## Abstract

Background. Acquired immune responses to malaria have widely been perceived to be short-lived, with previously immune individuals losing immunity when they move from malaria-endemic areas. However long-lived Plasmodium falciparum–specific antibody responses lasting for an individual's lifetime are frequently observed.

Methods. We fit mathematical models of the dynamics of antibody titers to P. falciparum antigens from longitudinal cohort studies of African children to estimate the half-lives of circulating immunoglobulin G (IgG) antibodies and IgG antibody-secreting cells (ASCs).

Results. Comparison of antibody responses in the younger Ghanaian cohort and the older Gambian cohort suggests that young children are less able to generate the long-lived ASCs necessary to maintain the circulating antibodies that may provide protection against reinfection. Antibody responses in African children can be described by a model 15 including both short-lived ASCs (half-life range, 2–10 days), which are responsible for boosting antibody titers following infection, and long-lived ASCs (half-life range, 3–9 years), which are responsible for maintaining sustained humoral responses.

Conclusions. The rapid decay of antibodies following exposure to malaria and the maintenance of sustained antibody responses can be explained in terms of populations of short-lived and long-lived ASCs.

In malaria-endemic areas, young children bear the major burden of disease, whereas older children and adults acquire substantial protection from severe malaria and death following exposure, but rarely, if ever, acquire sterile immunity [1]. It is widely perceived that acquired immune responses to malaria are short-lived [1, 2] and that previously immune individuals experience a loss of immunity when they move away from malaria-endemic areas. However, the true picture is more complex [3, 4]. Infants and young children are particularly vulnerable to malaria after physiological adaptations and maternally acquired antibodies have waned and before the development of effective adaptive immunity [5]. In contrast to other childhood infections, such as measles, rubella, and varicella, acquisition of immunity to malaria requires multiple infections. Although substantial protection from severe malaria and death is acquired after a small number of infections [6], episodes of febrile disease may continue for many years. While frequent reinfection is required to maintain high concentrations of antimalarial antibodies and because antibody responses can appear transient, especially in young children [2, 79], there is evidence that other components of the immune response to malaria are long-lived [3]. Circulating memory B cells specific for Plasmodium falciparum antigens can be detected at least 8 years after the most recent infection [10, 11] and may persist for the lifetime of the individual [12]. Furthermore, estimates of the half-life of antibody seropositivity indicate that individuals may remain seropositive for life for antibodies to conserved or relatively conserved antigens, even in areas with ongoing low levels of malaria transmission [13].

The cellular and molecular determinants of the duration of antimalarial antibody responses have been investigated in mouse models [14, 15] but remain poorly studied in humans. Memory B cells specific to Plasmodium antigens are detectable among human peripheral blood mononuclear cells, and studies have reported their expansion and contraction [16] and their longevity [10, 11, 17]. However, there are no comparable studies of the longevity of antibody-secreting cells (ASCs) in humans exposed to malaria. Such studies would be difficult to undertake, as ASCs are located primarily in bone marrow and lymphoid organs and are detectable in blood only in the short window between differentiation and migration to the bone marrow [15]. However, mouse models reveal a strong correlation between numbers of ASCs in tissues and serum antibody concentrations, suggesting that antibody titers are a good surrogate for ASC numbers [14].

To obtain quantitative estimates of the immune parameters determining the antibody response to malaria, we analyzed data from 2 longitudinal cohort studies of antibody responses to P. falciparum infection in African children. In the first study, 151 Ghanaian children were followed from birth for >2 years to investigate the association between maternal antibody and protection from malaria [18]. Serum samples were analyzed by enzyme-linked immunosorbent assays (ELISAs) for the presence of antibodies to the antigens apical membrane antigen 1 (AMA-1), merozoite surface protein 1 (MSP-1), merozoite surface protein 2 (MSP-2), and circumsporozoite protein (CSP). Because infants in malaria-endemic areas are born with maternally acquired immunoglobulin G (IgG) antibodies but no ASCs of their own, antibody titers decay in the first months of life. Throughout follow-up, children acquire ASCs and boost their IgG titers upon exposure to P. falciparum antigens, after which antibody titers decay again. In the second study, 124 Gambian children were followed for 3 months during the dry season (when there was little or no ongoing malaria transmission) to investigate antibody dynamics following exposure to P. falciparum during the previous wet season [8, 9]. Serum samples were analyzed by ELISA for antibodies to the antigens AMA-1, MSP-1, MSP-2, and erythrocyte-binding antigen 175 (EBA-175). The Gambian children ranged in age from 1 to 6 years, too old for maternal antibodies to be present in appreciable quantities [5]. Figure 1 shows the population-level pattern of boosting and decay of antibodies in both cohorts of children, as well as sample antibody trajectories from individual children.

