Re: Preventing Childhood Malaria in Africa by Protecting Adults from Mosquitoes with
Re: Preventing Childhood Malaria in Africa by Protecting Adults from Mosquitoes with
Methods
Overview
Here we used recently developed kinetic models of mosquito behaviour and mortality [
11,
13] to answer this question by considering the impact of ITNs on human host availability and feeding hazards to mosquitoes, as well as the consequences of such changes for malaria transmission intensity.
Protection was estimated in terms of protection against exposure to infectious mosquito bites, expressed as the relative change in the entomological inoculation rate (EIR).
EIR is a proven epidemiological indicator of malaria transmission intensity and a key determinant of disease burden [
17,
40].
Two common but ecologically distinct African malaria transmission systems are considered.
First, we modelled an
Anopheles gambiae Giles or
An. arabienis Patton (sibling species from the same species complex known as
An. gambiae sensu lato) population with access to human blood only.
Second, we considered
An. arabiensis populations in the presence of
abundant cattle, which can act as alternative blood sources.
An. gambiae greatly prefers humans, but
An. arabiensis will readily feed upon cattle [
42,
43], so populations of these species respond quite differently to increasing ITN coverage, with malaria transmission by the latter typically being lower to begin with but less sensitive to control with ITNs [
11].
In both transmission systems we considered ITNs with properties typical of those evaluated in rigorous clinical trials [
20] or those of emerging technologies with improved operational durability [
44?
47].
Note that coverage is expressed as the proportion of the total human population using an ITN each night, rather than in terms of ownership, because this value is the most direct indicator of both personal and communal protection.
Figure 1 provides an overview of how mosquito behaviour and survival were modelled as a function of host availability, ITN properties, compliance, and coverage. The approach described is essentially a behaviourally explicit extension of existing vector biodemography [
48] models, which predict epidemiologically relevant outcomes such as exposure to transmission (the biodemography?epidemiology model). The principles and utility of the biodemography?epidemiology models we have used [
27,
49,
50], as well as several others that are based on similar assumptions [
6,
18,
28,
51], are well established. Notably, this family of models realistically assumes that mosquito behaviour cycles between host seeking, feeding, resting, oviposition-site seeking, oviposition, and back to host seeking again [
51]. Similarly to recent analyses of the importance of oviposition [
7,
8,
10] and host acquisition [
11,
12] processes, here we explicitly modelled the underlying behavioural events that determine the input parameters of these biodemographic processes (the behaviour?biodemography model). Detailed consideration of mosquito behaviour and mortality upon encounter with individual hosts (the individual-level submodel) allows simulation of the impact of ITNs upon the foraging requirements and risks for mosquito populations at the community level (the community-level submodel). This hierarchical approach links individual- and community-level submodels into an integrated behaviour?biodemography model, which drives the outcome of the biodemography?epidemiology model and allows the influence of ITNs upon malaria transmission intensity to be estimated in terms of EIR experienced by both users and nonusers [
11,
27,
50].
Figure 1. A Schematic Outline of the Two-Tier Model Used for This Analysis, Adapted from Previous Detailed Descriptions
A detailed model of mosquito behaviour and survival as a function of host availability, ITN properties, compliance, and coverage [
11,
13] was used to estimate the key biodemographic parameters that determine malaria transmission intensity (behaviour?biodemography model). This model allowed the influence of ITN usage upon malaria transmission intensity to be estimated (biodemography?epidemiology model) in terms of EIR experienced by both users and nonusers [
11,
27,
50]. All terms and symbols are defined in detail elsewhere [
11,
27,
50,
52] and are summarized in Methods.
The specific modelling approach described here is almost identical to our recent exploration of the optimal properties of ITNs as a function of local ecology [
11], apart from subtle improvements in terms calculating mosquito diversion, mortality, and feeding probabilities per host encounter. It is also similar to and consistent with the approaches of others [
6,
12] but accounts for the fact that ITNs can act only during times of the night when they are actually in use, so that their overall protection is also influenced by subtle variations in the behavioural interactions between humans and mosquitoes [
13]. This model has already been evaluated through improved iterations in terms of sensitivity to variations in the assumed parameter values for the insecticidal and excito-repellent properties of ITNs [
11], the survival rate of mosquitoes while foraging for resources [
11], the innate resource preferences of vector populations [
11,
50,
52], and the availability of those resources, including oviposition sites [
50] and alternative blood meal hosts [
11,
50].
