Intervention results
Eleven scenarios are considered that span a range of baseline ITN coverage values and EIR values. Although spatial targeting should cause these two quantities to be positively correlated in practice, the large funding gap in ITNs [
10] suggests that the only coverage-EIR combination considered here that may be rare in practice is the 80 % coverage, EIR = 10 scenario.
The first of three main results from the model is that the targeted food policy achieves a nontrivial reduction in malaria mortality; e.g., under 20 % baseline ITN coverage, providing supplementary food to underweight children (i.e., those with WAZ \(<-2\)) reduces malaria mortality by 22.9, 10.8, 7.8 and 7.2 % when EIR = 1, 10, 100 and 500, respectively. The morbidity reduction in the model explicitly incorporates the herd effect of nutrition: children who receive supplementary food become less susceptibile to disease, which leads to fewer infected mosquitoes, which in turn reduces the likelihood of disease in children who do not receive supplementary food. The mortality reduction is larger than the morbidity reduction because the children who receive food are also the most likely to die if they do get infected with malaria, and so their direct protection via supplementary food has a synergistic effect on the overall mortality due to malaria. As with ITNs, the impact of the targeted food policy is lower in higher EIR settings.
As expected, the untargeted ITN policy has a much larger effect than the targeted food policy on clinical malaria prevalence, although this effect decreases with increasing EIR, which is consistent with results from randomized controlled trials [
6]. The model predicts malaria elimination when EIR = 1 with 60 % ITN coverage of the child population, which corresponds to 20 % of the total population. It also predicts that 100 % ITN coverage of children, which corresponds to 34 % coverage of the entire population, is insufficient to eliminate malaria when EIR
\(\ge 10\). The model predictions about the infeasibility of malaria elimination in many scenarios is not inconsistent with results from randomized controlled trials [
6] or other modelling studies (Table 1 in [
31]). A cost-effectiveness comparison between supplementary food and ITNs has not been performed because supplementary food may also directly reduce mortality from wasting and stunting and reduce the lifelong effects of stunting, in addition to reducing morbidity and mortality associated with other diseases such as pneumonia and diarrhoea.
The second main result is that in the hypoendemic and mesoendemic settings, the targeted ITN policy outperforms the untargeted ITN policy (it achieves elimination at a lower coverage, and significantly reduces mortality over a wide range of sub-elimination coverages). However, the targeted ITN policy is outperformed by the untargeted ITN policy for conventional WAZ thresholds (e.g., WAZ
\(\in [-3, -1]\)) in the hyperendemic setting because undernutritioned children in this case are likely to get infected despite being protected by an ITN. While ITN targeting is typically performed at the macro level based on spatial estimates of transmission intensity [
21], these results raise the possibility of additional targeting at the micro level in the hypoendemic and mesoendemic settings based on easily-obtained anthropometric measures such as WAZ, despite the fact that young children are not a major contributor to the infectious reservoir [
28]. In addition, targeting based on child undernutrition may be more politically feasible and practically implementable than means-testing, where family incomes are the basis for ITN distribution [
32]. This targeting approach is particularly appealing for sub-Saharan Africa, which incurs 90 % of malarial cases and deaths, and where the burden of disease is in young children (and pregnant women) [
33].
The policy that targets ITNs and food performs nearly the same as the targeted ITN policy when EIR = 1. This lack of improvement may be due to the positive correlation of the two interventions (i.e., they are targeting the exact same children); efficacy of a joint strategy is often improved if two interventions are negatively correlated, in that they generate higher coverage [
28]. However, the improvements from adding targeted food to targeted ITNs are sizeable in the mesoendemic and hyperendemic settings. The third main result is that in a hyperendemic setting with 80 % ITN child coverage, food targeting offers a larger reduction in malaria morbidity and mortality than increasing the child ITN coverage beyond 80 %, which is often a logistical challenge.
Overall, the study suggests that much of the heterogeneity in susceptibility is observable (in this case, via WAZ values) and hence exploitable for purposes of targeting, which is sufficient to generate meaningful reductions in clinical malaria prevalence in some settings. Coupling this effect with the dependence of mortality on WAZ leads to even larger reductions when considering malaria mortality.
Although beyond the scope of this study, a similar analysis—but with a Susceptible-Exposed-Infected-Removed (SEIR) model with heterogeneous susceptibility rather than a vector model as in (
2)–(
5)—could be performed for the cases of diarrhoea (e.g., rotavirus) or pneumonia (e.g., respiratory syncytial virus), using either partial differential equations [
34] or branching processes [
1]. Such an analysis could quantify the benefits of other targeted preventive measures—e.g., rotavirus vaccination—to undernutritioned children. The relative risks for morbidity associated with WAZ
\(<-2\) are 1.23 and 1.86, respectively, for pneumonia and diarrhoea [
13], and mortality rates for these two diseases decrease with increasing WAZ (Table 2.5 in [
13]).
A possible generalization of the model is to incorporate the possibility that children’s nutrition level (e.g., WAZ) decreases when they are infected [
14‐
16]. Capturing this effect and the subsequent catch-up growth (pages 182–183 of [
35]) would require generalizing Eqs. (
4)–(
6) to a partial differential equation model, where
\(\dot{x}_i(s)\) is replaced by
\(\frac{\partial x_i(s,t)}{\partial t}\) for
\(i=1,2\). This generalization, which would be more difficult to analyze, may not yield any new qualitative results because of the catch-up growth.