Figure 1.

Population-level antibody dynamics. Population-level dynamics of antibody titers to apical membrane antigen 1 (AMA-1; blue), merozoite surface protein 1 (MSP-1; pink), merozoite surface protein 2 (MSP-2; yellow), circumsporozoite protein (CSP; green), and erythrocyte-binding antigen 175 (EBA-175; purple) in cohorts of 151 Ghanaian children and 124 Gambian children. The solid colored lines show polynomial fits of the median antibody titer in each cohort. The shaded regions capture 50% and 95% of the variation in the observed data. Antibody trajectories from 2 randomly selected children from each cohort are shown in dashed lines. Ghanaian children were followed from birth for approximately 800 days. Maternal blood samples were collected by venipuncture, and children's samples were collected by heel prick at birth; 2, 4, and 6 weeks after birth; and then every 4 weeks. Blood samples were tested for parasites by microscopy and for parasite DNA by polymerase chain reaction. The Gambian children were followed for approximately 3 months after the end of the rainy season. Blood samples were collected every 2 weeks and tested for malaria parasites by microscopy. In the Ghanaian children, there is some evidence for a biphasic decay, with antibody titers dropping rapidly immediately after boosting and then decaying at a slower rate over a period of months to years. For the Gambian children, a slow decay in antibody titers is observed, punctuated by occasional boosts followed by rapid decay.

Figure 1.

Population-level antibody dynamics. Population-level dynamics of antibody titers to apical membrane antigen 1 (AMA-1; blue), merozoite surface protein 1 (MSP-1; pink), merozoite surface protein 2 (MSP-2; yellow), circumsporozoite protein (CSP; green), and erythrocyte-binding antigen 175 (EBA-175; purple) in cohorts of 151 Ghanaian children and 124 Gambian children. The solid colored lines show polynomial fits of the median antibody titer in each cohort. The shaded regions capture 50% and 95% of the variation in the observed data. Antibody trajectories from 2 randomly selected children from each cohort are shown in dashed lines. Ghanaian children were followed from birth for approximately 800 days. Maternal blood samples were collected by venipuncture, and children's samples were collected by heel prick at birth; 2, 4, and 6 weeks after birth; and then every 4 weeks. Blood samples were tested for parasites by microscopy and for parasite DNA by polymerase chain reaction. The Gambian children were followed for approximately 3 months after the end of the rainy season. Blood samples were collected every 2 weeks and tested for malaria parasites by microscopy. In the Ghanaian children, there is some evidence for a biphasic decay, with antibody titers dropping rapidly immediately after boosting and then decaying at a slower rate over a period of months to years. For the Gambian children, a slow decay in antibody titers is observed, punctuated by occasional boosts followed by rapid decay.

Longitudinal measurements of parasitemia were available for most children. However, there was poor agreement between detection of parasites and boosting of antibody titers, with P. falciparum parasites frequently detected without a boost in titers, titers boosted without detectable infection, and titers to one antigen boosted without an accompanying boost to titers of other antigens. This could be due to poor sensitivity or specificity of the parasite detection methods, polymorphism of parasite antigens, persistent antigen presentation by follicular dendritic cells [19], bystander activation [20], or clonal imprinting (ie, original antigenic sin [7]). We therefore analyzed the dynamics of antibodies to each antigen separately. When antibody titers were boosted above some threshold between consecutive samples (Supplementary Figure 1), we assumed antigen exposure to have occurred (which may or may not coincide with detection of parasites).

## MATERIALS AND METHODS

### Model 1

IgG antibody is generated in boosts following exposure to P. falciparum antigens and decays with a half-life of $da$ days. When IgG antibody is generated at rate α, the antibody dynamics can be described by

(1)
$dAdt=α−rA,$
where $r=log⁡(2)/da$ is the rate of decay of antibody. If maternal antibody $Am$ decaying at rate $m=log⁡(2)/dm$ is acquired at birth and antibody is generated in boosts of size $αi$ following antigen exposure at time $τi$, then equation (1) can be solved to give
(2)
$A(t)=Ame−mt+∑iH(t,τi)αie−r(t−τi),$
where H is a step function defined as
(3)
$H(t,τi)={0t<τi1t≥τi$
At the start of follow-up, the Gambian children do not have maternal antibody but instead have some initial titer of naturally acquired antibody (A0).

