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Research Article

# Is the Even Distribution of Insecticide-Treated Cattle Essential for Tsetse Control? Modelling the Impact of Baits in Heterogeneous Environments

• s.torr@greenwich.ac.uk

Affiliation: Natural Resources Institute, University of Greenwich, London, United Kingdom

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• Affiliations: Natural Resources Institute, University of Greenwich, London, United Kingdom, South African Centre for Epidemiological Modelling and Analysis (SACEMA), University of Stellenbosch, Stellenbosch, South Africa

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• Published: October 18, 2011
• DOI: 10.1371/journal.pntd.0001360

## Abstract

### Background

Eliminating Rhodesian sleeping sickness, the zoonotic form of Human African Trypanosomiasis, can be achieved only through interventions against the vectors, species of tsetse (Glossina). The use of insecticide-treated cattle is the most cost-effective method of controlling tsetse but its impact might be compromised by the patchy distribution of livestock. A deterministic simulation model was used to analyse the effects of spatial heterogeneities in habitat and baits (insecticide-treated cattle and targets) on the distribution and abundance of tsetse.

### Methodology/Principal Findings

The simulated area comprised an operational block extending 32 km from an area of good habitat from which tsetse might invade. Within the operational block, habitat comprised good areas mixed with poor ones where survival probabilities and population densities were lower. In good habitat, the natural daily mortalities of adults averaged 6.14% for males and 3.07% for females; the population grew 8.4× in a year following a 90% reduction in densities of adults and pupae, but expired when the population density of males was reduced to <0.1/km2; daily movement of adults averaged 249 m for males and 367 m for females. Baits were placed throughout the operational area, or patchily to simulate uneven distributions of cattle and targets. Gaps of 2–3 km between baits were inconsequential provided the average imposed mortality per km2 across the entire operational area was maintained. Leaving gaps 5–7 km wide inside an area where baits killed 10% per day delayed effective control by 4–11 years. Corrective measures that put a few baits within the gaps were more effective than deploying extra baits on the edges.

### Conclusions/Significance

The uneven distribution of cattle within settled areas is unlikely to compromise the impact of insecticide-treated cattle on tsetse. However, where areas of >3 km wide are cattle-free then insecticide-treated targets should be deployed to compensate for the lack of cattle.

## Author Summary

Eliminating Rhodesian sleeping sickness, the zoonotic form of Human African Trypanosomiasis found in East and Southern Africa, can be achieved only through eliminating the vectors, species of tsetse fly (Glossina). The deployment of insecticide-treated cattle is the most cost-effective means of achieving this. However, the even distribution of insecticide-treated cattle is seldom possible due to the patchy distribution of grazing, water and human settlement. We used a simulation model to explore the likely impact of such patchiness on the outcome of control operations against tsetse. The results suggest that even in areas that are highly suitable for tsetse, gaps of up to 3 km in the distribution of insecticide-treated cattle will not have a material impact on the success of an operation provided the overall mean density of cattle across all areas is adequate to achieve control (e.g., ~4 insecticide-treated cattle/km2 killing 10% per day of the tsetse in the area treated). If the gaps are larger than 3 km, then deploying insecticide-treated targets at densities of 4/km2 in the cattle-free areas will ensure success.

