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. The year was split into 24- and 15-day phases. Population-size changes were modelled by the recurrence equation x(j+1)=B(j)x(j), where j was the 15-day phase, x an age-class population size vector and B a fecundity-, mortality-, offtake- and intake-rate matrix. Given an initial vector x(1), annual dynamics were described by x(25)=B(24)...B(1)x(1)=Ax(1), where A was the annual 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 1988. Nineteen villages and 76 herds were involved in the experiment. Villages were randomly allocated to one of the four treatment combinations in a factorial 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 effect of deworming was found for both sexes. From the trial data, our model calculated that the overall ratio of offtakes (i.e. number of animals) for dewormed 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).