Modeling the Development of Acquired Clinical Immunity to Plasmodium falciparum Malaria

Individuals living in regions where malaria is endemic developan acquired immunity to malaria which enables them to remainasymptomatic while still carrying parasites. Field studies indicatethat cumulative exposure to a variety of diverse Plasmodiumparasites is required for the transition from symptomatic toasymptomatic malaria. This study used a simulation model ofthe within-host dynamics of P. falciparum to investigate thedevelopment of acquired clinical immunity under different transmissionconditions and levels of parasite diversity. Antibodies developedto P. falciparum erythrocyte membrane protein 1 (PfEMP1), aclonally variant molecule, were assumed to be a key human immunologicalresponse to P. falciparum infection, along with responses toclonally conserved but polymorphic antigens. The time to thedevelopment of clinical immunity was found to be proportionalto parasite diversity and inversely proportional to transmissionintensity. The effect of early termination of symptomatic infectionsby chemotherapy was investigated and found not to inhibit thehost's ability to develop acquired immunity. However, the timerequired to achieve this state was approximately double thatcompared to when no treatment was administered. This study demonstratesthat an immune response primarily targeted against PfEMP1 hasthe ability to reduce clinical symptoms of infections irrespectiveof whether treatment is administered, supporting its role inthe development of acquired clinical immunity. The results alsoillustrate a novel use for simulation models of P. falciparuminfections, investigation of the influence of intervention strategieson the development of naturally acquired clinical immunity.

INTRODUCTION

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Introduction

Plasmodium falciparum malaria is a common disease in many tropicalcountries. The majority of clinical P. falciparum cases areuncomplicated, but some individuals will develop complications,including severe anemia, coma, and death (24). These complicationsare more prevalent in populations such as the young, pregnantwomen, and nonimmune adults. Residents of regions where malariais endemic acquire partial immunity to the disease that reducesthe frequency of clinical attacks, although not necessarilyreducing parasite prevalence (14). This antidisease immunityis not sterile and requires continual boosting. The age at whichacquired immunity becomes evident varies depending on the levelof exposure, with higher exposure resulting in earlier developmentof clinical immunity (26). Children living in areas of highendemicity experience less frequent episodes of malaria afterthe age of 5 years (26), while people in areas of hypoendemicitymay never develop clinical immunity. Since clinical immunityto malaria is highly strain specific (30, 37), the speed withwhich immunity develops is inversely correlated to the sizeand diversity of the parasite population. It has also been shownthat the rate of the development of clinical immunity correlateswith the length of infection; asymptomatic status is reachedsooner when the infections are longer (30).

Asexual malaria parasites exist in two distinct stages withinthe human host, a developmental stage in hepatocytes and theblood-stage parasites. Immune responses are developed to bothstages (7, 31, 35), but long-term antidisease immunity has beenlinked to exposure to blood-stage parasites (36). During blood-stageinfections, parasites insert a number of proteins into the membranesof infected erythrocytes (15). Although many of these proteinsare immunogenic (8, 13, 16), the gradual development of acquiredimmunity and its reliance on repeated exposure suggest thatproteins that undergo antigenic variation may be fundamentalto the development of acquired immunity (9, 27). P. falciparumerythrocyte membrane protein 1 (PfEMP1) is the best characterizedof these proteins.

PfEMP1 is a clonally variant protein encoded by ${approx}$ 60 var genesper parasite (17). The development of specific antibody responsesto PfEMP1 variants occurs after exposure to parasites expressingthose variants (10, 20, 21), with sera from individuals fromregions where malaria is hyperendemic able to recognize manyvariants (12, 28).

Some of the intervention factors potentially affecting the developmentof clinical immunity have been investigated. While the effectof insecticide-treated bed nets is relatively easy to investigatein field studies (1, 36), other factors such as repeated chemotherapyare not as easily assessed in field studies due to ethical considerations.In these circumstances, mathematical modeling is one of thefew tools available to investigate the effect that various interventionmeasures may have on the development of acquired immunity.

