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Am. J. Trop. Med. Hyg., 73(3), 2005, pp. 546-552
Copyright © 2005 by The American Society of Tropical Medicine and Hygiene

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HABITAT-BASED MODELING OF IMPACTS OF MOSQUITO LARVAL INTERVENTIONS ON ENTOMOLOGICAL INOCULATION RATES, INCIDENCE, AND PREVALENCE OF MALARIA

WEIDONG GU* AND ROBERT J. NOVAK
Illinois Natural History Survey, Champaign, Illinois


ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 MODELS
 RESULTS
 DISCUSSION
 REFERENCES
 
Larval control of Anopheles mosquitoes has long been neglected in tropical Africa due to uncertainties about its impacts on incidence and prevalence of malaria. Population models of mosquitoes are a useful tool to provide qualitative and quantitative understandings of influences of larval interventions on malaria transmission. For these purposes, we develop a new modeling framework by conceiving a quantity of the total productivity in an area, which, in turn, can be partitioned into its constituent parts from individual habitats. Three scenarios of larval interventions were evaluated in relation to impacts on parasitological indicators of malaria transmission. Our results show that it is unnecessary to manage all aquatic habitats to obtain significant reductions in incidence and prevalence of malaria in situations of low and intermediate levels of transmission. We highlight that informed larval interventions featured by identifying and targeting prolific habitats can play a critical role in combating malaria in Africa.


INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
MODELS
 RESULTS
 DISCUSSION
 REFERENCES
 
Malaria is one of the most severe infectious diseases and takes a devastating toll on man and hinders economic development in sub-Saharan Africa. Although enormous efforts and resources have been devoted to combat the disease, malaria has not been contained and in recent years has become even more severe especially in tropical Africa.1 This continuing problematic situation calls for a reevaluation of the strategies for effective and sustainable vector management. Integrated mosquito management (IMM) has been advocated as a critical element to help combat malaria.2–4

As an integral component of IMM, the importance of larval interventions recently regained the attention in the professionals after a long obsolete status in malaria control.5 Larval control is not an entirely new strategy for managing malaria. Historically, many successful campaigns of mosquito eradication had heavily relied on management of larval habitats.6–9 The renewed interest in larval interventions has been accompanied with the development of environmental friendly and powerful microbial insecticides such as Bacillus thuringiensis israeliensis (Bti)10 and rapid accumulation of ecological data of distribution of aquatic habitats. Many investigations documented data of larval ecology and aquatic habitats in Africa.11–18 However, it remains unclear whether larval interventions can have a significant impact on malaria incidence and prevalence. With these concerns, current vector control programs have been almost exclusively targeted toward adult mosquitoes (e.g., domestic indoor residual sprays and insecticide-treated bed nets). Larval interventions are considered not appropriate, for example, to manage malaria epidemics on the African continent.19

Important issues need to be addressed in relation to larval control strategies of anopheline mosquitoes. First, is it feasible and necessary to manage all aquatic habitats to have a significant impact on incidence and prevalence of malaria? If not, what is the priority of control efforts of larval interventions? Second, to what extent should larval control be conducted to obtain the specified control objectives? Theoretical models are indispensable tools for developing qualitative and quantitative understandings for these issues.20 Over the past decades, many models have been developed with various motivations and successes. To date, most control intervention models of mosquito populations have assumed a general larval population in a hypothetical habitat. Larval control was simulated by assuming specified levels of coverage and larval mortalities.21–25 Recently, Killeen and colleagues26 developed a foraging model to examine how resource reduction of aquatic habitats can impact transmission potentials of malaria in an African setting. In their models, it was assumed that emerging adults were originated from a group of identical larval habitats. In African settings, however, Anopheles species use and exploit a variety of habitats that vary considerably in physiochemical properties, surface areas, vegetation, and productivity.12,27,28 Therefore, assumptions of a general larval population or identical habitats are untenable for a realistic evaluation of larval control interventions or the development of models to be empirically tested under field conditions.

In this paper, we have developed a new model framework to evaluate larval interventions on entomological inoculation rates (EIR), incidence, and prevalence of malaria. To account for the variability in adult productivity, we conceive a conceptual quantity, the total productivity, which consists of proportional contributions of emerging females from individual habitats. The impact of three scenarios of larval interventions on the parasitological indicators of malaria transmission was examined from the perspective of habitats. The objectives of our modeling effort are twofold: 1) to evaluate to what extent larval control should be undertaken to achieve specified goals in reducing incidence and prevalence of malaria, and 2) to put into perspective how ecological surveys of larval populations and aquatic habitats can assist in designing intervention programs.


