Improved models for the relationship between age and the probability of trypanosome infection in female tsetse, Glossina pallidipes Austen.

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.

Improved estimates of abortion rates in tsetse (Glossina spp.).

Abortion rates were assessed among 170, 846 tsetse (154,228 Glossina pallidipes and 19,618 Glossina morsitans morsitans) sampled in Zimbabwe in 1988-1999. The study produced improved estimates of abortion rates and how these varied with fly age and size and temperatures experienced during pregnancy. An abortion was diagnosed if the uterus was empty and the largest oocyte <0.82 of the expected mature length. Abortion rates for G. pallidipes and G. m. morsitans were 0.64% (95% ci: 0.59-0.69) and 0.83% (0.62-1.10) for trapped flies and 2.03% (1.77-2.31) and 1.55% (1.20-1.98) for flies from artificial refuges. Abortion rates increased with increasing temperature and decreased with increasing wing length and wing fray. Contrary to laboratory findings, abortion rates did not increase in the oldest flies. Percentages of tsetse with empty uteri, regardless of abortion status, were significantly higher than estimated abortion percentages. For tsetse from traps, 4.01% (95% ci: 3.90-4.13) of G. pallidipes and 2.52% (2.14-2.95) of G. m. morsitans had empty uteri; for flies from artificial refuges, the percentages were 12.69% (12.07-13.34) and 14.90% (13.82-16.02), respectively. Abortion losses are small relative to losses at all other stages of life.

Negative density-dependent dispersal in tsetse (Glossina spp): red flag or red herring?

A deterministic model of the distribution of tsetse flies (Glossina spp) was used to assess the extent to which the efficacy of control operations would be affected by three different modes of density dependence in per capita adult dispersal: (i) density-independent dispersal which has been commonly adopted in previous models, (ii) positive density-dependent dispersal which has occasionally been discussed in the tsetse literature, (iii) negative density-dependent dispersal (NDDD). The last has recently been suggested, from genetic studies, to change the dispersal rate of tsetse by up to 200-fold, thereby posing a severe risk for the success of tsetse control operations. Modelling outputs showed that NDDD poses no such risk, provided the mean daily dispersal of tsetse is below about 1 km, which is greater than any rate actually recorded in the field or indicated by the genetic studies. NDDD can be problematic only if tsetse disperse at rates that appear highly unlikely, or even impossible, on energetic grounds. Under some circumstances these high rates would help rather than hinder the control officer. NDDD is not necessary to explain the results of control operations, and not sufficient to explain the results of successful control programmes.

A model for the relationship between wing fray and chronological and ovarian ages in tsetse (Glossina spp).

Age-dependent mortality changes in haematophagous insects are difficult to measure but are important determinants of population dynamics and vectorial capacity. A Markov process was used to model age-dependent changes in wing fray in tsetse (Glossina spp), calibrated using published mark-recapture data for male G. m. morsitans in Tanzania. The model was applied to female G. m. morsitans, captured in Zimbabwe using a vehicle-mounted electric net and subjected to ovarian dissection and wing fray analysis. Rates of fray increased significantly with age in males but not females, where the rate was constant for ovarian categories 0-3. A jump in mean fray between ovarian categories 3 and 4 + 4n is consistent with the latter category including flies that have ovulated 4, 8, 12, 16 times and so on. The magnitude of the jump could, theoretically, facilitate improved mortality estimates. In practice, although knowledge of fly mortality was required for modelling wing fray, mortality estimates derived from ovarian dissection data are independent of patterns and rates of change in wing fray. Significantly better fits to ovarian age data resulted when age-specific mortality was modelled as the sum of two exponentials, with high mortality in young and old flies, than when mortality was constant at 2.3% per day.

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%.

Estimating tsetse fertility: daily averaging versus periodic larviposition.

