Background
A myriad of differences between individuals in a community affect the epidemiology of malaria. These differences arise in roughly four ways: heterogeneity of transmission; biological heterogeneity of the host in susceptibility and response to malaria infection[
1‐
4]; heterogeneity in host behaviour, including quality of housing, use and knowledge of protective measures such as insecticide-treated nets (ITN) and treatment-seeking strategies; and heterogeneity in the risk of co-morbidity and malnutrition.
The different sources of heterogeneity are unlikely to be independent. A factor, such as socio-economic status (SES), may be associated with several different heterogeneities. SES can influence transmission intensity through quality of housing, knowledge of protection measures and use of ITNs [
5‐
8]. Risks of co-morbidity and malnutrition may be associated with SES [
9,
10]. SES may influence treatment-seeking behaviour [
7]. Amongst those caring for children, treatment-seeking [
7,
11‐
13] and knowledge of danger signs [
10,
11] were worse in poorer families. Such inequalities tend to persist over time [
14]. Thus, covariance between different types of heterogeneity is plausible although the degree to which it occurs is likely to vary between sites.
Differences among individuals can lead to important patterns at the community level [
15,
16]. Different types of heterogeneity may have implications for both the interpretation of field data and for formulating and calibrating models of the effects of interventions, or alternatively may have little impact and could be safely ignored. Co-variation may describe sub-groups within a population, who perhaps respond differently to an intervention (for example [
17]) or who are reached neither by the health system nor by any of several interventions.
Assessing the effects of different kinds of heterogeneity using field datasets is not practical due to difficulties in collecting the relevant data and isolating the effects of each of the heterogeneities. Therefore, heterogeneity has been investigated using mathematical models. There are few examples of heterogeneity modelling studies specific to malaria (for example [
15,
18‐
25]) and very few incorporating multiple types of heterogeneity [
23,
24]. One reason may have been the models themselves. To study the effects of multiple types of heterogeneity, a model must be sufficiently comprehensive, dynamic to allow secondary effects, and be able to easily incorporate different kinds of heterogeneity.
A recently published model of
Plasmodium falciparum malaria epidemiology [
26] satisfies these criteria. It includes processes for infection, parasitaemia, acquired immunity, infectivity, morbidity and mortality and case-management. It is dynamic, allowing feedback effects such as the effects of high treatment coverage on transmission intensity. It is also individual-based, which provides a flexible framework to conveniently incorporate heterogeneity [
27‐
29].
This model is adopted as a base to investigate the effects of three different types of heterogeneity: transmission (including host behaviours such as bed net use and housing), co-morbidity (as a trigger for severe malaria and indirect mortality and reflecting the individual's general health and nutrition) and treatment-seeking (the chances of obtaining effective treatment). These heterogeneities are simulated singly, and in independent and co-varying pairs. This paper focuses on the effects of heterogeneity on fundamental measures of the malaria burden, age-prevalence and incidence curves. These curves are known to vary by the severity of the outcome, degree of seasonality and the overall levels of transmission intensity (reviewed in [
30]).
Discussion
This study describes the simulated effects of heterogeneity in transmission intensity, co-morbidity risk and treatment-seeking behaviour on the age-curves of a range of measures of the burden of malaria. Although this study is specific to malaria, our findings add more generally to studies of infectious diseases indicating that it is not only the absolute level of a variable, but also the presence of heterogeneity [
15,
22,
25,
40] and co-variation [
23,
28], which can produce important patterns at the community level.
The results show that the different types of heterogeneity have effects on different outcomes with large effects reserved for outcomes directly affected by the action of the heterogeneity, rather than dynamic feedback via acquired immunity. Transmission heterogeneity affected the age-curves for all outcomes. The peak parasite prevalence was reduced and all age-incidence curves crossed those of the reference scenario with a lower incidence in younger children and higher in older age-groups. Heterogeneity in the probability of seeking treatment reduced the peak incidence of first-line treatment and hospital admissions. Heterogeneity in co-morbidity risk showed little overall effect, but high and low values cancelled out for outcomes influenced by its action. Independently varying pairs of heterogeneities produced additive effects. More variable results were produced for co-varying pairs, with striking differences compared to independent pairs for some outcomes which were affected by both heterogeneities individually.
These findings have implications for both the interpretation of age-curves and their use in analysis and modelling. In pointing to where the different types of heterogeneity change the shape of the age-curves, this study also indicates where there is no need for concern. Since the greatest effects of single heterogeneities were reserved for outcomes directly affected or subsequent to their action, only modest effects would be expected for outcomes less directly linked unless transmission intensity is affected. Outcomes which were unaffected by single heterogeneities do not change substantially when there are concurrent heterogenous variables, either independent or co-varying.