### Model 2

Model 2 assumes rapid proliferation of ASCs following exposure to P. falciparum antigens. These plasma cells persist with a half-life of $da$ days, secreting IgG antibody throughout their life. When ASCs are generated at a rate β, the antibody kinetics can be described by

(4)
$dBdt=β−cBdAdt=gB−rA,$
where $c=log⁡(2)/db$ is the rate of decay of cells, and g is the rate at which antibody is secreted by plasma cells. If maternal antibody is acquired at birth and plasma cells are generated in boosts of size $βi$ at times $τi$, then equation (4) can be solved to give
(5)
$A(t)=Ame−mt+∑iH(t,τi)βir−c(e−c(t−τi)−e−r(t−τi)).$
The constant g has been absorbed into the boost size ($βi$) by normalization. At the start of follow-up, the Gambian children do not have maternal antibody but instead have some initial titer of naturally acquired antibody ($A0$) and some amount of ASCs ($B0$).

### Model 3

Model 2 is extended so that following antigen exposure, short-lived ASCs with a half-life of $ds$days (of the order of days/weeks) and long-lived ASCs with a half-life $dl$ (of the order of months/years) are generated. Short-lived ASCs are responsible for the rapid rise in antibody titers following initial antigen exposure. Long-lived ASCs form a vital part of immunological memory and are responsible for maintaining antibody titers after the infection has been cleared. If plasma cells are generated at rate β, a proportion (ρ) of which are short-lived and $1−ρ$ are long-lived, then the antibody dynamics can be described by

(6)
$dBsdt=ρβ−csBsdBldt=(1−ρ)β−clBldAdt=gBs+gBl−rA,$
where $cs=log⁡(2)/ds$ is the rate of decay of short-lived plasma cells, and $cl=log⁡(2)/dl$ is the rate of decay of long-lived plasma cells. If maternal antibody is acquired at birth and plasma cells are generated in boosts of size $βi$ at times $τi$, then equation (6) can be solved to give
(7)
$A(t)=Ame−mt+∑iH(t,τi)βi(ρr−cs(e−cs(t−τi)−e−r(t−τi))+1−ρr−cl(e−cl(t−τi)−e−r(t−τi))).$
Setting $ρ=1$, model 3 simplifies to model 2. At the start of follow-up, the Gambian children do not have maternal antibody but instead have some initial titer of naturally acquired antibody ($A0$), and some amount of short-lived ASCs ($Bs0$) and long-lived ASCs ($Bl0$).

### Model Fitting

The models were fitted to individual-level longitudinal data on antibody titers from the Ghanaian and Gambian cohorts. A mixed-effects framework was utilized, in which the mean and standard deviation of each parameter are estimated. For example, for model 1 we estimate the mean antibody half-life of all children in the cohort (da) and the standard deviation of the antibody half-life within the cohort (Σa). Parameters were estimated using Bayesian Markov Chain Monte Carlo methods (Supplementary Materials). Posterior median parameter estimates are presented in Table 1. We do not present formal statistical model comparisons because of the challenges of comparing mixed-effects models (Supplementary Materials).

Table 1.