Limitations of the study
The integrated nutrition-malaria model presented here simplifies aspects of nutrition and malaria. Undernutrition in this model is measured by WAZ (i.e., underweight), which can be viewed as a composite measure of HAZ (i.e., stunting), which is a long-term micronutrient deficiency that is caused by insufficiently balanced diets as well as repeated infection and psycho-social deprivation, and WHZ (i.e., wasting), which is an acute undersupply in energy and proteins (an alternative view is that wasting is a composite measure of stunting and underweight). Combining these into a single measure tends to muddle the interaction of nutrition with malaria. However, the best malaria mortality data [
13] explores its relationship only with WAZ and prevents us from developing a bivariate model using (HAZ,WHZ). If better data become available, a bivariate model may lead to a refinement of these findings, although the model would be considerably more difficult to analyse.
The malaria model ignores many complexities that have been incorporated in other malaria models, such as seasonality, spatial structure, age structure, immunity to infection (although this aspect did not improve the model fit in [
18]), and mosquito searching and feeding cycle (e.g., [
20,
28,
36]), and temporal issues related to the relative effectiveness of ITNs and the new generation of long-lasting insecticide-treated nets (LLINs). Nonetheless, given the research questions being raised (i.e., attempting to gain broad insights about targeted interventions as opposed to accurately predicting morbidity and mortality rates), these omissions seem appropriate, and the ITN parameters are estimated from the output of the more detailed model in [
20]. On the other hand, the model is more detailed (although much less broad) than the Lives Saved Tool [
37], which—while invaluable for broad resource allocation decisions for maternal and child health—is not able to address the type of targeting questions and policies considered here.
Despite these modelling limitations, the biggest shortcoming in this analysis relates to the estimation of the crucial parameter,
\(k_1\), which specifies the proportion of susceptibility heterogeneity that is due to undernutrition. First, the estimation of the total susceptibility heterogeneity (i.e., the parameter
k in the model and in [
18,
21]) is extremely difficult [
38]. Several modelling choices need to be made without supporting data. In [
18,
21], it was assumed that the susceptibility distribution had a gamma distribution. A much bolder assumption is made here that the undernutrition random variable is also gamma with the same shape parameter as the susceptibility distribution derived in [
21], so that only one new parameter (
\(k_1\)) needs to be estimated. It is further assumed that the left tail of the WAZ distribution corresponds to the right tail of the undernutrition distribution. In addition, the analysis in [
18] considers children up to 15 years of age, and their results are applied here to children up to 5 years of age. Turning to the data used to estimate
\(k_1\), the adjusted odds ratio of 0.76 (which gives an adjusted prevalence ratio of 0.77) in [
19] has a 95 % confidence interval (CI) of (0.51,1.13), and a p value of 0.177, and hence is not statistically significant at the traditional 0.05 level.
Interestingly, a more recent randomized controlled feeding trial [
39] of 54 g/day (slightly less than half the dose used in [
19]) of a lipid-based nutrient supplement had very similar results to [
19]: pooling the three intervention arms (milk-, soy- and corn-soy-based) and comparing to the control arm leads to an incident rate ratio of clinical malaria (fever and infection determined via microscopy) of 0.81 and a 95 % CI of (0.69, 0.94), which is statistically significant (in [
39], the three intervention arms were not pooled and did not achieve statistical significance). The results in [
39] cannot be directly pooled with those in [
19] because of the lower food dose, the restricted ages (6–18 months old), the higher pre-intervention nutrition levels (mean WAZ =
\(-\)0.8, mean WHZ = 0.4), and the higher malaria infection prevalence (0.13). Nonetheless, the consistency in results between these two studies suggests that this result may be robust.
If the relative risk of clinical malaria of 1.31 associated with WAZ
\(<-2\) [
13]—rather than the feeding trial data in [
19]—is used to estimate
\(k_1\), then
\(k_1=0.0095\) (Additional file
1: §2.5), which corresponds to 5.3 % of heterogeneity being due to undernutrition and which generates a negligible impact of food on malaria morbidity, although it still reduces malaria mortality. One would have expected
\(k_1\) based on [
13] to be larger than the
\(k_1=0.153\) estimate based on [
19] because the former includes the impact of confounding factors; on the other hand, the 1.31 estimate may incorporate some reverse causality: malaria causes low WAZ and partial immunity (although seen more in older children), and so low WAZ may also be associated with less malaria. The relative risk of 1.31 is based on only two observational studies and has a 95 % CI of (0.92,1.88), which also is not quite at the level of statistical significance (p value = 0.143). Indeed, the relative risk of malaria due to undernutrition is difficult to estimate from observational studies [
40].
Taken together, due to the nature of its design, the trial in [
19] is believed to offer the best data for estimating the impact that undernutrition has on malaria prevalence. Although the p value of 0.177 does not allow for the traditional level of statistical significance, the biological plausibility of this hypothesis (e.g., undernutrition down-regulates immune functioning [
41], including the anti-
P. falciparum antibody response [
42])—coupled with the similar results achieved in [
39] and the important policy implications if it is true—leads us to believe that this problem is worthy of study despite the tenuous nature of the results. In summary, the results may not be valid and certainly are not robust, but they nonetheless deserve serious consideration. Given that no relevant data to shed more light on this issue are likely to be generated in the near future (in particular, there are ethical concerns with feeding trials that have treatment-free control arms), the most appropriate next step may be a randomized trial. More specifically, a design that may be ethically and politically acceptable is a cluster (at the village level) randomized control trial in a hypoendemic or mesoendemic setting, where the control arm offers a partial subsidy of ITNs to all children and the treatment arm provides free ITNs to children with WAZ
\(<-2\) and a partial subsidy to children with WAZ
\(>-2\).