Explaining Observed Infection and Antibody Age-Profiles in Populations with Urogenital Schistosomiasis
[['Urogenital schistosomiasis , which is caused by the blood fluke Schistosoma haematobium , is a tropical disease of great public health importance , infecting more than 100 million people in sub-Saharan Africa [1] , [2] .', 'S . haematobium has a complex lifecycle , which includes free-living stages in the environment and asexual reproduction in intermediate freshwater snail hosts , as well as maturation and sexual reproduction within mammalian hosts [1] , [3] .', 'Humans acquire infection through contact with water bodies containing the infective stages ( cercariae ) .', 'Humans are exposed to the larval ( cercariae and schistosomulae ) , adult worm and egg stages of the schistosome life cycle .', 'The number of adult worms infecting a person cannot be measured directly , but is estimated from egg output in urine [4] , and the average life span of the adult worm is estimated to be around 3–10 years [5] , [6] .', 'Infection intensities in populations with endemic urogenital schistosomiasis consistently follow a ‘peaked’ ( or convex ) curve with age , with infection levels peaking between the ages of 6–20 years old , and lower infection intensities found in older adults [7] , [8] , [9] .', 'In areas with higher overall levels of infection , the peak in infection intensity tends to be higher and occurs at an earlier age than in areas with lower infection levels .', 'This pattern is described as a peak shift [10] .', 'Previous modelling work has demonstrated that the peak shift is consistent with the development of acquired protective immunity , as a function of cumulative exposure to schistosome antigens [11] .', 'Age-related changes in the nature of the immune response generated against schistosomes have also been reported .', 'Two studies in Zimbabwe have identified different groups of schistosome-specific antibody sub-classes ( isotypes ) which display contrasting age profiles .', 'One group of isotypes was shown to rise with host age while a second group declined in older individuals [12] , [13] .', 'Both studies reported negative correlations between antibodies from the two different groups .', 'The ‘switch’ between the different antibody responses occurred after the peak in infection intensity for both populations .', 'Some of the isotypes which increased with age in these populations have been associated with protection against re-infection in other studies , particularly IgE specific for adult worm antigen preparations [14] , but these protective responses tend to develop slowly with age , despite frequent exposure to infection from an early age [15] .', 'In this study , two hypotheses were explored for the slow development of protective immunity .', 'The first hypothesis was that dying worms are the main source of protective antigen .', 'It has been observed that treatment with the antihelminthic drug praziquantel , which kills adult worms , induces an antibody switch in young children similar to the switch seen occurring naturally in older children [16] .', 'It is hypothesised that the long life span of schistosome worms delays exposure to protective antigens , delaying the development of natural protective immunity [17] .', 'Second , it has been proposed that exposure to a certain threshold level of antigen is needed before protective responses can be stimulated [17] , [18] .', 'This is supported by the finding that , in a S . haematobium endemic area , older or more heavily infected groups produced detectable antibody against a wider range of schistosome antigens [18] .', 'Mathematical models of schistosome and other helminth infections have previously been used to identify mechanisms capable of explaining the peaked age-intensity curve and the peak shift [11] , [19] , [20] .', 'Such patterns can often be reproduced by several different models which imply different underlying mechanisms [21] , [22] .', 'Pattern-oriented modelling ( POM ) , an approach developed in ecological modelling , can be used to identify models which simultaneously replicate multiple different patterns observed in real systems at different levels or scales [23] .', 'This approach enables quantitative or qualitative patterns to be used , and the requirement for models to replicate multiple different patterns can greatly increase their discriminatory power .', 'POM has been used in ecological modelling to distinguish between possible model structures , for example to choose between different models for tree-thinning which made different assumptions about the distribution of initial plant size and growth rates , and were compared for their ability to give realistic levels of plant size inequality and canopy diameter , as well as reproducing the well-established relationship between plant density and plant size [24] .', 'POM has also been used in ecological modelling to reduce parameter uncertainty , for example in models of amphibian population dynamics , where there was greater confidence in the model structure , but certain key parameters ( juvenile and adult toad survival ) were unknown [25] .', 'A similar approach has also been used to infer pre-breeding survival rates for woodpeckers [26] .', 'This study used a pattern-oriented modelling approach to determine whether previously proposed epidemiological and immunological mechanisms were able to explain all of the key patterns in infection and antibody observed in field studies of S . haematobium .', 'Previous modelling work has generally focussed upon reproducing patterns of infection intensity rather than antibody responses , so it was of particular interest whether models could reproduce antibody patterns , particularly the antibody switch .', 'Robust patterns in infection and antibody data