When computing mean daily fertility in adult female tsetse, the common practice of taking the reciprocal of the interlarval period (called averaged fertility) was compared with the method of taking the sum of the products of daily fertility and adult survivorship divided by the sum of daily survivorships (called periodic fertility). The latter method yielded a consistently higher measure of fertility (approximately 10% for tsetse) than the former method. A conversion factor was calculated to convert averaged fertility to periodic fertility. A feasibility criterion was determined for the viability of a tsetse population. Fertility and survivorship data from tsetse populations on Antelope Is. and Redcliff Is., both in Zimbabwe, were used to illustrate the feasibility criterion, as well as the limitations imposed by survivorship and fertility on the viability of tsetse populations. The 10% difference in fertility between the two methods of calculation makes the computation of population feasibility with some parameter combinations sometimes result in a wrong answer. It also underestimates both sterile male release rates required to eradicate a pest population, as well as the speed of resurgence if an eradication attempt fails.

Models for the rates of pupal development, fat consumption and mortality in tsetse (Glossina spp).

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 from ovarian age distributions of the tsetse fly Glossina pallidipes Austen sampled in Zimbabwe suggest the need for new analytical approaches.

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.

A general model for mortality in adult tsetse (Glossina spp.).

Tsetse exhibit a U-shaped age-mortality curve, with high losses after eclosion and a well-marked ageing process, which is particularly dramatic in males. A three-parameter (k(1) -k(3) ) model for age-dependent adult instantaneous mortality rates was constructed using mark-recapture data for the tsetse fly Glossina morsitans morsitans Westwood (Diptera: Glossinidae). Mortality changed linearly with k(1) over all ages; k(2) affected only losses in roughly the first week of adult life, and k(3) controlled the ageing rate. Mortality pooled over age was twice as sensitive to changes in k(3) as in k(1) . Population growth rate was, however, similarly affected by these two parameters, reflecting the disproportionate effect of k(3) on mortality in the oldest flies that contribute least to the growth rate. Pooled-age mortality and growth rate were insensitive to changes in k(2) . The same model also provided good fits to data for laboratory colonies of female G. m. morsitans and Glossina austeni Newstead and should be applicable to all tsetse of both sexes. The new model for tsetse mortality should be incorporated into models of tsetse and trypanosome population dynamics; it will also inform the estimation of adult female mortality from ovarian dissection data.

A randomised placebo-controlled trial to explore the effect of suppressive therapy with acyclovir on genital shedding of HIV-1 and herpes simplex virus type 2 among Zimbabwean sex workers.

OBJECTIVES: To determine the effect of daily acyclovir on genital shedding of HIV-1 and herpes simplex virus type 2 (HSV-2) in a randomised placebo-controlled trial among rural Zimbabwean sex workers. METHODS: 214 women were recruited and tested for HIV-1 and HSV-2 antibodies, HIV plasma viral load, CD4 lymphocyte count and genital swabs for qualitative detection of HIV-1 and HSV-2 genital shedding. Women were randomly assigned to acyclovir 400 mg twice a day for 12 weeks or matching placebo and were followed weekly to detect HIV-1 or HSV-2 genital shedding. Shedding analyses were only undertaken on 125 women co-infected with HSV-2 and HIV-1. Data were analysed using logistic regression, with random effects modelling used to account for repeated measurements on the same women. RESULTS: All women were randomly assigned to acyclovir or placebo; 125 of whom were co-infected with HIV-1 and HSV-2. 69 women were randomly assigned to acyclovir and 56 to placebo. Although twice daily acyclovir reduced rates of HSV-2 genital shedding, (adjusted odds ratio (AOR) 0.24; 95% CI 0.12 to 0.48; less than p<0.001), it had no effect on the proportion of visits at which HIV-1 shedding was detected (AOR 1.08; 95% CI 0.48 to 2.42; p = 0.9). Adherence varied between participants but even when adherence was high (as determined by pill count and extent of HSV-2 suppression) HIV-1 shedding was not reduced. CONCLUSION: Among these HIV-1 and HSV-2-seropositive women, suppressive acyclovir therapy had no effect on the rate of HIV genital shedding despite a reduction in genital HSV-2. Treatment adherence and its measurement clearly affect the interpretation of these results.

Adoption of safer infant feeding and postpartum sexual practices and their relationship to maternal HIV status and risk of acquiring HIV in Zimbabwe.

