathematics Institute
• Dr. Caroline Bampfylde