### Introduction

Rhodesian sleeping sickness, caused by Trypanosoma brucei rhodesiense, is transmitted by tsetse flies (Glossina spp.) across East and Southern Africa. The disease is the zoonotic form of Human African Trypanosomiasis (HAT) in which the trypanosomes are harboured by reservoir hosts, primarily in wild and domestic suids and bovids. As a consequence, treating humans only cannot eliminate the disease. Rather, in addition to treating people carrying HAT, interventions must also be directed at removing trypanosomes from reservoir hosts and eliminating the vectors [1]. In cases where the reservoirs are wild mammals, the only practicable option is to control tsetse. Tsetse also transmit species of trypanosome (T. vivax, T. congolense, T. simiae and T. b. brucei) that cause Animal African Trypanosomiasis in livestock. Every year, more than a million cattle are killed by tsetse-transmitted trypanosomiases across sub-Saharan Africa, despite $30–40 million being spent annually on veterinary trypanocides [2]. The development and application of more cost-effective methods of tsetse control [3][5] combined with a strengthened political resolve across sub-Saharan Africa to tackle trypanosomiasis [6] has revived interests in interventions against tsetse [7], [8]. Insecticidal techniques for controlling tsetse flies (Glossina spp.) have been used successfully for 60 years, in many tens of thousands of square kilometres [9]. However, the control has not always proceeded as quickly and efficiently as required, for two main reasons. First, invasion from untreated areas nearby can re-infest all or much of the cleared territory [10], as after aerial spraying in Botswana during the 1980s [11]; this problem can be solved by creating invasion barriers of odour-baited targets treated with insecticide [4], [12], [13]. Second, the control measures have not always been applied at the same time and intensity throughout the operational area, so that residual pockets of infestation remain, as in the early aerial spraying operations in Botswana [11] and some of the ground spraying in Zimbabwe [14]. The difficulty of even cover can be particularly serious when control is based on pyrethroid-treated cattle since the animals available for treatment are often distributed patchily, due to the animals' need for adequate grazing and water [15], [16]. This is unfortunate since the cattle treatment is by far the most economical method of control [3], [17]. Finding solutions to the above problems should, ideally, refer directly to abundant data from a full range of technical options tried previously in a wide variety of circumstances. However, such data are scant since full population monitoring is a luxury achievable mainly during the first few trials with a new technique [14]. Moreover, to identify confidently the limits to a technology it is necessary to use it above and below the limits. Understandably, practitioners do not deliberately attempt something that might fail. If failure does occur, by mere happenstance, actions are taken to correct the problem quickly by any means available, as when dealing with pockets of infestation left by aerial spraying in Zimbabwe [14], Botswana [4] and Somalia (S. Torr, unpublished data). Thus, there are few opportunities to assess accurately the number, distribution and dynamics of flies in the problem situations, especially since the populations there are typically sparse and hence difficult to sample. To offset the paucity of data from actual field campaigns, we have much basic information for population dynamics in the field and laboratory [18], so allowing the modelling of tsetse control [10], [19], [20]. Previously we have used the simulation programme ‘Tsetse Muse’ [20] to assess the relative cost-effectiveness of insecticide-treated cattle and the sterile insect technique [20], and the performance of aerial spraying in Botswana [4]. The present paper employs Tsetse Muse to assess how the heterogeneous distribution of baits (insecticide-treated cattle and targets) affects their impact on tsetse populations, and how residual pockets of infestation might be avoided and/or eliminated. ### Materials and Methods #### Model The model is detailed by [20] and can be downloaded at www.tsetse.org and the parameters adopted for its present use are indicated in Table S1. It will be only summarised here. The numerical and spatial distributions of population components were tracked deterministically using the spreadsheet programme Microsoft Excel 2003, it being taken that the population occurred in parallel bands of habitat that were 1 km wide, with the habitat being uniform within bands but allowed to differ between bands (Fig. 1). Outputs showed the abundance of insects along a transect that ran straight across the bands. ##### Standard population. This population, occupying extensive blocks of good (i.e., highly suitable for tsetse) habitat, consisted of 2500 adult males/km2 and 5000 adult females/km2. Daily adult mortalities were age-dependent, averaging 6.14% for males and 3.07% for females, with maximum adult life spans of 89 and 178 days, respectively. In this paper mortality is taken as the complement of the survival probability and expressed, for ease of understanding, as a percentage. Mortality during the egg and larval period was set at 5%. Males were sexually mature at five days and females at three. The first larva was produced at age 16 days and the interlarval period was 9 days. The pupal duration was 28 days for males and 26 days for females, with a mortality of 25% during this period. Males and females emerged in equal numbers. Daily displacement of adults averaged 249 m for males and 367 m for females, to suit the field data for many tsetse species [21]. ##### Density dependence. Natural mortality of adults, pupae and eggs/larvae in each band declined linearly with reduction in population density, to be steady at 75% of standard values when the population density was ≤10% of standard – the density reference for the mortality of adults and eggs/larvae being the abundance of all adults, and for pupae being pupal abundance. Females found mates with a daily probability of 0.1 if there was only one mature male/km2. Provided the abundance of males was not critical, an isolated population could increase up to 8.4 times per year, i.e., roughly the rates observed for island populations [18]. If the male density was <0.1/km2 the population expired naturally. ##### Control methods. All simulated control was performed by baits that killed a constant percent of adults per day, albeit that the percent was varied between simulations. The percent was often set at 10%, to represent the percentages achievable against Glossina morsitans morsitans Westwood and G. pallidipes Austen by the use of artificial baits, i.e., traps or insecticide-treated targets deployed at about 5–10/km2 [14], [20], or by the application of insecticide to cattle [3], [16]. The value was sometimes allowed to be 50% this being the likely maximum achievable given that tsetse feed at minimum intervals of about two days. This theoretical maximum could be somewhat lower since some tsetse might feed on hosts other than cattle, and some tsetse contacting the treated animals might not die [3]. In approximate compensation for this, tsetse visit cattle several times during the hunger cycle [22], thereby increasing the chance of being killed. Unless stated otherwise, all control in a band ceased when the density of males there declined to <0.1/km2, i.e., the point at which the population was not self-sustaining. Although sparse populations were not self-sustaining, they did not expire if supplemented by invasion. Moreover, such populations were in principle detectable, especially since the modelling showed that there were often many times more females than males. Hence, it was assumed that the population would be undetectable in practice only when the density of adult females dropped to 0.1/km2. At this density, if survey traps were operated with an individual probability of catching 1% of the population per day [23], then 693 trap-days would be required to have a 50% chance of catching a female. The population was taken to be cleared when it was assumed to be undetectable. ##### Costs. An index of the running cost of cattle treatment, covering expendables, depreciation of equipment and monitoring, was made by first recording the cumulative number of square kilometres covered per day. This figure was then multiplied by daily imposed mortality, to allow that high mortalities are more expensive to produce. The procedure is admittedly crude. For example, if a certain number of baits are required to kill 10% of the tsetse per day, somewhat more than double that number are required to kill 20% per day since the additional baits act on an already reduced population. On the other hand, doubling the number of baits hardly doubles the supervision and survey costs. Thus, allowing that these matters roughly compensate for each other, the calculation procedure is judged acceptable for present purposes. The indices of running cost were then divided by 100 to bring them down to convenient levels at which, judging from costings in real terms [17], one unit of the present costs equates very roughly to US$1, and will be considered as such. For artificial baits the running costs were double those for cattle baits [17].

