Evidence Against Rapid Emergence of Praziquantel Resistance in Schistosoma haematobium, Kenya - Statistical Data Included

Emerging Infectious Diseases, Nov, 2000 by Charles H. King, Eric M. Muchiri, John H. Ouma

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Appendix

The following system of differential equations was used to model the level of schistosome infection and prevalence of resistant worms in the treated study population, where

[Sigma] is the number of sensitive schistosomes per host,

[Rho] is the number of resistant schistosomes per host, and

[Sigma] [Rho] = M, the mean number of worms per host.

If p = the proportion of treated infections each year, and

h = the efficacy of one course of treatment, then

c = - ln (1- ph) is the relative increase in the per capita death rate of sensitive worms due to treatment.

The basic death rate for sensitive and resistant parasites is an aggregate function of parasite and host death rates, represented in the equations as

[[Gamma].sub.s] = 1/sensitive parasite lifespan 1/host lifespan

and

[[Gamma].sub.r] = 1/resistant parasite lifespan 1/host lifespan

[R.sub.0] represents the basic reproductive rate of the susceptible worm. If [Phi] = the relative loss of reproductive fitness of the resistant phenotype (with value from 0 to 1), then [R.sub.0r] = [R.sub.0] (1 - [Phi]). X represents the spontaneous mutation rate of resistant worms. To reflect the impact of obligate sexual mating and unequal distribution of worms among hosts, F is a fecundity expression where