While the analysis outlined here could be implemented with either of the recently developed (and perhaps more elegant) alternative models [
6,
12], this particular form captures all of the same processes without necessitating the mathematical subtleties of integration, differentiation, equilibrium analysis, or limits. While these are inherently valuable tools for mathematical modelling, they often constitute ?black boxes? to nonmathematicians, including several authors of this article. We therefore chose a model that does not require mathematical complexities that might limit accessibility to some of the field biologists and epidemiologists for whom this analysis is most relevant. The model is presented as a downloadable spreadsheet (see
Protocol S1) and has proven valuable for teaching the ecological basis of malaria epidemiology and control to students in both the developed and developing world.
Modelling Mosquito Behaviour and Mortality at the Individual Level
Here we describe a submodel of behavioural and mortality processes that occur at the level of individual mosquitoes seeking, encountering, attacking, and feeding upon individual blood hosts. Another important simplification to consider is that, like most deterministic malaria transmission models, our approach assumed a ?malaria in a bottle? scenario in which populations of identical parasites, vectors, and hosts are mixed homogenously within an enclosed system [
53]. One important corollary of this assumption is that well-established variations of vulnerability to malaria infection within human populations [
16,
17] or associated variations in attractiveness and availability to mosquitoes [
9,
54?
56] are not explicitly modelled.
As defined previously [
52], the availability
(a) of any host
(j) of any species
(s) is the product of the rate at which individual vectors encounter it
(
<SUB>s,j</SUB>) and the probability that, once encountered, they will feed upon it
(<SUB>s,j</SUB>):
<CENTER>
</CENTER>
Note that this kinetic definition of
availability as a rate per unit time is consistent with applications of the same term to acquisition of oviposition sites [
10], the term
attraction rate for blood sources [
6,
57], and the terms
feeding rate and
oviposition rate for both resources [
8,
12].
We considered successful feeding as just one of three possible outcomes of a host encounter by a female vector, the other two being death while attempting to feed and diversion to seek another host (
Figure 1). We considered this a two-stage process in which the vector first either attacks the encountered host or is diverted away and searches for another, the probabilities of which we denote as
γ and
Δ, respectively. This definition of diversion includes the combined effects of noncontact repellency and contact-mediated irritancy, often referred to as excito-repellency [
58,
59]. Considering mean values for hosts of any given species
(s), the sum of these two probabilities is:
<CENTER>
</CENTER>
We then considered the second stage of the blood acquisition process, namely feeding. Knowing the probabilities that the vector will either feed successfully
(<SUB>s</SUB>) or die in the attempt
(μ<SUB>s</SUB>) per attack (rather than per encounter) allowed us to calculate the probability of a successful feed per encounter:
<CENTER>
</CENTER>
Specifically, the cases of cattle
(c) and unprotected humans
(h,u) were dealt with in a straightforward manner as follows, where
Δ<SUB>u</SUB> and
μ<SUB>u</SUB> represent a common parameter value for both types of host (
Table 1):
<CENTER>
</CENTER>
Table 1.
Behavioural and Host Availability Input Parameters for Both Vector Species
Personal protection measures such as bed nets, repellents, or domestic insecticide use were envisaged as three possible outcomes, the probabilities of which sum to 1: For a vector that would normally choose to feed upon an encountered unprotected human with a probability of
<SUB>h,u</SUB>, the presence of a net or other intervention is expected to influence this probability for protected humans
(<SUB>h,p</SUB>) as a function of the excess probability of diverting
(Δ<SUB>p</SUB>) and killing
(μ<SUB>p</SUB>) that vector (
Figure 1). The combined baseline and net-induced probabilities of diversion
(Δ<SUB>u</SUB><SUB>
+
p</SUB>
) or mortality
(μ<SUB>u+p</SUB>) were calculated as follows:
<CENTER>
</CENTER>
and
<CENTER>
</CENTER>
These parameters allowed us to calculate the feeding probability for a human who always uses and is protected by a net
(<SUB>h,p</SUB>):
<CENTER>
</CENTER>
These equations are parameterized using data from experimental hut trials in which the human participants slept within the net throughout the period of data collection (
Table 1). However, very few human beings spend their entire day asleep or using a net [
13] so the true probability of feeding upon a typical net user (
) is calculated by weighting
<SUB>h,u</SUB> and
<SUB>h,p</SUB> according to the proportion of normal exposure during which the host is actually covered
(π<SUB>i</SUB>):
<CENTER>
</CENTER>
Equations 5-7 differ slightly from those previously proposed [
11], which treated diversion and killing as independent events, conditional on the host having and using a net. At low values of
π<SUB>i</SUB> these changes relative to [
11] make little difference, but the model described here is more realistic at high values of
π<SUB>i</SUB>.