This study explores the development of acquired clinical immunitywith a computer simulation model of P. falciparum infectionswithin individuals. The immune response incorporated is skewedtowards the production of anti-PfEMP1 antibodies and demonstratesthat clinical immunity develops with repeated exposure to avariety of parasites. The time required to develop this immunitywas found to be proportional to parasite diversity and inverselyproportional to transmission intensity, features commonly foundin field studies. Simulation of repeated chemotherapy of symptomaticinfections indicated that clinical immunity took almost twiceas long to develop as in infections where no treatment was provided.This study demonstrates that an immune response primarily targetingPfEMP1 has the ability to reduce clinical symptoms of infectionirrespective of whether treatment is administered, supportingits role in the development of acquired clinical immunity.

MATERIALS AND METHODS

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Materials and Methods

Model. The simulation model reported previously (19) was used to mimicthe within-host dynamics of P. falciparum infections. A 48-htime step is used in the model in line with the replicationcycle of the parasite. Because this model was developed andcalibrated with data from malaria-naïve hosts, severalamendments were made to the assumptions of the model in orderto incorporate repeated infections and the corresponding immuneresponses. These changes are summarized below, with detailsof the model given in Fig. 1.

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FIG. 1. Flowchart of the simulation model used to mimic the within-host dynamics of P. falciparum infections. Bi(a,b) represents the use of a binomial distribution with sample size a and probability b. When a was large, a normal distribution was used as an approximation of the binomial. N(a,b) represents the use of a normal distribution with mean a and standard deviation b. Ab, antibody; NSI, nonspecific immunity.

The model incorporated three types of immune responses; a nonspecificimmune response that is responsible for the development of symptomssuch as fever, a clonal immune response that is parasite specificand acts to reduce the net replication rate of the parasites,and an anti-PfEMP1 antibody immune response. The anti-PfEMP1antibody response is produced after the number of parasitesexpressing a specific variant exceeded a given threshold andthe corresponding time lag had elapsed. This time lag incorporatedthe time required for the stimulation and development of antibody.When a PfEMP1 variant had not previously elicited an immuneresponse within the host, the threshold was assumed to be 12parasites/µl, based on field data that antibody is producedprior to or about the time that clinical symptoms develop (27).A lag of 7 days was used between the triggering and the productionof antibody. Following basic immunological principles that secondaryantibody responses are triggered more rapidly with less antigen,these values were reduced to 6 parasites/µl and 2 days,respectively. The model assumed limited cross-reactivity betweenanti-PfEMP1 antibodies with antibodies to a given variant killingapproximately 5% of parasites expressing other variants.

The function describing the clonal immune response consistedof two components. The first represented the response to conservedmalaria antigens, and the second was a response to the antigenspresented by a particular parasite genotype. Both componentsact to reduce the number of merozoites that survive one completereplication cycle, causing a reduction in the effective growthrate of the parasites. The first component develops during theinitial infection and is maintained through subsequent infections,while the second component is assumed to be unique to each parasitegenotype and is triggered by each new infection. Immune responsesto parasite antigens other than PfEMP1 were grouped under thisimmune response.

To simulate infections by different parasites, it was assumedthat there existed a pool of PfEMP1 variants (each encoded bya var gene) within the parasite population. Although it hasbeen hypothesized that strong immune pressure is likely to resultin independently transmitted strains (22), molecular studiesof PfEMP1 support an alternative scenario of frequent gene recombination(38) occurring in randomly mating P. falciparum parasites (2).This scenario of frequent and random recombination of var genesis assumed in the model. The var genes within the populationwere assigned to one of two groups; 20% formed a fast-switchinggroup, while the remaining 80% of the genes were classifiedas slow switching. The overall switch rate and the range ofswitching rates within the fast and slow groups were reportedpreviously (19), but the probabilities of switching for eachgene were adjusted to account for the large number of genesin the population compared to within one parasite. Fifty vargenes were randomly selected from those in the population foreach infecting parasite. This random allocation caused the characteristicsof each parasite to differ, particularly with respect to thenumber of fast-switching variants in its genome.

