Background
Plasmodium falciparum and
Plasmodium vivax malaria parasites cause persistent blood-stage infections in humans lasting for weeks, months, and occasionally years [
1]. The processes of parasite growth (as asexual merozoites invade red blood cells and periodically replicate every 48 h), density-dependent regulation, and the acquisition of adaptive immune responses cause complex patterns of blood-stage parasitaemia and infection dynamics [
2‐
5]. In addition to blood-stage parasite replication,
P. vivax has an alternative strategy for persisting in humans via the reservoir of hypnozoites in the liver [
6]. Following inoculation of
P. vivax sporozoites from an infectious mosquito, a proportion of sporozoites will develop into hypnozoites and remain arrested in the liver for weeks to years [
7,
8], until they activate to cause new blood-stage infections. Blood-stage infections arising from the activation of
P. vivax hypnozoites are referred to as relapses, and are a key distinguishing feature between the biology of
P. vivax and
P. falciparum [
9].
A recurrent infection is defined as a newly detectable episode of blood-stage parasitaemia occurring after a previous infection [
7]. A
P. falciparum recurrence can be due to: (i) re-infection from a new mosquito bite; or (ii) recrudescence, where blood-stage parasites originating from a previous infection persist at sub-patent densities where the probability of detection is low, before increasing in density to become detectable. A
P. vivax recurrence can be due to: (i) re-infection; (ii) recrudescence; or (iii) relapse. It is usually not possible to definitively distinguish between types of recurrences without detailed genotyping information. Re-infections can be excluded if an individual has moved to an area with no malaria transmission [
10]. Relapses can be excluded if individuals are treated with an effective regimen of primaquine [
11]—the only licensed drug capable of eliminating hypnozoites from the liver [
12]. However, even with directly observed treatment, primaquine does not guarantee clearance of hypnozoites in human patients with a low CYP2D6 metabolizer phenotype [
13]. Recrudescences can be excluded with high-sensitivity testing for blood-stage parasites, for example if prior to a positive blood sample an individual tested negative by qPCR, then it’s unlikely that the positive sample was due to a recrudescence.
Qualitative and quantitative descriptions of
P. falciparum and
P. vivax infection dynamics have been obtained through analysis of data from historic malaria-therapy studies used for the treatment of neuro-syphilis [
14,
15]. In these highly controlled studies, exposure to infectious mosquito bites was strictly regulated and blood-stage parasite densities measured frequently, often daily, allowing for detailed investigation of temporal patterns in blood-stage parasite densities [
2]. A number of limitations prevent the findings of these studies from being extrapolated to malaria-endemic regions, notably that subjects were malaria-naïve adults without pre-existing immunity, and the absence of super-infection with new strains.
In contemporary times, the dynamics of malaria infections may be studied in endemic regions using longitudinal cohort studies, where participants are followed over time and sampled frequently [
16,
17].
Participants will have varying degrees of naturally-acquired immunity and may be concurrently exposed to both
P. vivax and
P. falciparum infections. Genotyping of
Plasmodium parasites increases the information available from samples, allowing for super-infections to be identified, and multiplicity of infection to be estimated [
18,
19]. These data can be analysed using statistical and mathematical models to estimate epidemiological parameters of interest. The dynamics of genotyped
P. falciparum infections from longitudinal studies have previously been analysed using triplet or immigration-death models [
20,
21], where the frequencies of different patterns of samples are analysed to provide estimates of the duration of blood-stage infection; the detectability of genotypes; and the force of infection of each genotype. A limitation of these methods is the assumption that duration of infection is exponentially distributed. In an analysis of
P. falciparum samples from a longitudinal study in Ghana, Bretscher et al. [
22] overcame this limitation by fitting a range of distributions to the duration of blood-stage infection, but at the expense of assuming re-infection with the same genotype is a rare event. Accounting for the role of
P. vivax relapses in longitudinal studies remains a considerable challenge. Using data on time to relapse from malaria-therapy studies and keeping duration of blood-stage infection constant, Ross et al. [
17] fitted a population-level model to data from a cohort of Papua New Guinean children, and estimated that 80% of
P. vivax infections were attributable to relapses.
In this analysis, infection dynamics were estimated by estimating the times of acquisition and clearance of P. falciparum and P. vivax single-locus genotypes in each individual. Data from infections in all individuals were analysed simultaneously allowing estimation of the average duration of blood-stage infection, the probability of genotype detectability, and for P. vivax: the duration of liver-stage infection with hypnozoites and relapse frequency. Although a definitive classification of P. vivax infections into re-infection, recrudescence or relapse is not possible, it was possible to assign a probabilistic phenotype to each positive P. vivax sample, facilitating detailed investigation of the role of relapses in epidemiological studies.