for S . haematobium endemic populations were identified and quantified to draw up model criteria .', 'Deterministic models were used which described changing levels of infection and two separate antibody responses with age in a homogeneously exposed population .', 'Whilst such models do not capture all of the complexity and variability in this system , they should be sufficient to capture the patterns of interest: similar models have been used previously to identify factors leading to the peaked age-intensity curve and the peak shift [10] , and are expected to be able to identify the mechanisms underlying the antibody switch .', 'The models were used to test whether one or more of the following factors were necessary to reproduce these patterns: dying worms as the principal antigen ( versus other life cycle stages ) , non-exponential worm survival distribution ( expected to affect the timing of exposure to dying worms ) , an antigen threshold , or cross-regulation between the two antibody responses .', 'Each stage of the schistosome life cycle was considered as a potential source for protective antigen , since different immune responses have been shown to be stimulated by each of the different stages , which have different life spans and distinct patterns of exposure with age .', 'In animal models , cercariae stimulate local and systemic inflammatory responses [27] , whilst eggs are potent inducers of Th2 responses [28] .', 'Despite their relatively long life span , live adult worms are associated with less potent immune stimulation , which may be associated with reduced surface antigen expression and adsorption of host molecules [29] , [30] .', 'Cross-regulation of antibody responses was also considered specifically to see whether this was necessary to generate the antibody ‘switch’ pattern , in line with the antagonism known to exist between different cytokine responses , which are involved in determining which antibody isotypes are made [31] , [32] .', 'It was found that each of these factors enhanced the ability of the models to reproduce the required patterns , but none of them were necessary for the models to be able to reproduce patterns of infection and antibody consistent with field data .', 'The combination of the stage of the schistosome life cycle which stimulated each antibody response , and the stage of the life cycle targeted by the antibodies , was found to be informative .'], ['Key patterns of infection and antibody seen in field data were characterized and quantified where possible , and used to draw up criteria which must all be met by a successful model .', 'The following patterns were included: a peaked age intensity curve with control of infection in adults , a peak shift , reasonable mean worm life span and an antibody switch , occurring after the age of peak infection intensity .', 'Previous models have qualitatively reproduced the peaked age-intensity curve [11] , [21] , but here we wished to do this within limits drawn from field data .', 'Age-intensity curves from a variety of endemic settings were used to determine limits for two criteria: the age range over which the peak in infection intensity occurs for S . haematobium , and the extent to which infection is reduced in adults relative to the peak level seen .', 'The peak shift , which has previously been demonstrated for infection curves for S . mansoni in Kenya [21] and S . haematobium in Zimbabwe [33] , and has also been reproduced by previous models [11] , [21] , was used as a qualitative criterion .', 'Considerable variability in field data makes it difficult to put formal quantitative bounds on the peak shift , and also means that such a shift may not always be seen between any two particular study sites ( although it is a strong pattern across multiple populations ) .', 'The model criterion requires a shift to consistently be seen between parameter sets which differ only in their transmission rate , since the deterministic models used here do not incorporate many of the sources of variability which are likely to obscure this relationship in the data .', 'Previous modelling work has shown that in models with immune responses which kill adult worms , short worm life spans are predicted in older infected individuals [20] .', 'In order to avoid accepting models which predict an unrealistically short worm life span , a criterion determining the minimum average worm life span of worms in the oldest adults in the population was set ( the oldest individuals were used as worm lifespan is most likely to have settled at an equilibrium level by this age ) .', 'Studies which estimate the worm life span for S . haematobium and S . mansoni in populations in which transmission has been stopped give life span estimates of 3–10 years [6] , [34] , [35] .', 'A conservative cut-off of 1 year was used in the criterion to allow for uncertainties in the true duration of worm life span ( bearing in mind that field estimates came from people of a variety of ages , in whom immune pressure may have been waning as a result of transmission having stopped ) .', 'The antibody switch has previously been characterised for schistosome-specific IgA and IgG1 responses in two neighbouring populations [16] .', 'Here , we further examined data from these and other populations for which age-related S . haematobium-specific antibody data was available to determine how widespread the antibody switch was across different antibody isotypes and different settings , and to identify a criterion to test for the switch .', 'Since initial model simulations indicated that cross-regulation could lead to an antibody switch being predicted in very young individuals , the age of the antibody switch relative to the age of peak infection intensity was also examined in these studies , and an