Extrapolating Impacts of Insecticide-Treated Nets to the Community Level
Given the above submodel for the interactions of mosquitoes with individual mammalian hosts, it was possible to extrapolate the likely large-area effects of these small-scale influences on entire vector populations and the human communities they feed upon.
For any given number of cattle
(N<SUB>c</SUB>), unprotected humans
(N<SUB>h,u</SUB>), and protected humans
(N<SUB>h,p</SUB>), the mean seeking interval for vertebrate hosts
(η<SUB>v</SUB>) can be calculated as the reciprocal of total host availability
(A) [
52], using estimates of these feeding probabilities and their corresponding encounter rates, adapting
Equation 1 from our original formulation [
50]:
<CENTER>
</CENTER>
where
A<SUB>s</SUB> refers to the total availability of all hosts of species
s. In this case, the species or species categories considered were unprotected humans
(h,u), protected humans
(h,p), and cattle
(c). Values for
a<SUB>c</SUB> and
a<SUB>h,u</SUB> (previously
a<SUB>h</SUB> [
50]) were estimated exactly as described previously [
50] and
a<SUB>h,p</SUB> was calculated as follows:
<CENTER>
</CENTER>
where
λ<SUB>p</SUB> is the relative availability of protected versus unprotected hosts, estimated in terms of the ratio of their feeding probabilities:
<CENTER>
</CENTER>
Foraging for resources is an intrinsically dangerous undertaking for mosquitoes, and it is commonly assumed that survival during these phases is lower than while resting in houses [
6,
60]. We adapted
Equation 3 from our previous formulation [
50] to estimate the survival rate per feeding cycle
(P<SUB>f</SUB>) as the product of the probability of surviving the eventual attack on a host that may be protected
(P<SUB>γ</SUB>) and the probabilities of surviving the gestation
(g), oviposition site-seeking
(η<SUB>o</SUB>), and vertebrate host-seeking
(η<SUB>v</SUB>) intervals, with distinct daily survival probabilities for the resting
(P), foraging for either oviposition sites or vertebrate hosts
(P<SUB>ov</SUB>), and attacking
(P<SUB>γ</SUB>) phases:
<CENTER>
</CENTER>
The mean probability of mosquitoes surviving their eventual chosen host attack
(P<SUB>γ</SUB>) was calculated assuming that the proportion of all attacks that end in death is the sum of the mortality probabilities for attacking protected and unprotected hosts, weighted according to the proportion of all encounters that will occur on such hosts. Assuming that protection does not affect encounter rates, and that these rates are proportional to availability when unprotected, we applied this weighting approach to estimate total attack-related mortality rate and consequent survival as follows:
<CENTER>
</CENTER>
Similarly, the human blood index is calculated as the proportion of total host availability accounted for by humans [
52], similarly to
Equation 9:
<CENTER>
</CENTER>
The EIR for protected and unprotected individuals was then calculated from the total number of infectious bites upon humans that occur in the population as a whole
(β E) [
27,
49], the share of the total human availability represented by that group, and the population size of that group:
<CENTER>
</CENTER>
<CENTER>
</CENTER>
where
β is the mean number of infectious human bites each emerging mosquito takes in its lifetime and
E is the emergence rate of mosquitoes [
27]. Dividing
Equation 16 by
Equation 15, substituting with
Equation 10, and rearranging also leads to an intuitively satisfactory solution, consistent with independently formulated models of personal protection [
13]:
<CENTER>
</CENTER>
Otherwise, we modelled malaria transmission exactly as previously described [
50]. Note that this model has been adapted [
11,
50] from its original formulation [
27] to account for superinfection of mosquitoes [
28] and daily time increments to smooth the effects of changing host availability patterns on feeding cycle length [
50]. For ease of comparison and interpretation, the impact of ITNs is presented in terms of the relative transmission intensity EIR
<SUB>C</SUB>/EIR
<SUB>0</SUB> at a given coverage level (
C; note distinction from
c, which denotes cattle hosts) as a result of personal and communal protection amongst users and nonusers:
<CENTER>
</CENTER>
<CENTER>
</CENTER>
<CENTER>
</CENTER>
Baseline Mosquito Behaviour, Host Availability, and Survival Parameters
The parameter definitions and values used to implement this analysis are summarized in
Table 1. Namwawala, in the Kilombero Valley, southern Tanzania is the primary centre for parameterising our model because of the exceptionally detailed quantitative characterisation of malaria transmission and vector biodemography in this village and the surrounding area. This is a holoendemic village with intense seasonal transmission, stable high parasite prevalence in humans, and a heavy burden of clinical malaria [
61?