Discussion
The statistical model presented here allows infection dynamics to be investigated on both an individual and a population-level. Data from two populations with different study designs were analysed: (i) a treatment-reinfection study in Papua New Guinean children, with and without clearance of liver-stage hypnozoites by primaquine; and (ii) a longitudinal observational cohort study in Thai participants of all ages. The average duration of
P. vivax blood-stage infection in PNG was estimated as 24 (95% CrI 21, 28) days, slightly shorter than in Thailand (29 (95% CrI 27, 32) days), which had lower levels of
P. vivax transmission. In PNG, which had moderate levels of
P. falciparum transmission, the average duration of
P. falciparum blood-stage infection was 36 (95% CrI 29, 44) days, substantially shorter than has been reported in some African populations in higher transmission settings, where it has been estimated to be 70–179 days [
34]. In Thailand where infection with
P. falciparum was rare, the average duration of blood-stage infection was 135 (95% CrI 94, 191) days. The variation in the estimated duration of blood-stage infection between different populations may be due to differences in levels of naturally-acquired immunity, population genetic differences in host response to infection, variation in strains selected for differing local environments, or the choice of analysis method.
When the performance of the model was assessed against simulated
P. falciparum data, it was able to reliably estimate the population-level parameters (duration of blood-stage infection and detectability) across a wide range of parameter space. However, assessment of the statistical methods on simulated
P. vivax data sets reveals a substantial limitation, that the duration of blood-stage
P. vivax infection and the time to next relapse cannot be reliably estimated. This arises from a lack of identifiability between long blood-stage infections of a single-locus genotype and a short blood-stage infection rapidly followed by relapses of the same genotype. When a cohort was simulated assuming a long duration of blood-stage
P. vivax infection, the duration of blood-stage infection was substantially underestimated. For example, for a blood-stage infection lasting 90 days, the method assigns a higher likelihood that it is instead a short infection of duration 30 days, rapidly followed by two relapses each causing blood-stage infections of duration 30 days. This inability to consistently identify the parameters for the dynamics of
P. vivax infections is a major limitation of the method described here. It is possible that the model is mis-specified when applied to single-locus micro-satellite data with imperfect heterozygosity [
19,
27]. This issue may be resolved by an update of the model to account for the genetic relatedness in an inoculum of sporozoites and the resulting relatedness between parasites from a primary infection and relapse [
35], applied to genotyping data from more sophisticated technologies such as familial panels of microsatellites, amplicon sequencing, or genome-wide SNP panels [
36,
37].
Despite the inability of the method to accurately estimate the duration of blood-stage
P. vivax infection, the range of the estimates (24–29 days) can be considered consistent with the high proportion of individuals where no more than one consecutive sample was observed (Fig.
1). An alternative approach is to fit the model for
P. falciparum infection dynamics to the
P. vivax data. Although, this model does not account for relapses, estimates of the duration of blood-stage infection remain similarly short: 19 (95% CrI 16, 23) days in PNG and 34 (95% CrI 31, 39) days in Thailand. In contrast, data from malaria-therapy studies indicate that in non-immune adults blood-stage infections can persist for 60–70 days, and possibly even longer at sub-microscopic densities [
4,
14]. Based on these observations, it is hypothesized that a primary
P. vivax blood-stage infection may have a long duration (especially in malaria-naïve individuals), with relapses having a substantially shorter duration of infection. This concurs with other data from malaria-therapy studies demonstrating a reduction in parasite density between primary
P. vivax infection and secondary infection with a homologous strain [
14]. In individuals in the PNG and Thai cohorts with naturally-acquired immunity against
P. vivax parasites, it is likely that the duration of the primary blood-stage infection is also reduced. Further evidence can be obtained from observations of
Plasmodium cynomolgi: a simian malaria parasite that is genetically closely related to
P. vivax, with many biological similarities most notably the presence of relapses. In controlled infections in rhesus macaques, untreated blood-stage infections due to
P. cynomolgi had considerably shorter duration (approximately 10 days) than primary infection [
38].
Addressing the knowledge gap on the duration of blood-stage
P. vivax infections could have substantial clinical and public health value. The effectiveness of drug treatment strategies for reducing malaria transmission will depend on the duration of blood-stage infection: if the duration of infection is unknown, then the number of transmission events of gametocytes from humans to mosquitoes prevented by treatment can’t be assessed [
39,
40]. If blood-stage
P. vivax parasitaemia is sustained by multiple short infections, then clearing a single infection with a blood-stage drug such as artemisinin combination therapy (ACT) will cause very little reduction in transmission. In contrast, if the majority of
P. vivax infections have longer duration expected, increased ACT treatment can be seen causing a reduction in transmission, similar to what has been seen for
P. falciparum [
41].
