Transcript Modeling the 2000/1 Cholera Epidemic in South Africa

Modeling the 2000/1
Cholera Epidemic in South
Africa
Ignacio Ramis Conde
Martin Krkosek
Subramanian Ramamoorthy
Amber Smith
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
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, < 3 years
Model of Cholera Dynamics
with Aquatic Reservoir
Susceptible
S
Infected
I
e
k
Aquatic Cholera
B
r
Recovered
R
Equations & Parameters
Alternate Functional Forms
of
• Linear:
• Saturating
• Sigmoidal
Model Fitting
Fixed parameters
S0=1.4M
r=10-1 (days)-1
I0=900
=0.12 (days)-1
k-=-0.33 (days)-1
Fitted parameters
=2.91x10-4 L·day-1
e=1.99x10-4 L·day-1
Sources of data: WHO, Codeco (2001)
R0 Calculation
dS
  SB
dt
dI
 SB  (r   ) I
dt
dB
 eI  (k   ) B
dt
Assume intrinsic growth rate of
the free-swimming stage is
always negative – so -k>0
Pseudo steady state
approximation for B:
To calculate R0 introduce
1 infective individual in
a completely susceptible
population
eI
B
 k
1
e
R0 

r    k
Lifetime of infective
Rate of
encounter with
bacteria
Aquatic concentration of
bacteria produced by one infective
Control Strategies
1
e
R0 

r    k
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:

=> R0
Long-term Dynamics
Susceptible
S
bN
Infected
I
d
e
k
Aquatic Cholera
B
r
+d
Recovered
R
d
Long-term Dynamics, Con’t.
Long Term Dynamics
S
R
I
B
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
Seasonality con’t.
• Contamination Issues:
– Heavy rains/flooding increase water contamination
• i.e., Contact with contaminated water oscillates
• i.e., Contribution to contaminated water oscillates
Conclusions & Future Work
• Simple SIR-B model corresponds to data
– Ro=1.12
• 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
Acknowledgements
• Park City Mathematics Institute
• Dr. Caroline Bampfylde