additional criterion restricting the age of the antibody switch was drawn up .', 'Data on water contact for the Burma Valley area , which had been collected by direct observation of water contact sites , was taken from figure 1 in Chan et al . ( 2000 ) [39] using Datathief software .', 'A two-part linear function was fitted to this data by least squares , using the solver function in Microsoft Excel 2003 , with the initial part of the function constrained to pass through ( 0 , 0 ) .', 'Age-related development of schistosome infection and antibody responses were modelled using a set of differential equations , using a similar framework to earlier models of helminth immunity [11] , [20] , [40] and immune memory development [41] , [42] .', 'Two different structures for the immune response were explored: one with only plasma cells and the other including both plasma cell and memory B cell populations .', 'Different stages of the worm life cycle were allowed to provide the main antigenic stimulus for , and different stages of the life cycle were assumed to be the principle target of , each protective antibody response .', 'The model with plasma cells only is presented first , followed by the memory model and the models including antigen thresholds .', 'The equations are given below , and the model is represented schematically in figures 1–3 .', 'Parameters are defined , and parameter ranges given , in table 1 .'], ['Age infection profiles for six Zimbabwean communities with endemic S . haematobium infection are shown in figure 5 .', 'The key parameters of interest ( age and level of peak infection , and ratio between adult and peak infection levels ) for these populations are given in table 3 .', 'Note that data was only included for individuals up to the age of 34 , because data on water contact for the Burma Valley populations showed that this remained fairly stable for adults up to this age , although it declined at older ages ( figure 4; [39] ) .', 'Table 3 also includes information on the infection peak and its relationship to infection in adults for a number of studies of endemic schistosomiasis taken from the literature , which give mean infection intensities by age group , and cover a sufficiently wide age range to capture both the peak and adult levels .', 'The age group in which peak infection occurred ranged between 5–8 for Valhalla and 16–20 [9] or 13–23 for both Chipinda and Chitate .', 'Since 5–8 years was the youngest age group used in the Valhalla analysis , different age groupings were also used to show that infection peaks in the upper end of this age group ( data not shown ) , so that this age range truly reflects where the peak occurs .', 'The median values for these minimum/maximum age groups were used to give an overall estimated range for the age of the peak of 6–18 years old ( cf . 12–25 years old for S . mansoni [21] ) .', 'The criterion used for the models uses a range of 6–20 years old , to allow for the fact that wide age ranges were used when grouping adults in these studies ( owing to smaller sample sizes ) , reducing confidence in the actual maximum age of the peak .', 'Adult age groups for comparison with the peak were chosen to be as close to the range used in the analysis in figure 5 as possible .', 'Results from studies giving means of log-transformed egg counts were back-transformed to give geometric means .', 'It is difficult to compare these studies or use all of the estimates for the ratio between adult and peak levels of infection since the different studies use a range of types of means ( arithmetic or geometric mean , including the whole population or only those with infection ) , which give very different answers .', 'From the studies which use arithmetic means for S . haematobium infections , the ratio of final∶peak infection level is 0 . 5–26% .', 'Using different age groupings for the populations shown in figure 5 changed the ratio of final∶peak infection level substantially for some of the populations ( Valhalla - ratio up to 34% , Chipinda - ratio up to 30% ) , so the range used in the model criterion was 0–40% to allow for this instability at the top end of the range .', 'Testing for significant negative correlations between different antibody isotypes across the full population age range ( using an age range of 0–34 as in the previous analyses ) was able to discriminate well the dichotomous antibody relationship indicative of an antibody switch .', 'In the Burma Valley populations , these negative correlations all occurred between isotypes which changed significantly with age in opposite directions - i . e . one of the pair increased with age and the other decreased ( as assessed by Kruskal Wallis test , using age as a categorical variable in the five age groups used for the infection profiles ) .', 'In Kaswa , significant negative correlations were found between the IgG4 and IgA anti-SEA responses , IgG1 and IgA anti-WWH responses and the IgM and IgG1 anti-WWH responses as well as the SEA IgA and IgG1 antibodies ( figure 6A ) .', 'In Valhalla , all of these correlations were also seen , and additionally a negative correlation between IgA and IgM SEA antibodies ( figure 6B ) .', 'For the negative correlations which were significant at the 1% level , the correlation coefficient varied between −0 . 662 and −0 . 