A theoretical study of the invasion of cleared areas by tsetse flies (Diptera : Glossinidae)

Large-scale eradication campaigns against tsetse flies Glossina spp. are gi ving way to smaller operations aimed at disease and vector containment. The re has been little discussion of the effects of these changes in policy. Th is study estimates the rate at which tsetse re-infect treated areas after t he termination of control efforts. Movement is modelled as a diffusion proc ess with a daily root mean square displacement (lambda) of 0.2-1 km(-1/2) a nd population growth as logistic with a growth rate (r) less than or equal to 1.5% day(-1). Invasion fronts move as the product of lambda and root r. For r = 0.75% day(-1) a front advances at 2.5 km year(-1) for each 100 m in crement in lambda. If there are 0.001% survivors in 10% of the treated area , the population recovers to within 1% of the carrying capacity (K) within three years. If the control area is subject to invasion from all sides, a t reated block of 10,000 km(2) is effectively lost within two years - except at the lowest values of lambda and r. Cleared areas of 100 km(2) are lost i n a year, as observed in a community-based suppression programme in Kenya. If the treated area is closed to re-invasion, but if there is a block where tsetse survive at 0.0001-0.1% of K, the population recovers within 3-4 yea rs for up to 20 km outside the surviving block. If the surviving flies are more widely spread, re-infection is even more rapid. The deterministic appr oach used here over-estimates re-invasion rates at low density, but compari sons between control scenarios are still valid. Stochastic modelling would estimate more exactly rates of re-infection at near-zero population densiti es.