68]. At this site the bulk of transmission is mediated by
An. gambiae sensu lato (of which the main species involved in transmission is
An. arabiensis) and transmission intensity has been modelled with available field data [
27,
49].
As previously described [
27,
49], we based our estimate of human population size [
62] approximately upon those reported for this particular village during the early 1990s. Nevertheless, we used a human population size of 1,000 and, where relevant, a bovine population of the same size so that the EIR experienced by users and nonusers could be easily calculated at net coverage levels approaching 0% and 100%. By setting coverage to 0.001 or 0.999, this model simulates a single user or nonuser in the population, respectively.
Infectiousness of humans
(κ) is set to 0.030, reflecting a more precise recent estimate [
69] than was available previously [
61,
63]. In a typical holoendemic scenario, the infectiousness of the human population is thought to be largely insensitive to reductions in transmission intensity [
69]. In the interests of making conservative and generalizable predictions, we assumed that increasing coverage with ITNs will not affect
κ [
69], even though reduction of
κ is likely at EIR values below 10 infectious bites per person per year [
56].
We set mean daily survival of the resting phase
(P) at 0.90, reflecting a median value of daily survival at four well-characterised holoendemic sites [
27] and estimated daily indoor survival for
An. gambiae s.l
. in Tanzania [
70]. As previously described, the daily survival rate of mosquitoes while foraging for blood or oviposition sites
(P<SUB>ov</SUB>) was set at 0.80, representing a median value of plausible field values [
11]. The results of experimental hut studies [
34] were combined with host-choice evaluations [
71] and appropriate analytical models [
50,
52] to define the attack and mortality probabilities of
An. arabiensis encountering cattle or humans: we set the probability that
An. arabiensis will attack unprotected cattle or humans
(γ<SUB>u</SUB>), conditional upon encountering them, to be 0.90 and the chance that they will die in the attempt
(μ<SUB>u</SUB>) at 0.10.
Using these parameters and
Equation 3, we calculated that, for
An. arabiensis, the overall feeding probability upon either cattle
(<SUB>c</SUB>) or unprotected humans
(<SUB>h,u</SUB>) would be 0.81, a value similar to previous estimates of approximately 0.80?0.85 for the feeding success of
An. gambiae sensu lato on sleeping humans in Tanzania [
34,
62]. We also applied these same probabilities of attacking
(γ<SUB>u</SUB>), feeding
(<SUB>h,u</SUB>), and dying
(μ<SUB>u</SUB>) to
An. gambiae sensu stricto encountering unprotected humans. The availabilities of unprotected humans and cattle were calculated for
An. arabiensis using field measurements of the duration of the feeding cycle and were extended to
An. gambiae s.s., accounting for the lower estimated relative availability of cattle
(λ<SUB>c</SUB>) to this mosquito species as previously described [
52]. Note that
λ<SUB>c</SUB> is assumed to modify
a<SUB>c</SUB> by affecting the encounter rate only, indicating that these mosquitoes can differentiate between preferred and nonpreferred hosts at long ranges [
72?
74]. In the case of
An. arabiensis this assumption is consistent with the longer spatial range of attraction of cows relative to humans for zoophilic members of the
An. gambiae complex [
72?
74].
Parameters Reflecting the Effects of Insecticide-Treated Bed Nets
The parameter definitions and values describing the impacts of ITNs on vector behaviour and mortality at the level of individual interactions are listed in
Table 1. The impacts of ITNs very much depend on their excito-repellent and insecticidal properties, which are most representatively evaluated using well-established experimental hut methodologies [
59,
75,
76] that have been extensively applied to this particular intervention [
29?
34]. Furthermore, the interaction of these two properties, to yield varying levels of personal and communal protection, is complex and has crucial implications for ITN programmes across Africa [
11]. Sensitivity analysis of models similar to those used in this paper [
11] have previously been used to explore the influence that these properties might have upon the magnitude and equity of protection afforded by ITNs (
Figure 2). In order to validate this slightly revised model (see
Equations 4-8) and similarly investigate such interactions at ITN coverage levels that can be plausibly sustained, we examined usage data collected during routine socioeconomic status surveys of a long-standing demographic surveillance system in the Kilombero Valley, southern Tanzania, where social marketing programmes have been well established since 1997 [
77,
78]. Data from the annual ITN usage survey in 2004 were used because they overlap with detailed entomological surveys of malaria transmission (which will be reported elsewhere). These surveys of randomly sampled residents from across two rural districts indicate that 75% (11,982/16,086) net use was achieved although most of these nets were not effectively treated [
79]. In this sensitivity analysis, we assumed that new long-lasting ITN technologies [
44?
