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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