247 .', 'In Mutoko-Rusike , there were no significant negative correlations between different isotypes directed at the same antigen preparation ( for cercarial , egg or adult worm antigen preparations ) .', 'Most antibodies were significantly positively correlated with each other ( data not shown ) .', 'This may have been because relatively few adults were included in this dataset .', 'In a further published study [13] , for which the raw data were not available , negative correlations were also reported between antibody responses which have opposite trends with age: SEA IgE and SEA IgG4 , SEA IgE and SEA IgM , and WWH IgA and WWH IgM [13] , strongly suggesting similar antibody switch patterns .', 'Because testing for a correlation was not suitable for detecting an antibody switch in the deterministic models used here , an alternative metric was used to construct the antibody switch criterion: that the two antibody responses never simultaneously exceed n% of their respective maximum levels .', 'A suitable level for n was determined by selecting 10 parameter sets which passed the criterion only at each of the following cut-offs: 40% , 30% , 20% , 10% , 5% , and running a stochastic individual-based model based upon the same model framework to check the correlation across different ages .', 'While those which passed at 5% or 10% always gave a highly significant negative correlation in the stochastic version of the model , those which passed at 20% or 30% occasionally did so as well , and so a conservative threshold of 30% was chosen .', 'For all of the antibody switches detected in the datasets , the antibody switch occurred after the age of infection intensity and so this was used as an additional criterion .', 'The final set of model criteria is given in table 2 .', 'The combination of both the parasite life cycle stage providing the main antigenic stimulus for each antibody response , and the stage being targeted by the antibody responses ( ‘antigen:target combination’ ) , was critical in determining whether or not the models were able to reproduce all of the patterns identified from field data .', 'For this reason , results are presented and analysed by antigen:target combination within each model structure .', 'For each model structure ( described in the subsections below ) , the main outputs of interest were the number and consistent features of antigen:target combinations for which all of the model criteria could ever be met , and the proportion of total parameter space explored for which all of the criteria were met .', 'Note that the number of antigen:target combinations meeting the criteria for each model structure should not be taken as an indication of how ‘good’ each model is .', 'The proportion of parameter space explored for which all criteria were met gives some indication of how well each model agrees the data ( although this should be interpreted with caution – see Discussion section ) .', 'Proportions rather than absolute numbers were used because different numbers of parameter sets were explored for each model .'], ['It was shown that testing models for their ability to simultaneously reproduce multiple patterns seen in both infection and antibody data enabled a large number of potential model structures and parameter combinations to be rejected .', 'These results give insight into the likely mechanisms giving rise to these patterns .', 'It was found that both the stage of the life cycle which provided the main antigenic stimulus for each antibody response , and the stage of the life cycle which was targeted by a protective antibody response were critical in determining whether the models could reproduce infection and antibody profiles consistent with field data .', 'Some of the models which had dying worms as the main source of protective antigen were able to reproduce all of the required patterns .', 'However , some models which had other stages of the life cycle acting as the principal antigen source could also meet all of the criteria , suggesting that it is not necessary for dying worms to provide the main source of protective antigen to explain the patterns explored here .', 'Inclusion of cross-regulation , an antigen threshold or using approximately Gaussian-distributed worm survival each increased the number of antibody antigen-target combinations , and the range of parameter space for which it was possible to reproduce patterns seen in the field , but none of these were essential for enabling all of the field patterns to be replicated .', 'Other authors fitting models to data ranges using intensive Latin hypercube sampling of the parameter space suggest that the number of successful parameter sets gives an indication of how good a fit the model is [47] .', 'Since we sampled the parameter space in a less intensive way here , this relationship may not be as robust , but nonetheless suggests that threshold models , models with down-regulation of the longer-lived antibody response , and models with dying worm antigens ( in tandem with non-exponential worm survival ) are in better agreement with the data than other models .', 'From this analysis it is possible to exclude some combinations of life cycle stage providing the main antigenic stimulus for , and life cycle stage targeted by , each antibody response , and these combinations are listed in table 4 .', 'While previous modelling had demonstrated that different combinations of the stage acting as stimulus and target could give rise to qualitatively different population infection profiles [11] , the main differences identified there related to relative levels of infection in older age groups across different areas of varying transmission , which there is still insufficient data to test .', 'It was interesting to see that , here , many combinations with immune-induced worm death were excluded , mainly on the basis of a very short resulting worm lifespan , and that many of the models with dying worms as the main source of protective antigen were retained , adding support for this hypothesis .', 'The approach used here was a type of pattern-oriented modelling , testing a range of different model structures and parameter values for their ability to simultaneously reproduce multiple patterns seen in population data [23] .', 'Previous