OBJECTIVE: To examine the relationships between maternal knowledge and concern about HIV status, adoption of preventive practices and risk of acquiring HIV in Zimbabwe. METHODS: Knowledge and behavioural data were collected via interview from 2595 mothers enrolled in ZVITAMBO, a randomized trial of postpartum vitamin A supplementation that also offered education on safer infant feeding and sexual practices. Mothers were tested for HIV at delivery; those uninfected at baseline were retested during study follow-up. Logistic regression methods were used to identify variables associated with adoption of preventive behaviours and, for HIV-negative mothers, their relationship to risk of acquiring HIV post-delivery. RESULTS: A total of 518 mothers (20%) reported practicing safer sex and 289 mothers (11%) reported modifying their feeding behaviour because of HIV. Fear of transmitting HIV (50.4%) and protecting the baby's health (30.9%) were the most frequently cited reasons for behaviour change. Forty-nine HIV-negative mothers acquired HIV during the first postpartum year. After taking into account other significant covariates, mothers who were concerned about their own HIV status were 1.9 times more likely (95% CI: 1.05-3.52; P = 0.03), and those reporting safer sex practices were 58% less likely to become infected (adjusted odds ratio: 0.42; 95% CI: 0.17-1.04; P = 0.06). Married women who reported practicing abstinence to prevent HIV were 3.2 times more likely to become infected than non-abstaining mothers (P = 0.01), while there were no new HIV infections among abstaining single mothers. CONCLUSIONS: Greater emphasis should be given to safer sex practices among women who test negative in mother-to-child HIV prevention programmes.

HIV-1 and HIV-2 prevalence and associated risk factors among postnatal women in Harare, Zimbabwe.

Studies of antenatal women form the predominant source of data on HIV-1 prevalence in Africa. Identifying factors associated with prevalent HIV is important in targeting diagnostic services and care. Between November 1997 and January 2000, 14,110 postnatal women from Harare, Zimbabwe were tested by ELISAs reactive to both HIV-1 and HIV-2; a subset of positive samples was confirmed with assays specific for HIV-1 and HIV-2. Baseline characteristics were elicited and modelled to identify risk factors for prevalent HIV infection. HIV-1 and HIV-2 prevalences were 32.0% (95% CI 31.2-32.8) and 1.3% (95% CI 1.1-1.5), respectively; 4% of HIV-1-positive and 99% of HIV-2-positive women were co-infected. HIV-1 prevalence increased from 0% among 14-year-olds to >45% among women aged 29-31 years, then fell to <20% among those aged>40 years. In multivariate analyses, prevalence increased with parity, was lower in married women than in single women, divorcees and widows, and higher in women with the lowest incomes and those professing no religion. Adjusted HIV-1 prevalence increased during 1998 and decreased during 1999. Age modified the effects of parity, home ownership and parental education. Among older women, prevalence was greater for women who were not homeowners. Among younger women, prevalence increased with parity and low parental education. None of these factors distinguished women co-infected with HIV-2 from those infected with HIV-1 alone. Prevalent HIV-1 infection is associated with financial insecurity and weak psychosocial support. The ZVITAMBO study apparently spanned the peak of the HIV-1 epidemic among reproductive women in Harare.

Artificial larviposition sites for field collections of the puparia of tsetse flies Glossina pallidipes and G. m. morsitans (Diptera: Glossinidae).

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.

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.

Extinction probabilities and times to extinction for populations of tsetse flies Glossina spp. (Diptera: Glossinidae) subjected to various control measures.

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.

Insecticide-treated cattle against tsetse (Diptera: Glossinidae): what governs success?

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.

Optimized simulation of the control of tsetse flies Glossina pallidipes and G. m. morsitans (Diptera: Glossinidae) using odour-baited targets in Zimbabwe.

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 effect of temperature and saturation deficit on mortality in populations of male Glossina m. morsitans (Diptera: Glossinidae) in Zimbabwe and Tanzania.

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.

Mark-recapture and Moran curve estimates of the survival probabilities of an island population of tsetse flies Glossina morsitans morsitans (Diptera: Glossinidae).

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.

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

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.