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Between 1990 and 1999, at Rekomitjie Research Station, Zambezi Valley, Zimbabwe, 29,360 female G. pallidipes were dissected to determine their ovarian category and trypanosome infection status. Overall prevalences were 3.45 and 2.66% for T. vivax and T. congolense , respectively, declining during each year as temperatures increased from July - December. Fits to age-prevalence data using Susceptible-Exposed-Infective (SEI) and SI compartmental models were statistically better than those obtained using a published catalytic model, which made the unrealistic assumption that no female tsetse survived more than seven ovulations. The improved models require knowledge of fly mortality, estimated separately from ovarian category distributions. Infection rates were not significantly higher for T. vivax than for T. congolense . For T. congolense in field-sampled female G. pallidipes , we found no statistical support for a model where the force of infection was higher at the first feed than subsequently. The long survival of adult female tsetse, combined with feeding at intervals ≤3 days, ensures that post-teneral feeds, rather than the first feed, play the dominant role in the epidemiology of T. congolense infections in G. pallidipes . This is supported by estimates that only about 3% of wild hosts at Rekomitjie were harbouring sufficient T. congolense to ensure that tsetse feeding off them take an infected meal, so that the probability of ingesting an infected meal is low at every meal.

Environmental temperature is an important driver of the population dynamics of tsetse (Glossina spp) because the fly's immature stages are particularly vulnerable to temperatures (T) outside the range T = 16-32°C. Laboratory experiments carried out 50 years ago provide extensive measures of temperature-dependent rates of development, fat consumption and mortality in tsetse pupae. We improve on the models originally fitted to these data, providing better parameter estimates for use in population modelling. A composite function accurately models rates of pupal development for T = 8-32°C. Pupal duration can be estimated by summing the temperature-dependent daily percentage of development completed. Fat consumption is modelled as a logistic function of temperature; the total fat consumed during pupal development takes a minimum for T ≈ 25°C. Pupae experiencing constant temperatures <16°C exhaust their fat reserves before they complete development. At high temperatures, direct effects kill the pupae before fat stores are exhausted. The relationship between pupal mortality and temperature is well described by the sum of two exponential functions. Summing daily mortality rates over the whole pupal period does not reliably predict overall mortality. Mortality is more strongly correlated with the mean temperature experienced over pupal life or, for T ≤ 30°C, the fat consumption during this period. The new results will be particularly useful in the construction of various models for tsetse population dynamics, and will have particular relevance for agent-based models where the lives of individual tsetse are simulated using a daily time step.

Mortality estimates are central to understanding tsetse fly population dynamics, but are difficult to acquire from wild populations. They can be obtained from age distribution data but, with limited data, it is unclear whether the assumptions required to make the estimates are satisfied and, if not, how violations affect the estimates. We evaluate the assumptions required for existing mortality estimation techniques using long-term longitudinal ovarian dissection data from 144,106 female tsetse, Glossina pallidipes Austen, captured in Zimbabwe between 1988 and 1999. At the end of the hot-dry season each year, mean ovarian ages peaked, and maximum-likelihood mortality estimates declined to low levels, contrary to mark-recapture estimates, suggesting violations of the assumptions underlying the estimation technique. We demonstrate that age distributions are seldom stable for G. pallidipes at our study site, and hypothesize that this is a consequence of a disproportionate increase in the mortality of pupae and young adults at the hottest times of the year. Assumptions of age-independent mortality and capture probability are also violated, the latter bias varying with capture method and with pregnancy and nutritional status. As a consequence, mortality estimates obtained from ovarian dissection data are unreliable. To overcome these problems we suggest simulating female tsetse populations, using dynamical modelling techniques that make no assumptions about the stability of the age distribution.

Tsetse flies Glossina pallidipes Austen and G. morsitans morsitans Westwood deposit their larvae in warthog burrows, in August-November, at Rekomitjie Research Station, Zambezi Valley, Zimbabwe. Artificial burrows, made from 200-l steel drums, were used to sample these flies and to collect their puparia. Sand-filled plastic trays in the burrows served as a substrate for larval deposition. The sand was covered with c. 2 cm of leaf litter after it was shown that only 3% of larvae were deposited on bare sand if both substrates were available. Other burrow modifications - artificially shading the burrow entrance, increasing the relative humidity inside the burrow, or reducing the size of the burrow entrance - significantly decreased deposition rates. The use of burrows in the hot season results in a reduction in the temperature experienced by the puparium towards an assumed optimum level of 26 degrees C. Artificial burrows maintained a mean temperature of 28.5 degrees C during October-November 1998, c. 2.5 degrees C cooler than ambient; earlier work has shown that natural burrows can be c. 5 degrees C cooler than ambient at these times. This may explain why natural burrows in full sunlight were used for larviposition, whereas artificial burrows were used only when they were in deep shade, and why significantly higher proportions of G. pallidipes were found in natural (66%) than in artificial burrows (34%). Better-insulated artificial burrows might produce more puparia with higher proportions of G. pallidipes. Burrows become waterlogged during the rains and may be too cool for optimum puparial development during the rest of the year. The percentages of G. m. morsitans in catches of females from artificial burrows, refuges and odour-baited traps were 34, 26 and < 10% respectively. Traps are biased in favour of G. pallidipes; artificial burrows may show a bias in favour of G. m. morsitans that is a function of temperature. Artificial warthog burrows provide a convenient way of studying the puparial stage in tsetse and for the first time facilitate the capture of females as they deposit their larvae.