Infections were initiated in the model based on a specifiedinfection rate. Prior to simulating the first infection, themodel randomly assigned the days on which infection occurredbased on the nominated infection rate. This was done by comparingrandom numbers to the infection rate and declaring that an infectionstarted on the designated day if the random number was lessthan the infection rate. If this was not the case, the processwas repeated for the next infection period (48 h later). Thefirst infection always commenced on day 0, with subsequent infectionsstarting on the allocated days. Up to five infections were permittedto commence on the same day, and there was no limit on the numberof superinfections permitted within the host at one time. Themodel initially assumed a malaria-naïve host with no existingimmunity.

Treatment was incorporated into the model by terminating allinfections within the host when a fever occurred. It was assumedthat every treatment was 100% effective and that no drug resistancewas present.

The aim of this study was to investigate the onset of clinicalimmunity. For this purpose, clinical immunity was defined asexisting when less than 5% of simulations had more than 1 dayof fever (as defined in reference 19) in the first 30 days afteran infection commenced. This definition allowed an immune personto develop an occasional fever.

Simulations. Simulations were conducted for a variety of infection rates;the average intervals between infections were 14, 30, 60, 90,150, and 200 days. The effect of parasite diversity was incorporatedby changing the number of var genes present within the parasitepopulation (500, 1,000, 1,500, and 2,000). Under the random-matingassumption, a population with 500 var genes (or PfEMP1 variants)would have originated from 10 unique parasite clones, whilea pool of 2,000 variants would have originated from 40 uniqueparasite clones.

Each simulation mimicked up to 100 consecutive infections withinthe same host over a period of <20,000 days. The actual durationof the simulation varied depending on the specific infectionrate, but all simulations were conducted for periods in excessof the time required for 95% of the last simulated infectionsto terminate. Simulations were conducted for two extreme situations:when no chemotherapy was administered during the simulationperiod, and when chemotherapy was applied whenever a fever wasdetected.

We conducted 500 simulations of the model for each of the 24diversity-transmission combinations. From each simulation, anumber of summary variables were extracted, including the numberof days with parasite densities of >1,000 and >10,000/µl,length of the infection (days), number of days with a fever(as defined in reference 19), and maximum parasitemia. Datafor all variables were obtained from model output for the 30days following each infection and categorized by the infectionnumber. An additional summary variable, the proportion of simulationsin which an infection developed successfully (lasted >10days) was calculated for each infection. A regression equationof the form y = y₀ + a/{1 + exp[–(x – x₀)/b]}, wherex is the infection number, y is the proportion of infectionsthat developed successfully, and a, b, x₀, and y₀ are fittedconstants, was fitted to these data by using SigmaPlot (version4.00; SPSS Inc.) to obtain an estimate of the asymptote (y₀)for the proportion of infections that developed successfully.

RESULTS

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Results

Simulations with no chemotherapy. The number of occurrences of fever decreased with increasinginfection number for all diversity-transmission combinationsexamined (Fig. 2). This pattern was also noted for the numberof days with parasite densities of >1,000 and 10,000/µl(Fig. 2) and maximum parasitemia (data not shown).

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FIG. 2. Sample of output from 500 simulations with an infection approximately every 60 days and a population of 1,000 var genes. A) Number of fever occurrences, B) number of days with parasite density of >1,000/µl, and C) proportion of infections that were successful as blood-stage infections lasting more than 10 days. Shaded regions in A and B represent the interquartile range of the simulated data; dots represent the 5th and 95th percentiles. In C, the line represents the fitted regression model with an asymptote of 0.87.

The number of infections required before immunity developedincreased with parasite diversity and transmission rate. However,the average time taken to achieve clinical immunity (numberof infections multiplied by transmission rate) decreased withincreasing transmission (Fig. 3). At the onset of clinical immunity,between 34 and 70% of the simulations had no fever associatedwith infection. The highest values (67 to 70%) were associatedwith infections occurring every 14 days on average, even thoughsuperinfection was common at this transmission level. The lowestrates (34 to 39%) corresponded to less frequent infections occurringon average every 200 days.

