Patient variability in the blood-stage dynamics of Plasmodium falciparum captured by clustering historical data.

BACKGROUND: Mathematical models provide an understanding of the dynamics of a Plasmodium falciparum blood-stage infection (within-host models), and can predict the impact of control strategies that affect the blood-stage of malaria. However, the dynamics of P. falciparum blood-stage infections are highly variable between individuals. Within-host models use different techniques to capture this inter-individual variation. This struggle may be unnecessary because patients can be clustered according to similar key within-host dynamics. This study aimed to identify clusters of patients with similar parasitaemia profiles so that future mathematical models can include an improved understanding of within-host variation. METHODS: Patients' parasitaemia data were analyzed to identify (i) clusters of patients (from 35 patients) that have a similar overall parasitaemia profile and (ii) clusters of patients (from 100 patients) that have a similar first wave of parasitaemia. For each cluster analysis, patients were clustered based on key features which previous models used to summarize parasitaemia dynamics. The clustering analyses were performed using a finite mixture model. The centroid values of the clusters were used to parameterize two established within-host models to generate parasitaemia profiles. These profiles (that used the novel centroid parameterization) were compared with profiles that used individual-specific parameterization (as in the original models), as well as profiles that ignored individual variation (using overall means for parameterization). RESULTS: To capture the variation of within-host dynamics, when studying the overall parasitaemia profile, two clusters efficiently grouped patients based on their infection length and the height of the first parasitaemia peak. When studying the first wave of parasitaemia, five clusters efficiently grouped patients based on the height of the peak and the speed of the clearance following the peak of parasitaemia. The clusters were based on features that summarize the strength of patient innate and adaptive immune responses. Parameterizing previous within host-models based on cluster centroid values accurately predict individual patient parasitaemia profiles. CONCLUSION: This study confirms that patients have personalized immune responses, which explains the variation of parasitaemia dynamics. Clustering can guide the optimal inclusion of within-host variation in future studies, and inform the design and parameterization of population-based models.

The empirical support for the radical cure strategy for eliminating Plasmodium vivax in China.

BACKGROUND: With the recent certification by World Health Organization that the People's Republic of China is malaria-free, it is timely to consider how elimination of malaria was completed in People's Republic of China over the last 7 decades. Of the four widespread species of human malaria, Plasmodium vivax was the last to be eliminated by the national program of China. Understanding the incubation periods and relapses patterns of P. vivax through historical data from China is relevant for planning disease elimination in other malaria-endemic countries, with residual P. vivax malaria. METHODS: We collated data from both published and unpublished malaria parasite inoculation experiments conducted between 1979 and 1988 with parasites from different regions of the People's Republic of China. The studies had at least two years of follow-up. We categorized P. vivax incubation patterns via cluster analysis and investigated relapse studies by adapting a published within-host relapse model for P. vivax temperate phenotypes. Each model was fitted using the expectation-maximization (EM) algorithm initialized by hierarchical model-based agglomerative clustering. RESULTS: P. vivax parasites from the seven studies of five southern and central provinces in the People's Republic of China covering geographies ranging from the south temperate to north tropical zones. The parasites belonged to two distinct phenotypes: short- (10-19 days) or long-incubation (228-371 days). The larger the sporozoite inoculation, the more likely short incubation periods were observed, and with more subsequent relapses (Spearman's rank correlation between the number of inoculated sporozoites and the number of relapses of 0.51, p-value = 0.0043). The median of the posterior distribution for the duration of the first relapse interval after primary infection was 168.5 days (2.5% quantile: 89.7; 97.5% quantile: 227.69 days). The predicted survival proportions from the within-host model fit well to the original relapse data. The within-host model also captures the hypnozoite activation rates and relapse frequencies, which consequently influences the transmission possibility of P. vivax. CONCLUSIONS: Through a within-host model, we demonstrate the importance of clearance of hypnozoites. A strategy of two rounds of radical hypnozoite clearance via mass drug administration (MDA) deployed during transmission (summer and autumn) and non-transmission (late spring) seasons had a pronounced effect on outbreaks during the malaria epidemics in China. This understanding can inform malaria control strategies in other endemic countries with similar settings.