47] will enable sustained coverage with nets that are effectively treated even under the most rigorous programmatic field conditions.
Figure 2. The Simulated Protection ITNs Afford against Exposure to Malaria Transmission as a Function of Their Ability to Divert and Kill Host-Seeking Mosquitoes
Protection is expressed as relative exposure to malaria transmission (EIR
<SUB>C</SUB>/EIR
<SUB>o</SUB>) for individuals with (
Equation 19) and without (
Equation 18) nets is plotted as a function of their ability to divert
(Δ<SUB>p</SUB>) and kill
(μ<SUB>p</SUB>) mosquitoes attacking protected humans. To simulate the likely field properties of existing long-lasting insecticidal nets with a full range of insecticidal and excito-repellent properties, the parameters of this model reflecting increased mosquito mortality
(μ<SUB>p</SUB>) and diversion
(Δ<SUB>p</SUB>) were varied across a plausible range of 0?0.8. As described in the main text and previous publications, these results represent simulations in two distinctive scenarios:
An. gambiae sensu lato in the absence of cattle (results for both sibling species are identical) and
An. arabiensis in the presence of one head of cattle per person. The biodemographic parameters of the interacting vector and parasite are also exactly as described previously [
11,
13] with survival of foraging mosquitoes
(P<SUB>ov</SUB>) set at 0.8 per day. Coverage levels of 75% net usage was assumed, consistent with the results of surveys in the Kilombero Valley, southern Tanzania (see
Methods: Parameters Reflecting the Effects of Insecticide-Treated Bed Nets).
Figure 2 shows that, for the comparatively zoophilic vector
An. arabiensis, in the presence of alternative hosts, excito-repellency consistently enhances the benefits for both users and nonusers, regardless of the insecticidal properties of the net. Consistent with previous analyses using this model [
11], this simulation suggests that nets that are purely excito-repellent and lack insecticidal properties could slightly increase exposure of nonusers to
An. gambiae sensu lato by diverting mosquitoes to them where no alternative sources of blood are available. Thus, purely diversionary vector control strategies may indeed be ethically questionable, as was previously suggested [
31,
34,
80,
81]. Nevertheless, even modest insecticidal properties are expected to counterbalance this inequity and confer a useful communal reduction of EIR. While repellent properties do slightly reduce the benefits to nonusers exposed to anthropophagic vectors lacking an alternative host, this slight disadvantage is likely to be outweighed in practice by the advantage of improved personal protection for users: Excito-repellent properties and physical barriers add to the effectiveness of insecticides for personal protection because these two incentives constitute the major motivating force behind ITN uptake and use at the individual and subsequently the community level. It is also reassuring to note that the predictions and epidemiological implications of this slightly revised model are very similar to those reported for its previous iteration [
11].
We therefore concluded that the simulations described in the main text should consider ITNs with both insecticidal and excito-repellent properties, consistent with those of products currently on the market that have been evaluated in a variety of settings and experimental designs.
To simulate the likely properties of established ITNs under programmatic conditions, we conservatively assumed they will both divert and kill 40% more mosquitoes than an unprotected human (
μ<SUB>p</SUB> = 0.4 and
Δ<SUB>p</SUB> = 0.4). A net with such proper-ties would protect against 64% of indoor exposure (1 − [(1 − 0.4) ? (1 − 0.4)] = 0.64), as measured in a typical experimental hut trial [
46,
76]. To explore the best possible future scenario for the development of highly durable ITNs [
44?
47] or regular retreatment services [
82], we also simulated increasing co-verage with nets that divert and kill 80% more mosquitoes than with an unprotected human (
μ<SUB>p</SUB> = 0.8 and
Δ<SUB>p</SUB> = 0.8), providing 96% protection (1 − [(1 − 0.8) ? (1 − 0.8)] = 0.96). The proportion of normal biting exposure that occurs while nets are actually in use
(π<SUB>i</SUB>) has been estimated as 90% for
A. gambiae in southern Tanzania [
13], so we set
π<SUB>i</SUB> to a value of 0.90.