modelling studies have shown that individual patterns in macroparasite infection data can frequently be reproduced by more than one mechanism or combinations of mechanisms , particularly the peaked age-intensity curve and the peak shift [11] , [21] , [22] .', 'In this study , ‘successful’ models had to simultaneously pass six different criteria for infection and antibody profiles , including the peaked age-intensity curve ( within limits identified from field data ) , the peak shift , an antibody ‘switch’ and realistic mean worm survival , making it much more likely that these models incorporate the ‘true’ mechanisms determining field patterns .', 'It was shown that all of the criteria used were informative , as they were all able to exclude some parameter combinations single-handedly .', 'Thorough sensitivity analysis , using a balanced design where all possible combinations of levels of different parameters were investigated , increases confidence that all of the model structures which can possibly reproduce these patterns have been identified here .', 'Although the immune responses are represented in a simplistic fashion in these models , they should capture the important features of the antibody response , being based upon well characterised B cell maturation pathways [48] , and covering the main alternative theories for the persistence of antibody:', '( i ) antigen-independent mechanisms either through persistence of long-lived plasma cells or continual non-specific activation of memory cells to form short-lived plasma cells ( both represented by the plasma cell-only models ) , and', '( ii ) antigen-dependent mechanisms , with specific antigenic activation of memory cells to form short-lived plasma cells ( memory models ) [49] , [50] .', 'This approach was intended to identify the essential mechanisms underlying universal patterns of schistosome infection and antibody , by selecting models that give outputs consistent with a wide range of studies of endemic S . haematobium , rather than trying to accurately replicate patterns seen in individual studies .', 'To this end , patterns were chosen that were seen across multiple different studies .', 'However , some of these patterns are more robust than others; the age of the infection peak and the peak shift have been well characterised across numerous different studies , but fewer studies have reported specific antibody responses by age .', 'The antibody switch has been clearly identified in three Zimbabwean populations [12] , [13] , [16] , but was not seen in data from a fourth study [36] .', 'This pattern has not been specifically looked for in other published studies , meaning that it may not be universal .', 'This would prevent the generalisability of the findings to populations where an antibody switch is not seen .', 'However , the antibody switch was seen across a number of different isotypes in all three of these populations , making it a robust and striking pattern within these populations which deserves exploration .', 'The use of semi-quantitative criteria drawn from different studies also precluded the use of more statistical or likelihood-based model fitting techniques , which may be used when trying to replicate a particular data series [51] , but are not suitable in this instance , where we draw on evidence from numerous distinct data sets .', 'It was of interest to note that many of the models required a large difference in decay rates between the two immune responses .', 'The maximum estimated half-life of 9–90 years for the late response ( A2 or M2 ) is in line with estimates for the half-life of long-lived plasma cells ( 23 years; [52] ) and the half-life of vaccinia-specific antibody responses in the absence of re-exposure ( 92 years; [53] ) .', 'The minimum estimated half-life of 5–46 days for the early antibody response ( A1 or M1 ) fits with estimates for short-lived plasma cell half-life ( 3–10 days , [50] ) .', 'A potential limitation of these models is that they describe population averages without taking into account distributions of infection or antibody .', 'The assumption that all individuals within a certain population are exposed at the same rate is unlikely to be true , as most studies of water contact ( a good proxy for infection rate ) show highly over-dispersed contact patterns between individuals over set periods of time [54] , [55] .', 'While the assumption of homogeneous contact rates is not likely to affect the conclusions drawn about the factors underlying the antibody switch and other qualitative population level patterns , it may affect the precise quantitative conclusions drawn , and also prevents patterns in the distribution of infection or antibody from being used as additional criteria .', 'A good way to look at the effects of heterogeneous contact rates for these types of models is through the use of fully stochastic individual based models ( IBMs ) [39] , [56] , which would also allow patterns of aggregation of infection ( and antibody ) to be simulated and compared to field data , providing additional criteria against which to test the models .', 'However , it was not feasible in this study to cover the same breadth of model structures and parameter ranges with IBMs , which take longer to run and need to be repeated many times to account for stochastic variation in individual simulations .', 'A further pattern which could also be used to differentiate between different model structures is the observation that praziquantel treatment leads to a sustained antibody ‘switch’ in younger children similar to that seen occurring naturally with age [12] .', 'The models used here assumed that each antibody response was stimulated by a single stage of the schistosome life cycle and targeted a single stage .', 'In reality , overlapping antigen expression between different stages [57] means that antibody responses to a specific antigen could be stimulated by more than one stage of the life cycle and could have damaging effects upon multiple life stages .', 'The models described here could easily be extended to test this , although the number of potential combinations to be tested would vastly increase .', 'A more feasible first step might be to model responses to particular antigens for which the antigen-specific antibody responses have been measured and the stage-specific expression is known , such as Sm22 . 