Two distinct phases of operation were costed separately. The initial phase was the period required for the stabilisation of tsetse distribution, i.e., clearing as much territory as possible and bringing the treated area down to the minimum required to form an invasion barrier. The second phase was the maintenance of a barrier, costed as recurrent annual expenditure. Unless stated otherwise, all costs were expressed per kilometre of front. To get the costs per square kilometre cleared or held clear, the costs must be divided by the width of the cleared area.

##### Operational areas.

Two main scenarios were modelled and in both cases the area where tsetse control operations was applied (‘operational area’) was adjacent to an invasion source, i.e., an area highly suitable for tsetse where no interventions were applied and hence provides a source of tsetse which can invade the operational area. An imaginary line called the invasion front separated the operational area from the invasion source (Fig. 1).

##### Scenario L – a livestock farming area.

Scenario L modelled a settled area consisting mostly of a densely settled area with mixed crop-livestock farming in predominantly good habitat (Fig. 1A). The good habitat continued for 18 km into the operational area; thereafter the habitat became worse, with the mortality of all population components increasing linearly by 25%/km to reach a maximum of treble the standard values at distances >25 km from the front. This simulated the gross change in habitat that often occurs due to the scarcity of hosts, poor vegetation cover and adverse climate, e.g., in moving from a game park through increasingly degraded areas with higher densities of humans and their livestock. Examples of this include transects running: (1) south from the Zambezi valley of Zimbabwe through Makuti (16.3°S, 29.3°E) to the communal lands of Mashonaland, (2) south from the Vwaza Marsh Game Reserve of Malawi through Lake Kazuni (11.1°S, 33.6°E) into settled areas of Rumphi district, (3) north from the Serengeti National Park of Tanzania through Ikoma (2.1°S, 34.6°E) into surrounding farming areas.