Estimated Parameters for Antibody Dynamics in Each Cohort

Cohort, Parameter Variable AMA-1 MSP-1 MSP-2 CSP EBA-175
Ghanaian cohort (ages 0–2 y)
Model 1
Maternal antibody half-life dm 45 (37–56) 30 (25–38) 21 (18–24) 13 (7–24) …
IgG antibody half-life da 25 (18–37) 40 (31–56) 33 (27–43) 9 (7–13) …
Model 2
Maternal antibody half-life dm 44 (37–56) 32 (26–43) 22 (19–26) 16 (10–30) …
IgG antibody half-life da 30 (25–37) 29 (24–36) 28 (22–34) 17 (13–23) …
ASC half-life db 2 (1–8) 5 (3–8) 5 (4–9) 3 (2–5) …
Model 3
Maternal antibody half-life dm 46 (38–57) 33 (27–45) 27 (22–36) 24 (13–52) …
IgG antibody half-life da 17 (13–21) 19 (16–23) 21 (16–26) 14 (11–20) …
Short-lived ASC half-life ds 2.5 (2.1–3.1) 2.4 (1.9–3.1) 2.3 (1.9–2.8) 3.0 (2.4–4.0) …
Long-lived ASC half-life d1 2956 (1829–4513) 1901 (1115–3228) 3444 (2107–4702) 2881 (1530–4639) …
Proportion short-lived ρ 0.95 (0.89–0.98) 0.84 (0.74–0.92) 0.95 (0.89–0.98) 0.81 (0.64–0.97) …
Gambian cohort (ages 1–6 y)
Model 1
IgG antibody half-life da 60 (39–100) 72 (49–113) 60 (32–112) … 103 (65–176)
Model 2
IgG antibody half-life da 12 (9–16) 11 (8–16) 11 (8–14) … 12 (9–16)
ASC half-life db 214 (123–442) 108 (66–224) 95 (48–232) … 270 (147–567)
Model 3
IgG antibody half-life da 7 (6–9) 7 (6–9) 4 (3–5) … 11 (6–18)
Short-lived ASC half-life ds 4 (3–8) 10 (5–17) 4 (3–5) … 10 (5–18)
Long-lived ASC half-life d1 1050 (612–1742) 859 (473–1565) 1020 (547–1939) … 1607 (1030–2549)
Proportion short-lived ρ 0.83 (0.74–0.89) 0.70 (0.61–0.82) 0.75 (0.67–0.82) … 0.68 (0.59–0.77)
Cohort, Parameter Variable AMA-1 MSP-1 MSP-2 CSP EBA-175
Ghanaian cohort (ages 0–2 y)
Model 1
Maternal antibody half-life dm 45 (37–56) 30 (25–38) 21 (18–24) 13 (7–24) …
IgG antibody half-life da 25 (18–37) 40 (31–56) 33 (27–43) 9 (7–13) …
Model 2
Maternal antibody half-life dm 44 (37–56) 32 (26–43) 22 (19–26) 16 (10–30) …
IgG antibody half-life da 30 (25–37) 29 (24–36) 28 (22–34) 17 (13–23) …
ASC half-life db 2 (1–8) 5 (3–8) 5 (4–9) 3 (2–5) …
Model 3
Maternal antibody half-life dm 46 (38–57) 33 (27–45) 27 (22–36) 24 (13–52) …
IgG antibody half-life da 17 (13–21) 19 (16–23) 21 (16–26) 14 (11–20) …
Short-lived ASC half-life ds 2.5 (2.1–3.1) 2.4 (1.9–3.1) 2.3 (1.9–2.8) 3.0 (2.4–4.0) …
Long-lived ASC half-life d1 2956 (1829–4513) 1901 (1115–3228) 3444 (2107–4702) 2881 (1530–4639) …
Proportion short-lived ρ 0.95 (0.89–0.98) 0.84 (0.74–0.92) 0.95 (0.89–0.98) 0.81 (0.64–0.97) …
Gambian cohort (ages 1–6 y)
Model 1
IgG antibody half-life da 60 (39–100) 72 (49–113) 60 (32–112) … 103 (65–176)
Model 2
IgG antibody half-life da 12 (9–16) 11 (8–16) 11 (8–14) … 12 (9–16)
ASC half-life db 214 (123–442) 108 (66–224) 95 (48–232) … 270 (147–567)
Model 3
IgG antibody half-life da 7 (6–9) 7 (6–9) 4 (3–5) … 11 (6–18)
Short-lived ASC half-life ds 4 (3–8) 10 (5–17) 4 (3–5) … 10 (5–18)
Long-lived ASC half-life d1 1050 (612–1742) 859 (473–1565) 1020 (547–1939) … 1607 (1030–2549)
Proportion short-lived ρ 0.83 (0.74–0.89) 0.70 (0.61–0.82) 0.75 (0.67–0.82) … 0.68 (0.59–0.77)

Posterior median parameter estimates and 95% credible intervals for all 3 models, fitted to both the Ghanaian and Gambian datasets. All units, apart from proportions, are in days. In model 3, the estimates of the half-lives of long-lived ASCs (dl) and the proportion of the response (1 − ρ) that is long-lived are correlated­—a sustained antibody response may be due to a small number of long-lived cells or a larger number of cells with shorter half-life. The estimated half-lives for the long-lived ASCs are greater than the duration of longitudinal follow-up in both cohorts and, thus, are partially informed by prior information on the duration of antibody response. Estimates of the variation between individuals of each parameter are presented in Supplementary Table 2.

Abbreviations: AMA-1, apical membrane antigen 1; ASC, antibody-secreting cell; CSP, circumsporozoite protein; EBA-175, erythrocyte-binding antigen 175; IgG, immunoglobulin G; MSP-1, merozoite surface protein 1; MSP-2, merozoite surface protein 2.

## RESULTS

Three nested models of the immunological processes that might underlie antibody dynamics (Figure 2) were fitted to the Ghanaian and Gambian data. The simplest, model 1, assumes that antibodies are generated in a single, short pulse following P. falciparum infection and thereafter decay exponentially. Model 2 assumes that ASCs are generated in response to infection and decay exponentially. Throughout their life, the population of ASCs generates antibodies, which also decay exponentially. Finally, model 3 is similar to model 2 but assumes that infection induces 2 populations of ASCs, one short-lived and the other long-lived [21]; these 2 ASC populations are both assumed to generate antibodies but to decay at different rates. The parameters providing the best fit to both data sets are shown in Table 1. Sample model fits for 4 children are presented in Figure 3.

Figure 2.

