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A characteristic of malaria in all its forms is the potential for superinfection (that is, multiple concurrent blood-stage infections). An additional characteristic of Plasmodium vivax malaria is a reservoir of latent parasites (hypnozoites) within the host liver, which activate to cause (blood-stage) relapses. Here, we present a model of hypnozoite accrual and superinfection for P. vivax. To couple host and vector dynamics for a homogeneously-mixing population, we construct a density-dependent Markov population process with countably many types, for which disease extinction is shown to occur almost surely. We also establish a functional law of large numbers, taking the form of an infinite-dimensional system of ordinary differential equations that can also be recovered by coupling expected host and vector dynamics (i.e. a hybrid approximation) or through a standard compartment modelling approach. Recognising that the subset of these equations that model the infection status of the human hosts has precisely the same form as the Kolmogorov forward equations for a Markovian network of infinite server queues with an inhomogeneous batch arrival process, we use physical insight into the evolution of the latter process to write down a time-dependent multivariate generating function for the solution. We use this characterisation to collapse the infinite-compartment model into a single integrodifferential equation (IDE) governing the intensity of mosquito-to-human transmission. Through a steady state analysis, we recover a threshold phenomenon for this IDE in terms of a parameter [Formula: see text] expressible in terms of the primitives of the model, with the disease-free equilibrium shown to be uniformly asymptotically stable if [Formula: see text] and an endemic equilibrium solution emerging if [Formula: see text]. Our work provides a theoretical basis to explore the epidemiology of P. vivax, and introduces a strategy for constructing tractable population-level models of

Plasmodium vivax is one of the most geographically widespread malaria parasites in the world, primarily found across South-East Asia, Latin America, and parts of Africa. One of the significant characteristics of the P. vivax parasite is its ability to remain dormant in the human liver as hypnozoites and subsequently reactivate after the initial infection (i.e. relapse infections). Mathematical modelling approaches have been widely applied to understand P. vivax dynamics and predict the impact of intervention outcomes. Models that capture P. vivax dynamics differ from those that capture P. falciparum dynamics, as they must account for relapses caused by the activation of hypnozoites. In this article, we provide a scoping review of mathematical models that capture P. vivax transmission dynamics published between January 1988 and May 2023. The primary objective of this work is to provide a comprehensive summary of the mathematical models and techniques used to model P. vivax dynamics. In doing so, we aim to assist researchers working on mathematical epidemiology, disease transmission, and other aspects of P. vivax malaria by highlighting best practices in currently published models and highlighting where further model development is required. We categorise P. vivax models according to whether a deterministic or agent-based approach was used. We provide an overview of the different strategies used to incorporate the parasite's biology, use of multiple scales (within-host and population-level), superinfection, immunity, and treatment interventions. In most of the published literature, the rationale for different modelling approaches was driven by the research question at hand. Some models focus on the parasites' complicated biology, while others incorporate simplified assumptions to avoid model complexity. Overall, the existing literature on mathematical models for P. vivax encompasses various aspects of the parasite's dynamics. We recommend that future research should f

Plasmodium vivax is now the main cause of malaria outside Africa. The gametocytocidal effects of antimalarial drugs are important to reduce malaria transmissibility, particularly in low-transmission settings, but they are not well characterized for P. vivax. The transmission-blocking effects of chloroquine, artesunate, and methylene blue on P. vivax gametocytes were assessed. Blood specimens were collected from patients presenting with vivax malaria, incubated with or without the tested drugs, and then fed to mosquitos from a laboratory-adapted colony of Anopheles dirus (a major malaria vector in Southeast Asia). The effects on oocyst and sporozoite development were analyzed under a multi-level Bayesian model accounting for assay variability and the heterogeneity of mosquito Plasmodium infection. Artesunate and methylene blue, but not chloroquine, exhibited potent transmission-blocking effects. Gametocyte exposures to artesunate and methylene blue reduced the mean oocyst count 469-fold (95% CI: 345 to 650) and 1,438-fold (95% CI: 970 to 2,064), respectively. The corresponding estimates for the sporozoite stage were a 148-fold reduction (95% CI: 61 to 470) and a 536-fold reduction (95% CI: 246 to 1,311) in the mean counts, respectively. In contrast, high chloroquine exposures reduced the mean oocyst count only 1.40-fold (95% CI: 1.20 to 1.64) and the mean sporozoite count 1.34-fold (95% CI: 1.12 to 1.66). This suggests that patients with vivax malaria often remain infectious to anopheline mosquitos after treatment with chloroquine. Use of artemisinin combination therapies or immediate initiation of primaquine radical cure should reduce the transmissibility of P. vivax infections.