##### Scenario W – an isolated wilderness area.

In Scenario W, good habitat within the operational area was restricted to a band, 7 km wide at 12–19 km from the invasion front (Fig. 1B). Areas 0–12 km and 19–22 km from the front were poor habitat, with mortality being double the standard. Scenario W is roughly comparable to Mkwaja cattle ranch in Tanzania (5.8°S, 38.7°E), where the invasion source was a game park, from which an imaginary transect went first through mostly grassland, then through a wild wooded area where cattle seldom grazed, before going through grassland again and then onto the very poor habitat of sisal estates [15], [16].

Most consideration was given to Scenario L since its larger expanse of good habitat made it the more difficult for control.

### Results

#### Initial populations

Prior to any intervention, the number of adult males declined to <0.1 at >32 km from the front in Scenario L (Fig. 2A), and at >31 km in Scenario W (Fig. 2B), so defining the back edges of operational areas 32 km and 31 km wide, respectively. The areas deemed initially infested with tsetse were 3 km wider, at 35 km and 34 km, respectively. Whereas the percent of females in large expanses of good habitat was 67% (i.e., the percent defined for the standard population), the percent was higher in poorer habitats, reaching 92% in the 3 km beyond the back edges, and 79% in the centre of the belt of poor habitat at 0–12 km from the front in Scenario W. This was because many of the flies in the poor habitat were not born there but moved in; females were more likely to enter because they were more mobile per day and also because they lived longer, so being able to move further in their lifetime.

#### Even and near-even treatment

##### No gaps.

Simulations of insecticide-treated cattle operated in all bands of the operational area of Scenario L with imposed mortality varying between 2.5 and 40.0% of the tsetse per day for 1000 days showed, not surprisingly, that the width of the cleared area increased as the kill percent increased (Fig. 3). The reduction in population density extended for a few kilometres beyond the area where insecticide-treated cattle were present. This was because the number of tsetse diffusing out of the invasion source was not compensated by an equal number moving back; the number available to move back being reduced by the baits. In that part of the operational area near the front the log-density of tsetse initially declined linearly with increasing distance, but usually tailed off slowly at greater distance because the control measures had been halted there. The upshot was usually the existence of an area where the tsetse population remained just detectable but was not self-sustaining, being maintained by limited immigration from nearer the front.

In the above, and all later simulations, the tsetse abundance far from the invasion source showed a first-order decline with time. For example, with the 10% kill, above, the average modelled densities of females at 15–16 km from the front at 0, 1, 2, 3 and 4 months after treatment were 3626, 757, 99, 20 and 3.4/km2, respectively, showing a decline by about 80% per month. As expected, the rate of decline with time was not entirely steady since the age structure of the population took several pupal periods to stabilise, and density dependent reductions in natural deaths came into full play in the second month, i.e., when densities became <10% of standard. After four months, when densities had declined by 99.99%, the daily probability of a female finding a mate had dropped from the original 1.00 to 0.19 and was falling rapidly, to be 0.04 at the end of the fifth month. This would have enhanced greatly the rate of population decline had the population been entirely isolated. However, the rates of decline in the fifth and sixth months were 83% and 82% respectively, i.e., much as before, largely because the population at 15–16 km from the front was being supplemented temporarily by inseminated females invading from the denser, albeit reducing, populations nearer the front.

Baits affected not only the abundance of tsetse populations but also the sex and age structure, as exemplified by the 10% treatment. At 15–16 km from the front, i.e., far from the main invasion source, it was not surprising that the mean age of males and females dropped rapidly after control began, to be 13 and 16 days, respectively, after two months, compared to 20 and 43 days, respectively, at the start. The difference between the mean ages of males and females became less because the mortality imposed by baits far outweighed the differences in the natural mortality of the sexes. Associated with this, the percent of females in the population dropped to 51%, as against 65% initially. At 4–5 km from the front, the mean age of females remained high, being 39 days at five months. This was because the population there was subject to strong invasion; most invaders were older females because they were the more mobile and, in any case, invasion took time so that flies that arrived had to be older than when they left. The upshot was that the female percent in the population there was unusually high, at 77%, despite the presence of baits. Indeed, the effect was more marked the greater the imposed mortality, although then the invasion penetrated less far so it was pertinent to look closer to the front. For example, if the imposed mortality was 40% there were 90% females at 2–3 km from the front after 5 months. In general, an unusually high percent of females is a symptom of significant invasion.

