A steady-state approach of benefit-cost analysis with a periodic Leslie-matrix model. Presentation and application to the evaluation of a sheep-diseases preventive scheme in Kolda, Senegal

A seasonal population-dynamics matrix model (periodic Leslie-matrix model) was developed to model short production cycles and high seasonal variations occurring in demographic rates and offtake patterns for small ruminants. T he year was split into 24- and 15-day phases. Population-size changes were modelled by the recurrence equation x(j+1)=Bjx(j), where j was the 15-day p hase, x an age-class population size vector and B a fecundity-, mortality-, offtake- and intake-rate matrix. Given an initial vector x(1), annual dyna mics were described by x(25) = B-24 ... B(1)x(1) = Ax(1), where A was the a nnual projection matrix. A steady-state hypothesis was used to estimate offtake gains and financial returns from a trial of pasteurellosis vaccination and anthelminthic drench in traditionally managed sheep flocks in Senegal, from July 1987 to June 1 988. Nineteen villages and 76 herds were involved in the experiment. Villag es were randomly allocated to one of the four treatment combinations in a f actorial design, and subsequent demographic rates and net offtake patterns were measured. in the trial, vaccination had a negative effect on offtakes among females. No vaccination effect was observed for males. A positive eff ect of deworming was found for both sexes. From the trial data, our model c alculated that the overall ratio of offtakes (i.e. number of animals) for d ewormed over undrenched sheep was 1.2 (95% confidence interval: 1.1, 1.4). The deworming financial benefit-cost ratio was 3.7 (1.9, 5.4). (C) 2000 Els evier Science B.V. All rights reserved.