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

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Abstract
Large-scale eradication campaigns against tsetse flies Glossina spp. are giving way to smaller operations aimed at disease and vector containment. There has been little discussion of the effects of these changes in policy. This study estimates the rate at which tsetse re-infect treated areas after the termination of control efforts. Movement is modelled as a diffusion process with a daily root mean square displacement (λ) of 0.2–1 km−1/2 and population growth as logistic with a growth rate (r) ≤1.5% day−1. Invasion fronts move as the product of λ and √r. For r = 0.75% day−1 a front advances at 2.5 km year−1for each 100 m increment in λ. 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 treated block of 10,000 km2 is effectively lost within two years – except at the lowest values of λ and r. Cleared areas of 100 km2 are lost in 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 years 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 approach used here over-estimates re-invasion rates at low density, but comparisons between control scenarios are still valid. Stochastic modelling would estimate more exactly rates of re-infection at near-zero population densities.