Mechanistic within-host models of the asexual Plasmodium falciparum infection: a review and analytical assessment.

BACKGROUND: Malaria blood-stage infection length and intensity are important drivers of disease and transmission; however, the underlying mechanisms of parasite growth and the host's immune response during infection remain largely unknown. Over the last 30 years, several mechanistic mathematical models of malaria parasite within-host dynamics have been published and used in malaria transmission models. METHODS: Mechanistic within-host models of parasite dynamics were identified through a review of published literature. For a subset of these, model code was reproduced and descriptive statistics compared between the models using fitted data. Through simulation and model analysis, key features of the models were compared, including assumptions on growth, immune response components, variant switching mechanisms, and inter-individual variability. RESULTS: The assessed within-host malaria models generally replicate infection dynamics in malaria-naïve individuals. However, there are substantial differences between the model dynamics after disease onset, and models do not always reproduce late infection parasitaemia data used for calibration of the within host infections. Models have attempted to capture the considerable variability in parasite dynamics between individuals by including stochastic parasite multiplication rates; variant switching dynamics leading to immune escape; variable effects of the host immune responses; or via probabilistic events. For models that capture realistic length of infections, model representations of innate immunity explain early peaks in infection density that cause clinical symptoms, and model representations of antibody immune responses control the length of infection. Models differed in their assumptions concerning variant switching dynamics, reflecting uncertainty in the underlying mechanisms of variant switching revealed by recent clinical data during early infection. Overall, given the scarce availability of the biological evidence there is limited support for complex models. CONCLUSIONS: This study suggests that much of the inter-individual variability observed in clinical malaria infections has traditionally been attributed in models to random variability, rather than mechanistic disease dynamics. Thus, it is proposed that newly developed models should assume simple immune dynamics that minimally capture mechanistic understandings and avoid over-parameterization and large stochasticity which inaccurately represent unknown disease mechanisms.

Identifying key factors of the transmission dynamics of drug-resistant malaria.

Development of resistance to malaria treatments remains a great threat to continued malaria burden reduction and elimination. Quantifying the impact of key factors which increase the emergence and spread of drug resistance can guide intervention strategies. Whilst modelling provides a framework to understand these factors, we show that a simple of model with a sensitive-resistant dichotomy leads to incorrectly focusing on reducing the treatment rate as a means to prevent resistance. Instead we present a model that considers the development of resistance within hosts as a scale, and we then quantify the number of resistant infections that would arise from a single sensitive infection. By including just one step before full resistance, the model highlights that disrupting this development is more effective than reducing treatment rate. This result is compounded when the model includes the more realistic scenario of several intermediary steps. An additional comparison to transmission probabilities, where resistant infections are less likely to be transmitted (cost of resistance), confirms that preventing the establishment of resistance is more effective than controlling the spread. Our work strongly advocates for further studies into within-host models of resistance, including the potential of combination therapies to disrupt emergence.

Are extinction opinions extinct?

Extinction models vary in the information they require, the simplest considering the rate of certain sightings only. More complicated methods include uncertain sightings and allow for variation in the reliability of uncertain sightings. Generally extinction models require expert opinion, either as a prior belief that a species is extinct, or to establish the quality of a sighting record, or both. Is this subjectivity necessary? We present two models to explore whether the individual quality of sightings, judged by experts, is strongly informative of the probability of extinction: the 'quality breakpoint method' and the 'quality as variance method'. For the first method we use the Barbary lion as an exemplar. For the second method we use the Barbary lion, Alaotra grebe, Jamaican petrel and Pohnpei starling as exemplars. The 'quality breakpoint method' uses certain and uncertain sighting records, and the quality of uncertain records, to establish whether a change point in the rate of sightings can be established using a simultaneous Bayesian optimisation with a non-informative prior. For the Barbary lion, there is a change in subjective quality of sightings around 1930. Unexpectedly sighting quality increases after this date. This suggests that including quality scores from experts can lead to irregular effects and may not offer reliable results. As an alternative, we use quality as a measure of variance around the sightings, not a change in quality. This leads to predictions with larger standard deviations, however the results remain consistent across any prior belief of extinction. Nonetheless, replacing actual quality scores with random quality scores showed little difference, inferring that the quality scores from experts are superfluous. Therefore, we deem the expensive process of obtaining pooled expert estimates as unnecessary, and even when used we recommend that sighting data should have minimal input from experts in terms of assessing the sighting quality at a fine scale. Rather, sightings should be classed as certain or uncertain, using a framework that is as independent of human bias as possible.