Schematic representation of the fitted models. The top row represents how each model captures the underlying immunological processes, the middle row depicts the change in antibody titers over time (red, maternally acquired antibodies; blue, antibodies generated by short-lived antibody-secreting cells (ASCs); green, antibodies generated by long-lived ASCs), and the bottom row shows the mathematical description. In model 1, antibodies (A) are generated in sharp boosts following infection (at rate α) and then decay exponentially (at rate r). In model 2, ASCs (B) are generated (at rate β) in response to antigen exposure and decay at rate c. Antibodies (A) are produced by ASCs at rate g and decay at rate r. In model 3, ASCs are generated (at rate β) following antigen exposure, with a proportion (ρ) being short-lived ASCs (Bs) and decaying at rate cs and a proportion (1 − ρ) being long-lived ASCs (Bl) and decaying at rate cl. Antibodies (A) are produced by all ASCs at rate g and decay at rate r. In all 3 models, immunoglobulin G (IgG) antibody can additionally be acquired maternally.

Figure 2.

Schematic representation of the fitted models. The top row represents how each model captures the underlying immunological processes, the middle row depicts the change in antibody titers over time (red, maternally acquired antibodies; blue, antibodies generated by short-lived antibody-secreting cells (ASCs); green, antibodies generated by long-lived ASCs), and the bottom row shows the mathematical description. In model 1, antibodies (A) are generated in sharp boosts following infection (at rate α) and then decay exponentially (at rate r). In model 2, ASCs (B) are generated (at rate β) in response to antigen exposure and decay at rate c. Antibodies (A) are produced by ASCs at rate g and decay at rate r. In model 3, ASCs are generated (at rate β) following antigen exposure, with a proportion (ρ) being short-lived ASCs (Bs) and decaying at rate cs and a proportion (1 − ρ) being long-lived ASCs (Bl) and decaying at rate cl. Antibodies (A) are produced by all ASCs at rate g and decay at rate r. In all 3 models, immunoglobulin G (IgG) antibody can additionally be acquired maternally.

Figure 3.

Sample model fits for individual-level antibody dynamics. Model-predicted antibody dynamics for 2 Ghanaian children under model 1 (A and B), model 2 (C and D), and model 3 (E and F). Model-predicted antibody dynamics for 2 Gambian children under model 1 (G and H), model 2 (I and J), and model 3 (K and L). Dots represent data points, and the continuous lines represent model fits. The presence (red) or absence (black) of Plasmodium falciparum parasites detected by microscopy is indicated at the top of each plot. There was poor agreement between the time of detection of parasites and the boosting of antibody titers. Furthermore, in a given individual, the times of boosting of antibodies to different antibodies often differ. Note that the sustained antibody response in Ghanaian child 2 following infection is poorly captured by models 1 and 2 (B and D) but is captured by model 3 (F). Abbreviations: AMA-1, apical membrane antigen 1; ASC, antibody-secreting cell; CSP, circumsporozoite protein; EBA-175, erythrocyte-binding antigen 175; MSP-1, merozoite surface protein 1; MSP-2, merozoite surface protein 2.

Figure 3.

Sample model fits for individual-level antibody dynamics. Model-predicted antibody dynamics for 2 Ghanaian children under model 1 (A and B), model 2 (C and D), and model 3 (E and F). Model-predicted antibody dynamics for 2 Gambian children under model 1 (G and H), model 2 (I and J), and model 3 (K and L). Dots represent data points, and the continuous lines represent model fits. The presence (red) or absence (black) of Plasmodium falciparum parasites detected by microscopy is indicated at the top of each plot. There was poor agreement between the time of detection of parasites and the boosting of antibody titers. Furthermore, in a given individual, the times of boosting of antibodies to different antibodies often differ. Note that the sustained antibody response in Ghanaian child 2 following infection is poorly captured by models 1 and 2 (B and D) but is captured by model 3 (F). Abbreviations: AMA-1, apical membrane antigen 1; ASC, antibody-secreting cell; CSP, circumsporozoite protein; EBA-175, erythrocyte-binding antigen 175; MSP-1, merozoite surface protein 1; MSP-2, merozoite surface protein 2.

Under the simplest model (model 1), we estimate antibody half-lives of 9–40 days in Ghanaian children and 60–103 days in Gambian children. Under model 2, the observed antibody response in the Ghanaian children was estimated to be due to ASCs with a half-life of 2–5 days, generating antibodies with a half-life of 17–30 days. The antibody response in the Gambian children was estimated to be due to ASCs with a half-life of 95–270 days, generating antibodies with a half-life of 11–12 days. Models 1 and 2 capture the short-lived phase of the antibody response in the Ghanaian cohort but identify a phase of intermediate duration on the Gambian cohort.