MODELS
TOP
 ABSTRACT
 INTRODUCTION
 MODELS
RESULTS
 DISCUSSION
 REFERENCES
 
We envision an enclosed focal area of malaria transmission in which the migration of mosquitoes both in and out of the area is assumed to be negligible. Therefore, all emerging female mosquitoes are originated from a finite number of different aquatic habitats within the area. The habitats might vary in type (e.g., shaded pools, road ditches, marshlands, etc.) as well as other bionomic characters influencing the habitat productivity. Henceforth, we refer to the habitat productivity as numbers of emerging female mosquitoes from an aquatic habitat per unit time. The habitat productivity can be conventionally estimated based on empirical data of emerging trapping. Alternative measures such as estimates of larval or pupal density can substitute emerging trap samples for estimating emerging adult populations if empirical data show that the former is linearly related to the latter. The focal area can be a typical African village surrounded by a buffer zone (e.g., 1 km, encircled the village). Note our focal area is broader than that of Carter et al.,29 who delineate an individual aquatic habitat as the focus.

In practice, larval control measures are applied to individual habitats. Therefore, the effect of any intervention is reflected by treatment-induced changes in the adult productivity. In the following analyses, we assume that treatments applied to individual habitats are 100% effective in elimination of emerging adults, that is, treated habitats produce zero contribution to the total productivity, defined as the total emerging female mosquitoes. Larval control measures can range from resource reduction to environmental manipulation of habitats to the application of microbial larvicides.

For model building, we conceive a conceptual quantity, the total productivity, to represent the population of emerging female mosquitoes from all habitats. The total productivity can be partitioned into constituent parts from individual habitats. Therefore, the effect of larval interventions can be represented by corresponding reductions in the total productivity from the treated habitats. This model framework has two advantages over the previous models that assumed a general larval population from one "habitat" or identical habitats. First, our models are general and habitat-based although they are implicit regarding both numbers and locations of habitats. Second, the models can be specified with empirical data of estimates of the habitat productivity. This new model framework allows us to examine impacts of larval interventions from the perspective of habitats without delving into the complexity associated with landscape juxtapositions of individual habitats.

We consider three scenarios of larval control (S1, S2, and S3), which may be applicable in the field. First, S1 represents a situation in which all habitats are identical in contribution to the total productivity P. This scenario is similar to the assumption of Killeen and others26 except that our measure of productivity is proportional contributions of individual habitats rather than absolute numbers of emerging mosquitoes. Clearly, this difference is trivial in this scenario due to the assumption of identical habitats. For S1, reduction in the total productivity P is a linear function of levels of coverage (C) of habitats under treatment


In the next two scenarios, we consider more realistic situations where habitat productivities are not uniform with some prolific habitats contribute extremely large amounts of emerging adults. For untargeted interventions, S2, aquatic habitats are randomly chosen for treatment. This scenario occurs when larval control is conducted with little knowledge of habitat productivity. Because of enormous variability in adult productivity observed in the field,12,27,28 the majority of the total productivity in an area might originate from a small number of highly prolific habitats. Under this circumstance, the random choice of habitats for treatment is likely to miss those prolific habitats unless large proportions of habitats are selected for treatment. Therefore, the relationship between P and C can be generally described using a logistic function


where {alpha} and ß are constants (Table 1Go).


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TABLE 1
Symbols and values of parameters used in the models
 
In contrast, targeted interventions S3, represent a scenario where control interventions are targeted toward highly productive habitats. Therefore, management of small proportions of aquatic habitats can obtain large proportional reductions in the total productivity. The relationship between P and C can be approximated using an exponential curve


where {delta} is a constant reflecting degrees of aggregation in productivity among habitats (Table 1Go).

Equations 1–3 described here can be easily modified to represent a wide spectrum of larval control practices in the real world. In a specific larval control program, the relationship between P and C should be empirically estimated based on data of both larval and habitat surveys. For instance, the habitat productivity can be estimated as a product of estimates of emerging adults or pupal density (Di) and size (Si) of habitat i. Therefore, for a focal area with n habitats, the constituent contribution (Mi) to the total productivity from habitat i is estimated as


Because habitats often exhibit seasonal changes after rainfall patterns in tropical Africa, ranking and prioritizing habitats need to proceed to track the temporal changes in habitat productivity.

