Probability models to facilitate a declaration of pest-free status, with special reference to tsetse (Diptera: Glossinidae)

A methodology is presented to facilitate a declaration that an area is 'pest-free' following an eradication campaign against an insect pest. This involves probability models to assess null trapping results and also growth models to help verify, following a waiting period, that pests were not present when control was stopped. Two probability models are developed to calculate the probability of negative trapping results if in fact insects were present. If this probability is sufficiently low, then the hypothesis that insects are present is rejected. The models depend on knowledge of the efficiency and the area of attractiveness of the traps. To verify the results of the probability model, a waiting period is required to see if a rebound occurs. If an incipient but non-detectable population remains after control measures are discontinued, then a rebound should occur. Using a growth model, the rate of increase of an insect population is examined starting from one gravid female or one male and a female. An example is given for tsetse in which both means and confidence limits are calculated for a period of 24 reproductive periods after control is terminated. If no rebound is detected, then a declaration of eradication can be made.