In contrast, model 3, in which 2 populations of ASCs are incorporated (thus more accurately representing the underlying immunological processes), produced consistent estimates for the half-lives of both antibodies and ASCs between the Ghanaian and Gambian children. The half-life of antibodies was estimated to be 14–21 days in Ghanaian children and 4–11 days in Gambian children. These half-lives of the antibody response are similar to an estimate of 9.8 days previously reported in Kenyan children [2]. The half-life of maternally acquired antibodies from the Ghanaian cohort was estimated to be 13–45 days. These figures are consistent with estimates of the half-life of passively acquired IgG in adults, which varies from 11–70 days, depending on initial serum concentration and IgG subclass [22]. Because different malaria antigens have been found to induce different IgG subclasses (eg, with IgG1 predominating for AMA-1 and IgG3 predominating for MSP-2) and the extent of this varies with age and duration of exposure [23], an analysis of the proportions and kinetics of each IgG subclass for each antigen may begin to explain the differences in estimated antibody half-life shown in Table 1. Differences in estimated half-lives between antigens may be partially due to differences in the proportion of different IgG subclasses, since different subclasses are catabolized at different rates [24]. The shorter half-life of a child's own IgG antibodies, compared with that of maternally acquired IgG antibodies, may be explained by antibodies being used up to clear parasites in the case of active infection.

Under model 3, the half-life of short-lived ASCs was estimated to be 2–3 days in Ghanaian children and 4–10 days in Gambian children, whereas the half-life of long-lived ASCs was estimated to be 5–9 years in Ghanaian infants and 3–5 years in Gambian children. These estimates suggest a sustained, long-lived immune response in the order of years rather than days, revealing the limitations of models that do not capture the observed biphasic decay in humoral responses (eg, model 1 in this article and the work by Kinyanjui et al [2]). Furthermore, 81%–95% of ASCs are estimated to be short-lived in Ghanaian children, compared with 68%–83% in Gambian children. This difference in the production of long-lived ASCs may be attributable in part to differences in age, as has previously been observed for the Gambian cohort [8]. Although there were insufficient data to formally fit an age effect, the results are consistent with the capacity to mount a sustained response (captured here as a higher proportion of long-lived ASCs) improving with age. Moreover, in the youngest infants (those <100 days old) from the Ghanaian cohort, antibody titers were rarely boosted, even though the infants were regularly exposed to Plasmodium parasites. This suggests that young infants may be unable to mount their own B-cell response, perhaps because high-avidity maternal antibodies sequester the antigen and reduce its availability to prime the child's naive B cells.

## DISCUSSION

The models described here are necessary simplifications of the complex processes underlying the generation of antibody responses. Antigen exposure is assumed to induce rapid proliferation and differentiation of naive B cells or memory B cells into ASCs, and sudden bursts of IgG secretion from newly minted ASCs leads to a sharp increase in antibody titer (ie, boosting). However blood-stage Plasmodium infections can persist for weeks or months (up to at least 40 weeks for a single parasite clone in the Ghanaian cohort [25]), continuously exposing emerging naive B cells and memory B cells to antigen and generating less discrete waves of ASCs and antibodies. A model incorporating data on the duration of infection may provide additional insights into the maintenance of long-lived antibody responses. Furthermore, the simple models investigated here do not distinguish between primary infection and reinfection [26]. It has been observed in mice that functional memory B cells generated in a primary Plasmodium infection give rise to a faster ASC and antibody response upon reinfection [14]. Alternative model formulations could consider the possibility of faster and stronger secondary antibody responses and a greater likelihood of memory B cells differentiating into long-lived ASCs, compared with naive B cells. However, our data were insufficient to distinguish between these models of increased complexity. More-complex models could be tested against data from mouse studies, in which frequent sampling of both the humoral and cellular components of immunity is possible [14, 15].

The data and model presented here can explain both the transient antibody response observed in very young children and the development of sustained humoral immunity following repeated exposure to P. falciparum infection. It also suggests that there may be a lower age limit for the efficient generation of long-lived ASCs. This information may be useful in interpreting the recent RTS,S/AS01 malaria vaccine trials, in which a biphasic exponential decay of anti-CSP antibody titers was observed (with titers waning rapidly in the first few weeks after vaccination followed by a slower decay during extended follow-up over several years [27]) and in which vaccine efficacy was higher in those receiving the vaccine at 5–17 months of age group than in those vaccinated at 6–10 weeks of age [28, 29]. Comparable longitudinal studies of other naturally acquired infections are needed to determine whether the kinetics of humoral immune responses to malaria are typical of other infections or are in some way aberrant. More-extensive sampling of narrowly defined age cohorts throughout child development will also be important, as a substantial age effect on antibody longevity has previously been seen among children 3–8 years old in the Gambia [8]. Also, the findings of model 3, which incorporated both short and long-lived components of the antimalarial antibody response, need to be validated against data from other longitudinal studies. Importantly, these studies will need both a period of frequent sampling to detect the short-lived antibody decay and extended follow-up to capture long-term trends. Finally, the indication that Plasmodium infections can give rise to very long-lived ASCs, which continue to secrete low levels of antibodies for very long periods in the absence of reinfection, provides a plausible explanation for the maintenance of protective immunity after decades of negligible malaria exposure in migrants [3] or long periods of effective malaria control in areas where malaria was previously endemic [30] and has implications for the use of serological testing for mapping temporal changes in malaria transmission [31].