Note that P, ranging from 0 to 100%, is the percent productivity associated with levels of coverage of habitats under treatment. It has been well recognized that the goals of any malaria control intervention should be established based on both mosquito abundances and transmission intensities.30 To represent variability in mosquito abundance in various areas, we introduce a parameter {gamma} as the base level of emerging female mosquitoes per person per day. {gamma} reflects local characters influencing mosquito proliferation such as abundance and quality of larval habitats in the area. Therefore, emerging females per person per day under the scenarios of larval interventions can be calculated as {gamma}P. In the following sections, we chose two base levels {gamma} = 1 and 5 for the following analysis because these values gave rise to low and intermediate levels of transmission intensities. In practice, parameter {gamma}, not directly measurable in the field, can be estimated from man-biting rates or entomological inoculation rates as described in the following section.

Transmission intensity, measure by EIR, is a fundamental predictor of incidence and prevalence of malaria.31–35 Conventionally, EIR is estimated as a product of man biting rate (ma) and proportion of sporozoite (s) infected mosquitoes as EIR = mas. Because only proportions of emerging female mosquitoes that survive the extrinsic incubation period (T) are capable of transmitting the parasite. By assuming that daily mosquito mortality (d) is age-independent, we can substitute m with {gamma}Pe–dT in equation 4. Therefore, EIR is calculated using


The values of the parameters are listed in Table 1Go. These estimates yield monthly EIR values of 0.55 and 2.8 (6.6 and 33.6 annually), for the two levels of {gamma}, respectively. These EIR levels correspond to low and intermediate levels of transmission intensity typically found in tropical Africa.36 We did not extend the analyses to situations of high transmission because then the relationships between incidence and prevalence and transmission intensity are complicated due to acquired protective immunity.37,38 Equation 4 establishes a relationship between EIR and the total productivity P, which in turn is a function of the level of coverage of larval habitats C based on Equations 1–3. Therefore, it is possible to incorporate control interventions targeting adult mosquitoes such as with indoor residual spray by manipulating mortality rate d in Equation 4.

Next, we examine how changes in EIR influence both malaria incidence and prevalence. Association between incidence and EIR is affected by several factors including vector competence and host susceptibility. Several studies have shown that not every infectious bite leads to an infection in the susceptible host.39–41 There are evidences that infection rates tend to decline with age suggesting an enhanced protective immunity based on repeated exposures.37 Additionally, various mosquito species may have different vector competence. In traditional malaria models, this complexity is incorporated into a parameter reflecting the probability of an uninfected person becoming infected due to an infectious bite b.42,43 Assuming that the outcomes of individual infectious bites on an uninfected host are independent, we can use a binomial model to describe the probability of infection (I) as a function of EIR


If assuming exposure to infectious bites is uniform among humans, the probability of infection I is equivalent to the proportion of uninfected persons (N) who were exposed and then became infected. Therefore, the incidence rate can be approximated as a product of N and I. We have examined the relationships between infection rates and the three scenarios of larval control by setting N = 100 and b = 0.5.

In situations where bednets are used in addition to larval control interventions, equation 5 can be modified to incorporate the protection of bednets. This can be obtained by dividing the human hosts into two groups based on whether bed-nets are used


where w is the percent of individuals who slept under bednets, f is the percent reduction in exposure protected by bednets. We analyzed a situation where larval control interventions are combined with a bednet program in which half (w = 0.5) of the population sleeping under bednets with f = 80%.26

Finally, we use the established relationship between prevalence (p) and EIR to examine the impact of larval control on malaria prevalence.25,31,42 The relationship between prevalence and EIR can be described by the following equation in areas of low and intermediate transmission without consideration of acquired protective immunity


where r is recovery rates, as measured by the reciprocal of the infection period. For calculation purposes, EIR and r should have the same unit, either daily or monthly. We chose r = 0.01 as this value has been used in some modeling studies.43,44 However, our previous studies on the coastal Kenya35 and others45 suggested much lower recovery rates. Generally, adoption of lower recovery rates makes the effect of larval control on prevalence less remarkable than we observed here.


RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 MODELS
 RESULTS
DISCUSSION
 REFERENCES
 
Effects of larval control on the total productivity. Larval control under scenario S1 predicts a linear reduction of productivity with an increase in levels of coverage (Figure 1Go). In comparison, scenario S2 performed poorly with only marginal reductions in adult productivity at low levels of habitat coverage. Unsurprisingly, targeted larval control S3 exhibits efficient control with a 70% reduction in the total productivity with coverage of only 30% of the habitats (Figure 1Go).