The results illustrate the effect of heterogeneity on the ability to infer from one outcome to another. The utility of passive case detection to estimate the burden of clinical disease depends on assumptions about the underlying distribution of treatment-seeking behaviour. Similarly, the use of clinical episodes to infer effects on mortality depends on heterogeneity in the risk of co-morbidity and treatment-seeking. Patterns of heterogeneity are also important when estimating transmission from prevalence or clinical data.
A logical consequence of the findings is that estimating parameter values by fitting a model to data from a single field site falsely assuming either homogeneity or independently varying variables is liable to produce incorrect values, as found elsewhere [
15,
23,
25].
This study has several limitations. The adopted representation of the patterns of heterogeneity was very crude. Whilst the strength of the impact will differ, the conclusions are not dependent on the values chosen for the high and low risk groups, on the distribution of individuals between groups or on whether there is a gradual increase in risk across individuals as long as the overall values are equal in the heterogeneity and comparison scenarios. Thus, although the scenarios do not exhibit realistic patterns, the findings nevertheless provide insights on the substantive effects of different types of heterogeneity. Likewise, there was no intention to realistically portray SES. There are complex pathways between poverty, economic activity, health-care seeking and malaria [
7,
13,
41]. The scope of this study is limited to the incorporation of simple heterogeneity in three variables which are plausibly related to SES into a model of malaria epidemiology. It was also assumed that the individual's relative levels for transmission, co-morbidity risk and treatment-seeking are constant throughout their life. This simplification ignores the impact of malaria on poverty [
13,
42] and mobility [
43]. More sophisticated simulations may address the need to disaggregate SES [
44] and identify interventions of particular benefit to the poor (such as [
45]).
Assumptions were made about the likely direction of co-variation, matching high transmission to a high risk of co-morbidity and low probability of seeking treatment. In different settings and ecotypes, these directions may be reversed. Individuals are assumed to be distributed spatially at random. Spatial patterns could be better incorporated by grouping individuals into households.
Objective criteria are lacking for determining whether two age-curves differ. However, the patterns observed were clear-cut. In this study, heterogeneity in transmission had the strongest effects on the age-curves. It is plausible that this would also be the case in many real settings. However, this study does not use use a realistic patterns and degrees of heterogeneity, and so conclusions cannot be drawn about the relative importance of the three heterogeneities on the shape of the age-curves.
The average annual level of transmission was fixed to remain constant so that the effects observed were solely due to heterogeneity when compared to the reference scenario. However, heterogeneity may also alter the absolute level of transmission intensity via dynamic feedback to the infectious reservoir.
The base model used is comprehensive and individual-based providing a flexible framework for unravelling the effects of different heterogeneities. Limitations of the model components are discussed elsewhere [
26,
31‐
33,
46‐
49]. Some assumptions are especially relevant to this study. Non-malaria co-morbidity is assumed to prompt an acute episode to lead to either a severe episode or an indirect death, and the risk of co-morbidity is assumed to be age-dependent. This is reflected in the age-curves for both the reference scenario and the inclusion of heterogeneity in co-morbidity risk. The base model assumes constant probabilities for seeking treatment within a five-day period for all individuals with either acute or severe episodes. However, treatment-seeking may be age-dependent, due to differences in the recognition of fevers or perceived need for treatment in adults, children and infants and also to the tendency for different symptoms to manifest at different ages such as severe malarial anaemia in young children [
50]. The five-day time step constrains the model components for both treatment-seeking and case-management to be very simple. The time steps are currently being shortened to one day and a more sophisticated case-management model is in development.
Effects of heterogeneity on outcomes other than age-curves were beyond the scope of this paper. Heterogeneity is likely to have important effects on receptivity and elimination [
15,
19‐
21], on individual differences and equality, and on the impact of different interventions [
22‐
24]. Some interventions may lessen the differences between individuals in a population, but the effects of reducing heterogeneity are not yet known. In addition to further simulation studies, future work should also extend the analysis of available field data to describe the pattern of heterogeneity in different settings. Innovative methods are needed to estimate sources of heterogeneity that are difficult to measure, such as for micro-transmission [
25,
51,
52], and multivariate analysis estimating the degree and patterns of co-variation would enable more realistic scenarios to be considered.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
AR conceived the study, designed the simulations and drafted the manuscript. TS edited the manuscript. Both authors have read and approved the final manuscript.