A stochastic branching process was used to derive equations for the mean and variance of the probability of, and time to, extinction in tsetse populations. If the remnant population is a single inseminated female, the extinction probability increases linearly with adult mortality and is always certain if this mortality >3.5% per day even for zero pupal mortality. If the latter mortality is 4% per day, certain extinction is only avoided if adult mortality <1.5% per day. For remnant female populations >1, the extinction probability increases in a non-linear manner with adult mortality. Extinction is still certain for adult mortality >3.5% per day but, when the remnant population is >16, extinction is highly unlikely for adult mortality <2.5% per day if all females are inseminated. Extinction probability increases with increasing probability of sterile mating in much the same way as it does with increasing adult mortality. Extinction is assured if the probability of insemination can be reduced to 0.1. The required reduction decreases with increasing adult mortality. For adult mortality = 6-8% per day, the time to extinction increases only by one generation per order of magnitude increase in the starting population. Time to extinction is less sensitive to changes in the pupal than in the adult mortality. Reductions in the probability of insemination only become important when adult mortality is small; if the adult mortality is 8% per day, reducing the insemination probability from 1 to 0.1 only reduces the expected time to extinction by two generations. Conversely, increases in adult mortality produce important reductions in the required time even when the probability of insemination is 0.1. The practical, economic implication for the sterile insect technique is that the low-tech methods used to suppress tsetse populations should not be halted when the release of sterile males is initiated. The sterile insect technique should only be contemplated when it has been demonstrated that the low-tech methods have failed to effect eradication. The theory is shown to be in good accord with the observed results of tsetse control campaigns involving the use of odour-baited targets in Zimbabwe and the sterile insect technique on Unguja Island, Zanzibar.

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.

The distributions of insecticide-treated cattle from sites in Tanzania and Zimbabwe were assessed from interviews with livestock owners, analysis of secondary livestock data and mapping technologies. The time-course of tsetse control operations at these sites were then simulated using a mathematical model that assumed diffusive movement and logistic growth in fly populations. A simulation of a tsetse control operation in Mudzi district, north-east Zimbabwe, was in accord with observations that the use of insecticide-treated cattle was unable to prevent substantial re-invasion of tsetse from Mozambique, consequent on the patchy distribution of cattle. The simulation was also consistent with the observed efficacy of a 10-km wide barrier of insecticide-treated targets deployed evenly at 4 km/(-2). Simulation of a control operation on Mkwaja Ranch in Tanzania was in accord with the observation that the use of insecticide-treated cattle reduced the tsetse population on the ranch by c. 90%. Insecticide-treated cattle were used to better effect in the Kagera Region of Tanzania. Simulation of this operation predicts that the deployment of 35,000 treated cattle in the area would result in > 99% control of the tsetse population, consistent with the observed decline, by 1-2 orders of magnitude, in cases of trypanosomiasis in the region. The greater success of the Kagera operation was due to the size and shape of the treated area and, particularly, to the restriction of re-invasion to 20% of the perimeter, compared with > 80% on Mkwaja. Simulation was used to assess how tsetse control could have been improved at Mkwaja. The results suggest that splitting herds into smaller, more numerous, units could have achieved some improvement but, in general, the disease problem would not have been solved by the use of insecticide-treated cattle alone. Only by deploying odour-baited targets in ungrazed areas, or in a 1-3-km barrier around the ranch, could substantially better control (99-99.9%) have been achieved. Sensitivity analyses of the Mkwaja simulation showed that the general conclusions were robust to assumptions regarding cattle distribution and the rates of fly movement and growth. Properly managed and appropriately applied insecticide-treated baits are powerful weapons for tsetse control but should not be used without regard to potential levels of re-invasion, consequent largely on considerations of the size and shape of the treatment area and the density and distribution of the baits.