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  		    FIGURE 1. Effect of larval control on the total productivity ({diamond} uniformed habitats, {blacksquare} the untargeted intervention, and {blacktriangleup} the targeted intervention).

 
Effect of larval control on EIR. The patterns of change in EIR in response to larval control under the three scenarios are similar to the ones described in the preceding section due to the linear relationship between the total productivity and EIR. S3 yielded an efficient control with a 70% reduction in EIR associated with a 30% reduction in coverage of habitats, compared with only a 5% reduction in S2 (Table 2Go). When levels of coverage reached high levels (e.g., 80%), the difference between S2 and S3 strategies diminished because many of prolific habitats might be included in an untargeted larval control program when large proportions of habitats were treated (Table 2Go). Reduction rates of EIR remained constant with respect to transmission intensity. However, to reduce EIR to specified levels, required levels of coverage were different in areas with different transmission intensity. For instance, to reduce monthly EIR to 0.1, coverage of treated habitats in the targeted larval control (S3) would be 40 and 80% in areas with the low and intermediate levels of transmission, respectively (Figures 2a and 2bGo).


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TABLE 2
Reduction rates (%) in entomological inoculation rates (EIR), incidence, and prevalence of malaria at the levels of coverage of 30%, 50%, and 80% of larval habitats under three scenarios of larval control
 


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  		    FIGURE 2. Effect of larval control on the entomological inoculation rate in the areas of the low (a) and intermediate (b) levels of transmission intensity ({diamond} uniformed habitats, {blacksquare} the untargeted intervention, and {blacktriangleup} the targeted intervention).

 
Effect of larval control on malaria incidence. Reductions in incidence rates in response to changes in levels of coverage under scenarios S1 and S2 was notably smaller than those in S3 (Figure 3Go). The targeted larval control yielded a 66% reduction in incidence for the coverage of 30% habitats in the intermediate transmission. This is compared with a 4% reduction under S2. For the same level of coverage of larval habitats, interestingly, reduction rates were lower in the low transmission than in the intermediate transmission (Table 2Go). This finding suggests that, in areas of low transmission intensity, it is necessary to have sufficient sample sizes for monitoring incidence rates to have adequate powers of detecting change in incidence rates attributable to the various intervention programs.



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  		    FIGURE 3. Effect of larval control on malaria incidence rates in the areas of the low (a) and intermediate (b) levels of transmission intensity ({diamond} uniformed habitats, {blacksquare} the untargeted intervention, and {blacktriangleup} the targeted intervention).

 
Effect of larval control on prevalence. As previously reported,35 even in the case of the low transmission, prevalence can be as high as 60% (Figure 4aGo). This figure could be even higher with lower recovery rates. In the intermediate transmission area, S3 produced a 45% reduction with 30% coverage of larval habitats. This is compared with a 2% reduction under S2. Similar to the pattern observed with incidence in the preceding section, the reduction rates in prevalence in the area of the low transmission were lower than those found for the intermediate transmission (Table 2Go). Generally, prevalence was insensitive to larval interventions under scenarios S1 and S2 (Figure 4Go).



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  		    FIGURE 4. Effect of larval control on malaria prevalence in the areas of the low (a) and intermediate (b) levels of transmission intensity ({diamond} uniformed habitats, {blacksquare} the untargeted intervention, and {blacktriangleup} the targeted intervention).

 

DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 MODELS
 RESULTS
 DISCUSSION
REFERENCES
 
Our models have generated important messages with respect to planning of larval interventions. First, management of all aquatic habitats often is unnecessary for obtaining specified objectives of reductions in incidence and prevalence of malaria. This is especially important because of aquatic habitats are not uniform in productivity and availability of limited resources in African communities. Second, given enormous variability observed in anopheline productivity between habitats,12,27,28 effective larval interventions can be achieved by targeting control efforts toward productive habitats. In many situations, the majority of female mosquitoes in a focal area are likely to emerge from prolific habitats, which might account only for a small proportion of habitats. Targeted larval interventions have a great potential to maximize limited resources and should be vigorously pursued in integrated malaria management in Africa. Third, for targeted larval interventions, it is crucial to survey aquatic habitats to estimate their adult productivity. Beyond habitat mapping and surveying for the presence of anopheline mosquitoes, targeted interventions require quantification of habitat productivity based on sample data, e.g. larval density and surface size of habitats.