##### Small gaps.

– The impact of patchy baits was investigated with Scenario L. Simulations were made of treating one band in every two, three, four or five, i.e., leaving untreated areas one, two three or four kilometres wide, respectively, The imposed mortality in the bands was increased to ensure that the mortality averaged over all bands was 10%, e.g., a 50% kill in the treated band when only one band in five was treated. Not surprisingly, the gaps in treatment caused the stabilised density of tsetse to decline irregularly on moving from the invasion front into the operational area (Fig. 4). However, the irregularity was negligible when treating one band in two or three, i.e., when the gaps were 1–2 km wide.

#### Timing and costs

##### Scenario L.

With the even treatments a rise in the imposed mortality shortened the time to stability, reduced the required width of the invasion barrier and increased the area cleared (Table 1). However, since the higher imposed mortalities involved greater costs per km2/day there was relatively little difference in the initial, stabilisation costs. Moreover, although the recurrent costs were higher with the greater imposed mortalities, these were offset by a greater area kept clear. For the uneven treatments at an average of 10% kill, the time to stability and hence the initial and recurrent costs increased with an increase in the unevenness, although there was little or no change in the area cleared, relative to the 10% treatment of all bands. For the special treatment in Table 1, the imposed mortality over the operational area was 10%, except that in the first 4 km from the front the imposed mortality was increased to 40% to form what would eventually become the stand-alone invasion barrier. This combination of treatments reduced the time to stability by only 15 days but increased the stabilisation costs by nearly half, compared to the uniform 10% treatment. Other than ensuring that the invasion barrier was narrower, there was no material benefit from extra kills at the invasion front during the stabilising phase.

##### Scenario W.

The greater expanse of poor habitat in Scenario W meant that the time to stability with each type of bait treatment was lower than in Scenario L, and hence the initial costs were lower. Moreover, the poor habitat near the front was itself a restriction to invasion, so that the required width of the invasion barrier was also lower, thereby reducing the recurrent costs and increasing the area held clear. For example, with an even treatment at 10% kill, stability occurred in 158 days at a cost of $366, compared to figures of 203 days and$474 in Scenario L; the barrier was 7 km wide and the recurrent costs was $256 in Scenario W, compared to figures of 9 km and$329 in Scenario L.

### Discussion

The modelling performed here uses inputs for the dynamics of births and deaths that are essentially the same for all tsetse [18]. However, the inputs for the daily displacement refer primarily to savannah species, such as G. morsitans. For these species, the present results suggest that in the typical farming areas of East and Southern Africa, where cattle are abundant but unevenly spread, small (<3 km) cattle-free pockets within a larger operational area are unlikely to have a deleterious impact on the efficacy of using insecticide-treated cattle to control tsetse. Larger pockets will delay and/or prevent the achievement of effective control even when there are high densities of cattle adjacent to the pockets. In these circumstances, the simplest and most cost-effective strategy is to deploy insecticide-treated targets where cattle are absent.

The usefulness of the model and its outputs is to be judged by the extent to which the general pattern of its outputs accord with field observations, as below.

#### Density

In areas far from an invasion source, tsetse abundance showed a first-order decline with time, as observed in the field with a variety of tsetse species [11], [14], [25], [26]. Similarly, in areas subject to constant reinvasion tsetse can penetrate various distances into an operational area according to (i) the density of tsetse in the invasion source and (ii) the distribution and abundance of baits. In Zimbabwe, tsetse were detected up to 5 km into an operational area where baits exerted a daily mortality of ~10% in accordance with the present simulations (see Fig. 3). As a consequence of invasion, small areas (i.e., <10 km across) cannot be cleared of Morsitans-group tsetse using standard densities of baits (e.g., 4 insecticide-treated targets or cattle/km2) as shown by the present simulations (Fig. 5A) and seen in practice [11], [27], [28].