## Supplementary Data

Supplementary materials are available at The Journal of Infectious Diseases online (http://jid.oxfordjournals.org/). Supplementary materials consist of data provided by the author that are published to benefit the reader. The posted materials are not copyedited. The contents of all supplementary data are the sole responsibility of the authors. Questions or messages regarding errors should be addressed to the author.

## Notes

Financial support. This work was supported by the Bill and Melinda Gates Foundation (grant to M. T. W. and support to A. C. G.), the United Kingdom Medical Research Council (fellowship to J. T. G. and support to A. C. G.), and the Wellcome Trust (grant 040328 for sample and data collection in Ghana). Sample and data collection in The Gambia was funded by the UK Medical Research Council.

Potential conflicts of interest. All authors: No reported conflicts.

All authors have submitted the ICMJE Form for Disclosure of Potential Conflicts of Interest. Conflicts that the editors consider relevant to the content of the manuscript have been disclosed.

## References

1
Langhorne
J
Ndungu
FM
Sponaas
AM
Marsh
K
Immunity to malaria: more questions than answers
Nat Immunol
,
2008
, vol.
9
(pg.
725
-
32
)
2
Kinyanjui
SM
Conway
DJ
Lanar
DE
Marsh
K
IgG antibody responses to Plasmodium falciparum merozoite antigens in Kenyan children have a short half-life
Malaria Journal
,
2007
, vol.
6
pg.
82

3
Struik
SS
Riley
EM
Does malaria suffer from lack of memory?
Immunol Rev
,
2004
, vol.
201
(pg.
268
-
90
)
4
Achtman
AH
Bull
PC
Stephens
R
Langhorne
J
Longevity of the immune response and memory to blood-stage malaria infection
Curr Top Microbiol Immunol
,
2005
, vol.
297
(pg.
71
-
102
)
5
Riley
EM
Wagner
GE
Akanmori
BD
Koram
KA
Do maternally acquired antibodies protect infants from malaria infection?
Parasite Immunol
,
2001
, vol.
23
(pg.
51
-
9
)
6
Gupta
S
Snow
RW
Donnelly
CA
Marsh
K
Newbold
C
Immunity to non-cerebral severe malaria is acquired after one or two infections
Nat Med
,
1999
, vol.
5
(pg.
340
-
3
)
7
Taylor
RR
Egan
A
McGuinness
D
, et al.  .
Selective recognition of malaria antigens by human serum antibodies is not genetically determined but demonstrates some features of clonal imprinting
Int Immunol
,
1996
, vol.
8
(pg.
905
-
15
)
8
Akpogheneta
OJ
Duah
NO
Tetteh
KKA
, et al.  .
Duration of naturally acquired antibody responses to blood-stage Plasmodium falciparum is age dependent and antigen specific
Infect Immun
,
2008
, vol.
76
(pg.
1748
-
55
)
9
Akpogheneta
OJ
Dunyo
S
Pinder
M
Conway
DJ
Boosting antibody responses to Plasmodium falciparum merozoite antigens in children with highly seasonal exposure to infection
Parasite Immunol
,
2010
, vol.
32
(pg.
296
-
304
)
10
Wipasa
J
Suphavilai
C
Okell
LC
, et al.  .
Long-lived antibody and B cell memory responses to the human malaria parasites, Plasmodium falciparum and Plasmodium vivax
PLoS Pathog
,
2010
, vol.
6
pg.
e1000770