The guiding principal of integrated malaria control in any area is to tailor interventions to the local entomological and epidemiologic characteristics.30 One of the key local determinants of transmission is abundance, distribution and adult productivity of larval habitats.29 Therefore, inventory of aquatic habitats regarding their productivity can provide critical information for characterizing species-specific oviposition habitat selection and planning of integrated mosquito managements. Our results also indicate that larval control will probably have little impacts on malaria incidence, if interventions are untargeted and levels of coverage limited. This may explain why in some situations control interventions by larviciding apparently failed to alleviate malaria incidence.46

As previously discussed, the habitat productivity is ideally measured from estimates of emerging adults of individual habitats. In most situations, a practical approach is to use larval density as an alternative for estimates of emerging adults. However, experimental studies show that An. gambiae Giles displayed density-dependent regulations with delayed developmental rates of larvae and smaller body sizes of emerging adults when they reared in crowding conditions in artificial habitats47,48 although this phenomenon may be uncommon in natural habitats such as rice fields.49,50 It should be emphasized that large habitats with low density of emerging adults can be more productive than small water bodies with high density (e.g., a roadside ditch of low larval density probably ranking higher than a hoof print with high density). In large habitats like rice paddies, distribution patterns of anopheline larvae are useful to accurately estimate productivity. For example, larvae tend to aggregate along edges of water, thus estimation of productivity should be made by stratifying the habitats in terms of larval density and obtaining corresponding estimates from each strata.

It should be noted that our quantitative predictions are nothing but a combination of adopted assumptions and values of parameters. For instance, we assume that contacts between hosts and blood feeding mosquitoes are uniformly distributed in the focal area, whereas studies has shown blood feedings of mosquitoes tended to aggregate in space.51 Various assumptions of values of some parameters (e.g., the daily mortality rate d and the recovery rate r), can substantially alter numerical predictions of our models. Using these simple models, however, we attempted at providing qualitative understandings of larval interventions from the habitat perspective, which should hold when parameter values are in the reasonable ranges encountered in the field.

Macdonald’s seminal work back in the 1950s had shown that adulticiding was more effective in reducing the basic reproductive rate than larviciding of anophelines.42 The failure of the global eradications of malaria by solely relying on indoor residual sprayings in during the period of 1960s to 1970s demonstrated the need of integrated mosquito managements. Due to environmental concerns and rapid development of resistance to insecticides, adult control has constraints in applications although it is one of the powerful tools to rapidly reduce exposures to mosquito bites. At present, adult control often focuses on uses of treated bed nets.30,46 By contrast, larval control with ecological manipulations of habitats and/or microbial insecticides such as Bti is environmentally sound and can be effective in alleviating malaria incidence as shown here. Although targeted larval interventions have a great potential in reducing transmission intensity and incidence of malaria, we do not proposed that larval control is a panacea for combating malaria in all settings of Africa. Combined with other interventions in an integrated manner, larval interventions can be successful in situations where major habitats are limited and manageable. We emphasize that informed larval interventions guided by habitat-based modeling can play an important role in managing entomological features of local malaria transmission. Given the constraint of resources throughout Africa, we believe that targeted larval interventions have a great potential for combating malaria, especially in areas of low to intermediate transmission.

Our modeling results are also applicable to management of other mosquito borne diseases such as West Nile virus. Larval control interventions play an important role in containing West Nile virus during transmission seasons in North America where Culex mosquitoes are implicated as major vectors.52,53 Although larval control has been widely implemented in the UNited States, very few efforts have been made to collect data for designing of targeted interventions of larval populations. For larval control to be effective, it is crucial to maximize control efforts by targeting prolific habitats.

Received March 16, 2005. Accepted for publication April 19, 2005.

Acknowledgments: The authors thank J. Beier, R. Lampman, and J. Keating for their insightful comments.

Financial support: This research was supported by NIH (UO1 A154889-NIH).

* Address correspondence to Weidong Gu, Illinois Natural History Survey, Champaign, IL 61820. E-mail: wgu{at}inhs.uiuc.edu Back

Authors’ address: Weidong Gu and Robert J. Novak, Illinois Natural History Survey, Champaign, IL 61820, Telephone: 217-333-1186, Fax: 217-333-2359.

Reprint requests: Weidong Gu, Illinois Natural History Survey, Champaign, IL 61820, Telephone: 217-333-1186, Fax: 217-333-2359, E-mail: wgu{at}inhs.uiuc.edu.


REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 MODELS
 RESULTS
 DISCUSSION
 REFERENCES
 

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