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FIG. 3. Relationship between parasite diversity (size of the var gene pool) and transmission rate (expressed as the average number of days between infections) and the time (years) required to develop clinical immunity (contours) in the absence of chemotherapy.

Once immunity was established, all diversity-transmission combinationsindicated that not every infection that was initiated developedinto a successful blood-stage infection lasting more than 10days. The highest proportion of successful infections (0.98)was associated with the combination of largest parasite diversityand lowest transmission rate. Conversely, the low-diversityand high-transmission setting provided the lowest success rate(<0.70). The proportion of infections that failed to developalmost perfectly reflected the ratio of the number of circulatinganti-PfEMP1 variant antibodies within the host to the totalnumber of var genes within the population. For the highest infectionrate considered (one infection approximately every 14 days),a regression model was not fitted to the proportion of successfulinfections because the proportion of successful infections oscillatedover time. These oscillations were greatest when combined withthe lowest values of parasite diversity. This feature is primarilydue to infections generating anti-PfEMP1 antibodies to a largeproportion of the PfEMP1 variants within the population in ashort time, causing the subsequent number of successful infectionsto decrease. Since most of these antibodies are developed overa relatively short period, they tend to wane at approximatelythe same time, which leaves the door open for new infections.These new infections again create a burst of antibody activity,and the cycle repeats itself.

Effect of chemotherapy on development of immunity. Simulations investigating the effect of repeated chemotherapyon the development of clinical immunity were only conductedat infection rates of one infection every 30 and 60 days. Tocompare the rate of development of clinical immunity betweenuntreated and treated populations, the proportion of infectionsoccurring with no fever in the untreated population was comparedto the proportion of infections not requiring treatment in thetreated population (since chemotherapy was administered whenevera fever presented) (Fig. 4, Table 1). In every case, the treatedpopulation showed a trend of decreasing treatment rate withincreasing number of infections. However, the proportion ofinfections with fever requiring treatment (in the treated population)was always more than the number of fever occurrences in theuntreated population. On average, the time required for 60%of simulations to not require treatment was double that foran equivalent immunological state to be achieved in the untreatedpopulation (Table 1).

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FIG. 4. Comparison of the number of infections without a fever (untreated population; dotted line) and the number not requiring treatment (treated population; solid line) for an infection rate of one infection every 60 days and a population of 1,000 var genes.

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TABLE 1. Number of infections required before 60% of simulations do not have a fever associated with infection or do not require chemotherapy for the untreated and treated populations, respectively

DISCUSSION

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Discussion

The development of acquired clinical immunity is an importantfeature of P. falciparum malaria because it reduces the frequencyof symptomatic episodes and thus disease-associated morbidityand mortality. It is generally accepted that the gradual developmentof this immunity is directly related to the requirement thatthe host's immune system be repeatedly exposed to a wide varietyof diverse parasite antigens. The development of immunity istherefore related to the transmission intensity and diversityof parasites. These two parameters often have a direct correlation,i.e., high transmission intensity is accompanied by a largeparasite population repertoire with high diversity. The combinedeffect of these parameters on the speed of immunity developmentwas the focus of this theoretical investigation. The outcomeof the modeling indicated that increasing parasite diversityby increasing the number of unique PfEMP1 proteins within apopulation increases the time required to achieve immunity irrespectiveof transmission intensity. This is an intuitively obvious resultif one assumes that disease occurs as a result of holes in theantigenic repertoire recognized by the host. Likewise, the modeloutput indicated that increased transmission intensity decreasedthe time until acquired immunity developed. This result is supportedby field observations of differences in the age when acquiredimmunity develops between areas of different transmission intensity(26), with older ages predicted under low-transmission-intensityconditions.

Although transmission intensity and parasite diversity bothimpact on the time required before immunity develops, parasitediversity was predicted to have a larger influence than transmissionrate. For instance, a 20% increase in diversity (with transmissionintensity remaining constant) was predicted to increase thetime required to develop immunity by between ${approx}$ 13 and 38%, dependingon the initial level of diversity and transmission. In comparison,a decrease of 20% in the transmission rate (keeping diversityconstant) increased the predicted time to immunity by ${approx}$ 5 to 18%.