11
Ndungu
FM
Olotu
A
Mwacharo
J
, et al.  .
Memory B cells are a more reliable archive for historical antimalarial responses than plasma antibodies in no-longer exposed children
Proc Natl Acad Sci U S A
,
2012
, vol.
109
(pg.
8247
-
52
)
12
Migot
F
Chougnet
C
Henzel
D
, et al.  .
Anti-malaria antibody-producing B cell frequencies in adults after a Plasmodium falciparum outbreak in Madagascar
Clin Exp Immunol
,
1995
, vol.
102
(pg.
529
-
34
)
13
Drakeley
CJ
Corran
PH
Coleman
PG
, et al.  .
Estimating medium- and long-term trends in malaria transmission by using serological markers of malaria exposure
Proc Natl Acad Sci U S A
,
2005
, vol.
102
(pg.
5108
-
13
)
14
Ndungu
FM
ET
Coulcher
J
, et al.  .
Functional memory B cells and long-lived plasma cells are generated after a single Plasmodium chabaudi infection in mice
PLoS Pathog
,
2009
, vol.
5
pg.
e1000690

15
Nduati
EW
Ng
DHL
Ndungu
FM
Gardner
P
Urban
BC
Langhorne
J
Distinct kinetics of memory B-cell and plasma-cell responses in peripheral blood following a blood-stage Plasmodium chabaudi infection in mice
PLoS One
,
2010
, vol.
5
pg.
e15007

16
Weiss
GE
Traore
B
Kayentao
K
, et al.  .
The Plasmodium falciparum-specific human memory B cell compartment expands gradually with repeated malaria infections
PLoS Pathog
,
2010
, vol.
6
pg.
e1000912

17
Dorfman
JR
Bejon
P
Ndungu
FM
, et al.  .
B cell memory to 3 Plasmodium falciparum blood-stage antigens in a malaria-endemic area
J Infect Dis
,
2005
, vol.
191
(pg.
1623
-
30
)
18
Riley
EM
Wagner
GE
Ofori
MF
, et al.  .
Lack of association between maternal antibody and protection of African infants from malaria infection
Infect Immun
,
2000
, vol.
68
(pg.
5856
-
63
)
19
Tew
JG
Wu
JH
Qin
DH
Helm
S
Burton
GF
Szakal
AK
Follicular dendritic cells and presentation of antigen and costimulatory signals to B cells
Immunol Rev
,
1997
, vol.
156
(pg.
39
-
52
)
20
Bernasconi
NL
Traggiai
E
Lanzavecchia
A
Maintenance of serological memory by polyclonal activation of human memory B cells
Science
,
2002
, vol.
298
(pg.
2199
-
202
)
21
Slifka
MK
Antia
R
Whitmire
JK
Ahmed
R
Humoral immunity due to long-lived plasma cells
Immunity
,
1998
, vol.
8
(pg.
363
-
72
)
22
Waldmann
TA
Disorders of immunoglobulin metabolism
N Engl J Med
,
1969
, vol.
281
(pg.
1170
-
7
)
23
Tongren
JE
Drakeley
CJ
McDonald
SLR
, et al.  .
Target antigen, age, and duration of antigen exposure independently regulate immunoglobulin G subclass switching in malaria
Infect Immun
,
2006
, vol.
74
(pg.
257
-
64
)
24
Spiegelberg
HL
Biological activities of immunoglobulins of different classes and subclasses
,
1974
, vol.
19
(pg.
259
-
94
)
25
Franks
S
Koram
KA
Wagner
GE
, et al.  .
Frequent and persistent, asymptomatic Plasmodium falciparum infections in African infants, characterized by multilocus genotyping
J Infect Dis
,
2001
, vol.
183
(pg.
796
-
804
)
26
Moncunill
G
Mayor
A
Jimenez
A
, et al.  .
Cytokine and antibody responses to Plasmodium falciparum in naive individuals during a first malaria episode: effect of age and malaria exposure
PLoS ONE
,
2013
, vol.
8
pg.
e55756

27
Olotu
A
Fegan
G
Wambua
J
, et al.  .
Four-year efficacy of RTS,S/AS01E and its interaction with malaria exposure
N Engl J Med
,
2013
, vol.
368
(pg.
1111
-
20
)
28
Agnandji
ST
Lell
B
Soulanoudjingar
SS
, et al.  .
First results of phase 3 trial of RTS,S/AS01 malaria vaccine in African children
N Engl J Med
,
2011
, vol.
365
(pg.
1863
-
75
)
29
Mian-McCarthy
S
Agnandji
ST
Lell
B
, et al.  .
A phase 3 trial of RTS,S/AS01 malaria vaccine in African infants
N Engl J Med
,
2012
, vol.
367
(pg.
2284
-
95
)
30
Deloron
P
Chougnet
C
Is immunity to malaria really short-lived
Parasitol Today
,
1992
, vol.
8
(pg.
375
-
8
)
31
Corran
P
Coleman
P
Riley
E
Drakeley
C
Serology: a robust indicator of malaria transmission intensity?
Trends Parasitol
,
2007
, vol.
23
(pg.
575
-
82
)

## Author notes

a
E. M. R. and A. C. G. contributed equally to this study.