#### Sex composition

The simulations showed that changes in mortality due to natural factors (e.g. habitat) or control efforts will alter the sex composition of tsetse populations. These results accords with field observations of high percentages of females in catches in poor habitats, e.g., [29], although before the demonstration that females move more than males [30], [31] it was usually considered that high proportions of females indicated starving populations [32]. Since it was mostly females that diffused from the good to poor habitats, the model's output for the proportion of females in good habitat was slightly lower than the standard 67% if there was poorer habitat within a few kilometres.

#### Age structure

Baits also affected age structure. For instance, for tsetse 15–16 km from the invasion front, i.e., far from the main invasion source, with the standard bait density (10% daily mortality rate) applied under Scenario L, the mean age of males and females dropped to 13 and 16 days, respectively, after two months, compared to 20 and 43 days, respectively, at the start. This has important epidemiological implications particularly for the transmission of Trypanosoma brucei spp, the causative agents of sleeping sickness, which requires a development period of ~20 days in the fly. Again, these results accord with field observations where the mean age of females caught from traps declined following the start of control operations [33].

The general agreement between the outputs of Tsetse Muse and reliable field data available for populations of medium to high density offers prima facie evidence that the modelling is not seriously awry with very sparse populations for which satisfactory field data are not available. The worst unknowns are the density-dependant changes in population dynamics [18]. However the high mortality imposed by baits are sufficient to swamp any density-dependant reductions in natural mortality, so elimination is achievable even if there were no natural deaths at low population density.

#### Lessons learned

The results provide several new insights that have important implications for the control of tsetse and trypanosomiasis.

First, since population decline due to baits is logarithmic, the rate of decline seems to decrease on a normal scale. Such observations can be misinterpreted as being indications that an operation is becoming less effective as control proceeds. Related to this general phenomenon, because baits reduce tsetse populations rapidly on a normal scale, there is the danger of believing mistakenly that control efforts can be relaxed to complete the task.

Second, while the present estimates of control costs are crude, they do highlight the general pattern of how costs change with technical options. The main finding is that without gross variation in costs there is much latitude in tailoring robust bait measures to suit the required rate of control, implementation capacities, risks and economic conditions, in a range of operational areas.

Third, heterogeneities in the deployment of baits are inevitable with insecticide-treated cattle - the behaviour of cattle along with the demands of providing adequate grazing, water and security means that cattle are never evenly distributed. The present results provide a preliminary framework for understanding the likely implications of the problem and possible solutions. In particular, patchy distributions of baits will be serious if the gaps occur in good habitat, are broader than about 10 times the daily displacement of tsetse (e.g. ~3 km for G. morsitans, and are not recognised until many months after control begins. The problem can be solved by deploying targets in the gaps since their mode of operation is closely similar to cattle baits – both offer continuous control of resident and invading flies for as long as necessary, and can be planned to work at roughly similar rates. By contrast, treating the gaps by sequential spraying of non-residual insecticide offers no protection against invasion since during and after each application the flies can enter from unsprayed areas nearby [31]. This ensures that two months later, when all applications are complete, a residual population remains. The problem could be overcome by extending the spraying into much of the surrounding area, to kill potential invaders, but this would be very expensive [17], especially if the gap is relatively small and so requires the high fixed costs of an aerial spraying cycle to be spread over a small area.

Finally, the indication that progressive clearance by baits is not grossly more expensive than mere barrier up-keep reinforces the prospect of clearing tsetse from the whole of international fly-belts, thus eventually avoiding the invasion problem [6]. The speed of clearance could be enhanced by a combination of baits and large aerial spraying campaigns [4] with the spraying occurring mostly in places where cattle are absent and ground access is difficult.

### Supporting Information

Table S1.

Features of the tsetse population in good habitat before any interventions.

doi:10.1371/journal.pntd.0001360.s001

(DOC)

### Author Contributions

Conceived and designed the experiments: GAV SJT. Performed the experiments: GAV. Analyzed the data: SJT GAV. Wrote the paper: SJT GAV.

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