The parameters used in the model were calibrated based on infectionsof neurosyphilis patients with the P. falciparum El Limon andSantee Cooper parasite strains. The relationship between thisparameter set and the characteristics of field isolates remainsto be determined, but it has already been noted that differencesexist in the pyrogenic thresholds (18), maximum parasitemia(19), and replication rates (34) of different parasites. Additionally,a febrile event has been defined here as a temperature of >40°C.This value is somewhat arbitrary because it is difficult tolink the value of model parameters to actual body temperature.Hence, it should be viewed simply as an indicator of fever.As such, the model output represents a generalized system thatcan be used to look at the factors affecting the developmentof immunity; these factors would be expected to have the sameeffects under modified parasite-host parameters.

The model incorporates the detailed process of parasite antigenicvariation in PfEMP1 and the corresponding host immune response.This is not meant to undervalue the contribution of other parasiteantigens in the development of acquired clinical immunity. Althoughnot specified individually, the host's immune responses to otherparasite antigens are incorporated via the clonal immunity function.Emphasis has been placed on antigenic variation because thisparasite feature appears to be one of the primary limiting factorsin the speed of development of clinical immunity to a parasitepopulation.

The PfEMP1 switching process and rates assumed in the modelare similar to those reported previously to produce simulatedinfections with characteristics similar to those of observedclinical cases in malaria-naïve hosts (19). Recently itwas proposed that a PfEMP1 variant may elicit a long-lived immuneresponse unique to the variant and also short-lived transientresponses to one or more shared epitopes (32). Our model currentlycontains a specific medium-lived antibody response to a particularvariant and also a limited amount of cross-reactivity betweenthis antibody and all other variants. The simplest assumptionof cross-reactivity was used due to the lack of experimentaldata related to the degree of cross-reactivity between specificantibodies and PfEMP1 variants and the dynamics of such responses.Changes to the scope and/or magnitude of this cross-reactivitycould affect the length of infection, which may in turn impactour predictions relating to the development of immunity. However,any such changes would be expected to be minimal.

Direct extrapolation of the model predictions to field situationsrequires further validation against field data. This is difficultdue to the lack of data containing estimates of transmissionintensity, parasite diversity, and age of onset of immunityfor a particular field site. Additionally, the model assumesconstant infection rates, while many regions exhibit seasonaltransmission. There are, however, a limited set of field sitesfor which data can be extrapolated to validate the model output.

In western Kenya, the entomologic inoculation rate varied from ${approx}$ 0.02 to 10.0 infected bites per person per night (equivalentto one infectious bite every 50 and 0.1 days, respectively),with at least 43 different merozoite surface protein 1 allelesdetected (6). In very broad terms, this equates to ${approx}$ 2,150 differentPfEMP1 variants within the population, assuming that each parasitesampled had a unique repertoire of 50 var genes. In this setting,>10% of children 3 years of age experienced febrile outbreaks(6). The model output from simulations of a similar transmissionenvironment (one infection every 14 days; 2,000 var genes inthe population) predicted that the onset of immunity would occurat approximately 5 years of age. This value appears to be roughlyin the correct time frame, since clinical immunity at the fieldsite (by our definition) occurred after 3 years of age. Additionally,the actual infection rate is probably lower than the estimatedentomologic inoculation rate because not all bites from sporozoite-infectedmosquitoes result in infections (11, 33).

At the other end of the spectrum, Morong in the Phillipineshas a much lower prevalence of P. falciparum. Although muchof the region has little or no malaria, ${approx}$ 5% of the populationlive in higher-transmission areas which have a point prevalenceof ${approx}$ 10% (5). Assuming a patency of 15 to 20 days before detection,this equates to an average probability of infection on the orderof 0.005 to 0.006 per person per day, or one infection approximatelyevery 160 to 200 days. Antibody seropositivity against P. falciparumantigen appears to plateau in this population at approximately10 years of age, although this may not equate to clinical immunitybecause many adults still suffer symptomatic attacks (5). Parasitediversity within Morong appears to be relatively constrained,with only seven apical membrane antigen 1 sequence types andeight merozoite surface protein 1 sequence types detected in113 and 103 parasite isolates, respectively (29). Assuming atotal parasite reservoir of 10 to 20 different isolates, thevar gene population would consist of approximately 500 to 1,000different genes. According to the model output, with infectionsoccurring approximately every 200 days and a var gene populationof 1,000, acquired clinical immunity would be predicted by 11.5years of age. This age generally reflects the plateau seen inantibody prevalence (5).