In 1984-1985 insecticide-treated targets were deployed in the 600-km2 Rifa Triangle, Zambezi Valley, Zimbabwe. Trap catches of Glossina pallidipes Austen were modelled using a function combining logistic growth with diffusive movement. A simulation routine was linked to a non-linear least-squares optimization programme and fits optimized with respect to population carrying capacities, rates of growth and movement, and to levels of imposed mortality. In March-September 1984, the overall additional mortality was 2% per day of adult female G. pallidipes, increasing thereafter to 8% per day, due to the deployment of more targets, the onset of the hot, dry season and the ground-spraying of the adjoining Zambezi escarpment with DDT. For G. m. morsitans Westwood the corresponding estimates were 1 and 2% per day. For both species, the deployment of four targets km(-2) in a closed population will ensure eradication. For G. m. morsitans a halving of target efficacy would reduce the killing rate to the point where eradication would be unlikely. Estimated daily displacements were c. 200 m for G. m. morsitans and 660 m for G. pallidipes. The lower rate for G. m. morsitans means that, while targets kill this species less effectively, re-invasion of cleared areas is slower. Targets do not markedly affect robust populations outside the deployment area. The Zambian tsetse population adjacent to the Rifa Triangle declined markedly during the experiment, however, suggesting that it is largely maintained by immigration. The methods developed here will be applied to data from other campaigns with the aim of improving the efficiency of tsetse control programmes.

The methods of Bailey and of Jolly and Seber were used to provide maximum likelihood estimates of population parameters for Jackson's classical mark-recapture experiments on males of the tsetse fly Glossina m. morsitans Westwood. These were compared with Jolly-Seber (J-S) estimates for the same fly from more recent work on Antelope Island, Lake Kariba, Zimbabwe. The Bailey estimates of birth and death rates and total population size had markedly lower variances than Jackson's originals. Both sets of estimates provided moving averages over 6-week periods, whereas the Jolly-Seber analysis provided independent weekly estimates and their variance is consequently higher. Saturation deficit and maximum temperature (Tmax) accounted for 11 and 16% respectively of the variance in independent 4-week means of the weekly J-S survival probabilities. Analysis of covariance, carried out on a joint data set of smoothed J-S estimates of the survival probability in Tanzania and Zimbabwe, showed a significant effect of Tmax on survival. When this effect was removed, the survival probability in the Tanzania studies was found to be 8% lower than on Antelope Island. The two effects accounted for 50% of the variance in the joint data. When saturation deficit was substituted for Tmax, regression only accounted for 35% of the variance. If saturation deficit is important in determining tsetse survival, it must act on stages other than the post-teneral adult. Given the continuous increase in mortality, even at moderate temperatures, it is hard to envisage a direct effect of Tmax. There may be an indirect effect, however, via the number of hunger-related deaths resulting from the increase in the feeding rate with increasing temperature.

A study on populations of Glossina morsitans morsitans Westwood on Antelope Island, Lake Kariba, Zimbabwe provided Jolly-Seber (J-S) mark-recapture estimates of adult survival and Moran curve estimates of the overall survival of all developmental stages. For females, Moran survival estimates derived using ox fly-round catches showed similar trends to, but were more variable than, those calculated from J-S population estimates. Regression of one set on the other removed only 26% of the variance. Undue emphasis should not be placed on small changes in Moran survival estimates based on sequences of catches. Catch data cannot provide Moran estimates of male survival probabilities and no comparison is thus possible with estimates from the J-S data. The J-S and the Moran approaches were combined to estimate survival probabilities of the immature stages of male and female tsetse. The overall survival per three-week period averaged 45% for males and 59% for females, comprising mature adult survivals of 27 and 46%, and pooled survivals of immature stages of 59 and 77%, respectively. The high survival of immature flies is due to the sheltered, inactive nature of pupal life. Adult and overall survival probabilities were highly correlated in males (r(2) = 0.61) but less so in females (r(2) = 0.24) where capture rates were lower and variance in the results greater. Immature and overall survival was more highly correlated for both sexes, with r(2) = 0.77 and 0.53 for males and females respectively. When a fixed pupal mortality of 1% per day was assumed, estimates of the survival of young adult males suggested that these were even lower than the survival of mature flies at the harshest times of the year, but were not markedly different when overall survival was high. Assuming equal mortality in all adults enabled the estimation of pupal survival. These had high variances but there was no evidence of any difference between the survival probabilities of male and female pupae.

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 (lambda) of 0.2-1 km-1/2 and population growth as logistic with a growth rate (r) < or =1.5% day-1. Invasion fronts move as the product of lambda and radicalr. For r = 0.75% day-1 a front advances at 2.5 km year-1 for each 100 m increment 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 treated block of 10,000 km2 is effectively lost within two years - except at the lowest values of lambda 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.