6 [58] .', 'These results suggest that gradual accumulation of exposure to protective antigens is sufficient to explain the slow development of protective immunity , without it being necessary to invoke a major role for dying worms or an antigen threshold , but do suggest that high levels of exposure to the relevant antigen throughout life are most likely to induce such a protective response .', 'These models have suggested that protective immunity could primarily target worm fecundity , which was not routinely considered in earlier immuno-epidemiological models .', 'They have also shown that the assumed worm survival curve can make a considerable difference to the outcome , challenging the usual assumption of exponential worm survival , which is mathematically convenient but has not been empirically demonstrated .', 'This analysis has highlighted the importance of the combination of the stage of the life-cycle stimulating and targeted by protective antibody responses in determining age infection and antibody profiles , and has excluded a large number of potential combinations as being incompatible with field data .', 'We have shown that pattern-oriented modelling can be a useful approach to use to distinguish between different hypotheses and conceptual models for immune development in human schistosome infection .']]
['Introduction', 'Methods', 'Results', 'Discussion']
['Urogenital schistosomiasis is a tropical disease infecting more than 100 million people in sub-Saharan Africa .', 'Individuals in endemic areas endure repeated infections with long-lived schistosome worms , and also encounter larval and egg stages of the life cycle .', 'Protective immunity against infection develops slowly with age .', 'Distinctive age-related patterns of infection and specific antibody responses are seen in endemic areas , including an infection ‘peak shift’ and a switch in the antibody types produced .', 'Deterministic models describing changing levels of infection and antibody with age in homogeneously exposed populations were developed to identify the key mechanisms underlying the antibody switch , and to test two theories for the slow development of protective immunity: that', '( i ) exposure to dying ( long-lived ) worms , or', '( ii ) experience of a threshold level of antigen , is necessary to stimulate protective antibody .', 'Different model structures were explored , including alternative stages of the life cycle as the main antigenic source and the principal target of protective antibody , different worm survival distributions , antigen thresholds and immune cross-regulation .', 'Models were identified which could reproduce patterns of infection and antibody consistent with field data .', 'Models with dying worms as the main source of protective antigen could reproduce all of these patterns , but so could some models with other continually-encountered life stages acting as the principal antigen source .', 'An antigen threshold enhanced the ability of the model to replicate these patterns , but was not essential for it to do so .', 'Models including either non-exponential worm survival or cross-regulation were more likely to be able to reproduce field patterns , but neither of these was absolutely required .', 'The combination of life cycle stage stimulating , and targeted by , antibody was found to be critical in determining whether models could successfully reproduce patterns in the data , and a number of combinations were excluded as being inconsistent with field data .']
['Urogenital schistosomiasis is a tropical infectious disease caused by schistosome blood flukes , infecting more than 100 million people in sub-Saharan Africa .', 'Protective immunity develops against schistosomes , but takes many years to do so , with children acquiring multiple infections with long-lived parasites .', 'It is important to understand how this protection develops , both to aid vaccine development , and to understand the long-term implications of other control strategies which may reduce or alter natural exposure to the parasite .', "We used mathematical models to investigate possible explanations for this slow development of protection , including the possibility that when worms die ( after surviving in the host for 3–10 years ) they release large quantities of the molecules needed to stimulate a protective immune response , or the idea that an individual's infection burden needs to exceed a threshold number of parasites before they mount a protective immune response .", 'We found that these mechanisms were consistent with patterns of levels of infection and antibody measured in populations with schistosome infection , but that neither was essential to explain these patterns .', 'We found that the combination of the stage of the parasite life cycle which stimulated protective immunity , and the life cycle stage targeted by this immunity , was critical .']
['humoral immunity', 'medicine', 'public health and epidemiology', 'infectious disease epidemiology', 'immunity to infections', 'immunology', 'parasitic diseases', 'mathematics', 'infectious diseases', 'epidemiology', 'biology', 'infectious disease modeling', 'differential equations', 'schistosomiasis', 'immunity', 'calculus']