Another substantial limitation concerns the use of single-locus genotype markers. A single infectious mosquito bite may inoculate batches of parasites with different genotypes that may be unrelated or meiotic siblings that differ at the locus of interest [
35,
37]. Furthermore, unrelated parasites may have the same genotype at the locus considered, although the expected heterozygosity of the genotyping markers is > 90%. It is also possible that a relapse may have a different genotype to its primary infection, but still be a half-sibling. To overcome these challenges, multiple-locus genotype markers are being developed, which should provide an even richer pattern of
P. falciparum and
P. vivax infection dynamics. In particular, the utilization of multi-locus genotype markers may resolve the issue of identifiability faced here by allowing a relapse to be distinguished from a primary blood-stage infection in cases where they are meiotic siblings.
There are a number of other limitations to the analytic methods applied here. Firstly, the role of heterogeneity and seasonality in exposure to mosquito bites are not accounted for, which is likely to increase the prevalence of co-infection with multiple
P. falciparum and
P. vivax genotypes. However, application of the methods to simulated data assuming heterogeneity or seasonality in exposure suggested that population-level parameters can still be estimated. Secondly, it is assumed that during co-infection, infections of different genotypes (both within and between species) are independent of one another. However it is likely that they interact due to induced innate immune responses and density-dependent regulation [
42]. Thirdly, it is assumed relapses have a tropical phenotype [
7,
8] and occur at a constant rate following primary infection, thus the authors do not account for the variation in relapse rate that may arise due to variation in the number of hypnozoites in the liver [
29]. In particular, it is assumed that time to next relapse is exponentially distributed when the data may be better described by a more flexible distribution such as a Weibull distribution [
17].
The predicted results may also depend on the frequency of sampling. To investigate this, alternate samples from individuals in the PNG cohort were excluded, and after repeating the analysis found only limited differences in the estimated population-level parameters (see Additional file
4: Fig. S4.2). The results may also depend on genotype detectability. Prior information from a series of experiments was relied upon where two blood samples were taken 24 h apart and the presence of genotypes compared between the two samples [
43]. Higher parasite densities were found to increase genotype detectability, and increased multiplicity of infection (MOI) was found to reduce detectability. In addition, data from malaria-therapy studies has demonstrated a reduction in parasite density between primary
P. vivax infection and secondary infection with a homologous strain [
14]. Therefore, the assumption of constant genotype detectability may be a limitation of the method, leading to underestimation of the proportion of
P. vivax relapses which may go undetected because of their lower blood-stage parasite densities. Finally, 100% specificity of genotype detection is also assumed. Imperfect specificity and density-dependent sensitivity will be investigated in future work.
Despite increasingly detailed observations of hypnozoites in vivo [
44], the biological processes regulating hypnozoite activation remain unknown [
9]. The combination of longitudinal data collection, genotyping of samples, and statistical modelling presented here provides a new approach for investigation of
P. vivax recurrences. Whilst recurrences cannot be definitively classified into re-infections, recrudescences or relapses, the probability of each can be estimated, allowing a probabilistic relapse phenotype to be assigned to a
P. vivax positive sample and, therefore, investigate the statistical association between relapses and epidemiological covariates.
The association between anti-malarial treatment and the incidence of
P. vivax relapses in a population is complex, and depends on the duration of prophylactic protection provided by the drug [
27]. After the initial treatment regimen of AL plus CQ in the placebo arm of the PNG cohort, a rebound in
P. vivax genotype prevalence is observed (Fig.
6b). Similar findings have been reported by Tarning et al. [
45], where a surge in the incidence of
P. vivax relapses is predicted at 3, 6 and 9 weeks following treatment with dihydroartemisinin-piperaquine. It is hypothesized that this is due to the suppression by treatment prophylaxis of blood-stage parasites originating from relapses, with parasite densities rebounding after drug concentrations have waned.
The statistical model presented here provides a useful tool for detailed analysis of P. falciparum and P. vivax infection dynamics in longitudinal cohort studies. There are potentially important contributions to be made in the study of P. vivax, where infections can be assigned a probabilistic relapse phenotype allowing investigation of the association between epidemiological covariates and the incidence of relapses, facilitating a better understanding of the contribution of relapses to P. vivax transmission.
Authors’ contributions
Conceived and designed the epidemiological studies: IM, IF, WN, JS, RL, LR. Designed and implemented the genotyping: IF, CK, RL, RW, NH. Developed the analysis plan: MW, SK, TS, AG, IM. Analysed the data: MW, SK. Wrote the manuscript: MW. All authors read and approved the final manuscript.