Extinct or still out there? Disentangling influences on extinction and rediscovery helps to clarify the fate of species on the edge.

Each year, two or three species that had been considered to be extinct are rediscovered. Uncertainty about whether or not a species is extinct is common, because rare and highly threatened species are difficult to detect. Biological traits such as body size and range size are expected to be associated with extinction. However, these traits, together with the intensity of search effort, might influence the probability of detection and extinction differently. This makes statistical analysis of extinction and rediscovery challenging. Here, we use a variant of survival analysis known as cure rate modelling to differentiate factors that influence rediscovery from those that influence extinction. We analyse a global data set of 99 mammals that have been categorized as extinct or possibly extinct. We estimate the probability that each of these mammals is still extant and thus estimate the proportion of missing (presumed extinct) mammals that are incorrectly assigned extinction. We find that body mass and population density are predictors of extinction, and body mass and search effort predict rediscovery. In mammals, extinction rate increases with body mass and population density, and these traits act synergistically to greatly elevate extinction rate in large species that also occurred in formerly dense populations. However, when they remain extant, larger-bodied missing species are rediscovered sooner than smaller species. Greater search effort increases the probability of rediscovery in larger species of missing mammals, but has a minimal effect on small species, which take longer to be rediscovered, if extant. By separating the effects of species characteristics on extinction and detection, and using models with the assumption that a proportion of missing species will never be rediscovered, our new approach provides estimates of extinction probability in species with few observation records and scant ecological information.

Estimating the extent and structure of trade in horticultural orchids via social media.

The wildlife trade is a lucrative industry involving thousands of animal and plant species. The increasing use of the internet for both legal and illegal wildlife trade is well documented, but there is evidence that trade may be emerging on new online technologies such as social media. Using the orchid trade as a case study, we conducted the first systematic survey of wildlife trade on an international social-media website. We focused on themed forums (groups), where people with similar interests can interact by uploading images or text (posts) that are visible to other group members. We used social-network analysis to examine the ties between 150 of these orchid-themed groups to determine the structure of the network. We found 4 communities of closely linked groups based around shared language. Most trade occurred in a community that consisted of English-speaking and Southeast Asian groups. In addition to the network analysis, we randomly sampled 30 groups from the whole network to assess the prevalence of trade in cultivated and wild plants. Of 55,805 posts recorded over 12 weeks, 8.9% contained plants for sale, and 22-46% of these posts pertained to wild-collected orchids. Although total numbers of posts about trade were relatively small, the large proportion of posts advertising wild orchids for sale supports calls for better monitoring of social media for trade in wild-collected plants.

Assessing uncertainty in sighting records: an example of the Barbary lion.

As species become rare and approach extinction, purported sightings can be controversial, especially when scarce management resources are at stake. We consider the probability that each individual sighting of a series is valid. Obtaining these probabilities requires a strict framework to ensure that they are as accurately representative as possible. We used a process, which has proven to provide accurate estimates from a group of experts, to obtain probabilities for the validation of 32 sightings of the Barbary lion. We consider the scenario where experts are simply asked whether a sighting was valid, as well as asking them to score the sighting based on distinguishablity, observer competence, and verifiability. We find that asking experts to provide scores for these three aspects resulted in each sighting being considered more individually, meaning that this new questioning method provides very different estimated probabilities that a sighting is valid, which greatly affects the outcome from an extinction model. We consider linear opinion pooling and logarithm opinion pooling to combine the three scores, and also to combine opinions on each sighting. We find the two methods produce similar outcomes, allowing the user to focus on chosen features of each method, such as satisfying the marginalisation property or being externally Bayesian.