It must be noted that it is assumed in the model that the parasitepopulation is constant. It is unlikely that the parasite populationmeets this assumption over long periods of time in all but themost isolated areas. If new parasites are introduced to a region,it is likely that individuals infected with this new parasitewill become ill because they will have no recognition of thePfEMP1 variants expressed by the parasite. This predispositionto cause illness will persist until individuals start to bereinfected with the same parasite or until the antigenic repertoireof the new parasite is diluted through mating with other parasites.This may partially explain why many adults still experienceclinical symptoms in regions of low transmission and why occasionalepidemics occur in an otherwise immune population.

Studies of malaria incidence among transmigrants moving fromregions of almost no malaria to where malaria is endemic suggestthat protection can be established after a relatively briefperiod (4). This appears to contradict our results, but thecriteria used to define immunity differ between the studies.Although Baird et al. (3) claim that clinical immunity occurredin individuals experiencing four infections in 2 years, theynote that only 36 (62%) of the 58 subjects obtained clinicalimmunity (parasitemia without fever). Given that the study areawas a newly developed village relatively isolated from othervillages and all new residents received prophylaxis for 90 daysafter arrival (25), it is likely that parasite diversity isrelatively limited. The model output for infections occurringevery ${approx}$ 150 days (that is, four times in 2 years) with 500 differentvar genes in the population indicated that after four infections,21% of the simulated infections resulted in no febrile event,while 64% experienced only one febrile day. This representeda significant decrease in the risk of experiencing a fever afterfour infections, a finding similar to that of Baird et al. (3).

Use of a simulation model to mimic the development of clinicalimmunity within a host provided the opportunity to investigatethe influence of early termination of infections through chemotherapy.Only the extreme situation of treating every infection thatbecame symptomatic was considered. There was a consistent trendof delayed onset of immunity associated with repeated treatment,such that immunity took almost twice as long to develop comparedto when infections were left untreated. This delay is due tothe reduced exposure of the host to the range of parasite variantantigens. However, it is important to note that immunity diddevelop in the treated population. Hence, rapid treatment ofsymptomatic infections, which can potentially reduce the occurrenceof severe complications and anemia, does not exclude the developmentof clinical immunity; it simply delays its onset. This trendof delayed immunity with frequent administration of drugs hasbeen noted in Africa (23).

This study used a simulation model of the in-host dynamics ofP. falciparum infections to explore the factors influencingthe development of clinical immunity to P. falciparum malaria.Incorporating antibody responses to PfEMP1 along with generalresponses to other nonvariant antigens was sufficient to mimicthe development of immunity and produce estimates of the ageof immunity which appear to generally agree with that observedin the field. This supports the role of anti-PfEMP1 antibodiesin the development of immunity. The simulation study also allowedthe impact of regular chemotherapy to be assessed, concludingthat clinical immunity will develop under such conditions butthe age of onset is delayed.

ACKNOWLEDGMENTS

This work was supported in part by NIH grant # AI47500-03. M.L.G.is funded by a University of Queensland Postdoctoral ResearchFellowship.

The opinions expressed herein are those of the authors and donot necessarily reflect those of the Defense Health Servicesor any extant Defense policy.

FOOTNOTES

* Corresponding author. Mailing address: Malaria and Scabies Group, Queensland Institute of Medical Research, PO Royal Brisbane Hospital, Queensland 4029, Australia. Phone: 61 7 3362 0416. Fax: 61 7 3362 0104. E-mail: michellG{at}qimr.edu.au.

Editor: W. A. Petri, Jr.

REFERENCES

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