Estimating tsetse fertility: daily averaging versus periodic larviposition

Modelling optimal timing and frequency of insecticide sprays for eradication or knockdown of closed populations of tsetse flies Glossina spp. (Diptera: Glossinidae)

A population model for tsetse species was used to assess the optimal number and spacing of airborne sprays to reduce or eradicate a tsetse population. It was found that the optimal spray spacing was determined by the time (days) from adult emergence to the first larviposition and, for safety, spacing was assigned to that duration minus 2 days. If sprays killed all adults, then the number of sprays required for eradication is determined by a simple formula. If spray efficiency is less than 100% kill per spray, then a simulation was used to determine the optimal number, which was strongly affected by spray efficiency, mean daily temperature, pupal duration, age to first larviposition and the acceptance threshold for control, rather than eradication. For eradication, it is necessary to have a spray efficiency of greater than 99.9% to avoid requiring an excessive number of sprays. Output from the simulation was compared with the results of two aerial spraying campaigns against tsetse and a least squares analysis estimated that, in both cases, the kill efficiency of the sprays was not significantly less than 100%.

Extinction probabilities as a function of temperature for populations of tsetse (Glossina spp.)

Significant reductions in populations of tsetse (Glossina spp) in parts of Zimbabwe have been attributed to increases in temperature over recent decades. Sustained increases in temperature might lead to local extinctions of tsetse populations. Extinction probabilities for tsetse populations have not so far been estimated as a function of temperature. We develop a time-homogeneous branching process model for situations where tsetse live at different levels of fixed temperature. We derive a probability distribution pk(T) for the number of female offspring an adult female tsetse is expected to produce in her lifetime, as a function of the fixed temperature at which she is living. We show that pk(T) can be expressed as a geometric series: its generating function is therefore a fractional linear type. We obtain expressions for the extinction probability, reproduction number, time to extinction and growth rates. The results are valid for all tsetse, but detailed effects of temperature will vary between species. No G. m. morsitans population can escape extinction if subjected, for extended periods, to temperatures outside the range 16°C-32°C. Extinction probability increases more rapidly as temperatures approach and exceed the upper and lower limits. If the number of females is large enough, the population can still survive even at high temperatures (28°C-31°C). Small decreases or increases in constant temperature in the neighbourhoods of 16°C and 31°C, respectively, can drive tsetse populations to extinction. Further study is needed to estimate extinction probabilities for tsetse populations in field situations where temperatures vary continuously.