In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a probability generating function for the transient occupancy distribution of the network and prove that it is necessary and sufficient for ergodicity that the expected occupancy time for each batch be finite. Further, we recover recurrence relations for the transient probability mass function formulated in terms of a distribution obtained by compounding the batch size with a multinomial distribution.

Plasmodium vivax is the most geographically widespread malaria-causing parasite resulting in significant associated global morbidity and mortality. One of the factors driving this widespread phenomenon is the ability of the parasites to remain dormant in the liver. Known as 'hypnozoites', they reside in the liver following an initial exposure, before activating later to cause further infections, referred to as 'relapses'. As around 79-96% of infections are attributed to relapses from activating hypnozoites, we expect it will be highly impactful to apply treatment to target the hypnozoite reservoir (i.e. the collection of dormant parasites) to eliminate P. vivax. Treatment with radical cure, for example tafenoquine or primaquine, to target the hypnozoite reservoir is a potential tool to control and/or eliminate P. vivax. We have developed a deterministic multiscale mathematical model as a system of integro-differential equations that captures the complex dynamics of P. vivax hypnozoites and the effect of hypnozoite relapse on disease transmission. Here, we use our multiscale model to study the anticipated effect of radical cure treatment administered via a mass drug administration (MDA) program. We implement multiple rounds of MDA with a fixed interval between rounds, starting from different steady-state disease prevalences. We then construct an optimisation model with three different objective functions motivated on a public health basis to obtain the optimal MDA interval. We also incorporate mosquito seasonality in our model to study its effect on the optimal treatment regime. We find that the effect of MDA interventions is temporary and depends on the pre-intervention disease prevalence (and choice of model parameters) as well as the number of MDA rounds under consideration. The optimal interval between MDA rounds also depends on the objective (combinations of expected intervention outcomes). We find radical cure alone may not be enough to lead to P. vivax elimina

With emerging resistance to frontline treatments, it is vital that new antimalarial drugs are identified to target Plasmodium falciparum. We have recently described a compound, MMV020291, as a specific inhibitor of red blood cell (RBC) invasion, and have generated analogues with improved potency. Here, we generated resistance to MMV020291 and performed whole genome sequencing of 3 MMV020291-resistant populations. This revealed 3 nonsynonymous single nucleotide polymorphisms in 2 genes; 2 in profilin (N154Y, K124N) and a third one in actin-1 (M356L). Using CRISPR-Cas9, we engineered these mutations into wild-type parasites, which rendered them resistant to MMV020291. We demonstrate that MMV020291 reduces actin polymerisation that is required by the merozoite stage parasites to invade RBCs. Additionally, the series inhibits the actin-1-dependent process of apicoplast segregation, leading to a delayed death phenotype. In vitro cosedimentation experiments using recombinant P. falciparum proteins indicate that potent MMV020291 analogues disrupt the formation of filamentous actin in the presence of profilin. Altogether, this study identifies the first compound series interfering with the actin-1/profilin interaction in P. falciparum and paves the way for future antimalarial development against the highly dynamic process of actin polymerisation.

Investigation of the diversity of malaria parasite antigens can help prioritize and validate them as vaccine candidates and identify the most common variants for inclusion in vaccine formulations. Studies of vaccine candidates of the most virulent human malaria parasite, Plasmodium falciparum, have focused on a handful of well-known antigens, while several others have never been studied. Here we examine the global diversity and population structure of leading vaccine candidate antigens of P. falciparum using the MalariaGEN Pf3K (version 5.1) resource, comprising more than 2600 genomes from 15 malaria endemic countries. A stringent variant calling pipeline was used to extract high quality antigen gene 'haplotypes' from the global dataset and a new R-package named VaxPack was used to streamline population genetic analyses. In addition, a newly developed algorithm that enables spatial averaging of selection pressure on 3D protein structures was applied to the dataset. We analysed the genes encoding 23 leading and novel candidate malaria vaccine antigens including csp, trap, eba175, ama1, rh5, and CelTOS. Our analysis shows that current malaria vaccine formulations are based on rare haplotypes and thus may have limited efficacy against natural parasite populations. High levels of diversity with evidence of balancing selection was detected for most of the erythrocytic and pre-erythrocytic antigens. Measures of natural selection were then mapped to 3D protein structures to predict targets of functional antibodies. For some antigens, geographical variation in the intensity and distribution of these signals on the 3D structure suggests adaptation to different human host or mosquito vector populations. This study provides an essential framework for the diversity of P. falciparum antigens to be considered in the design of the next generation of malaria vaccines.

Investigation of the diversity of malaria parasite antigens can help prioritize and validate them as vaccine candidates and identify the most common variants for inclusion in vaccine formulations. Studies of vaccine candidates of the most virulent human malaria parasite, Plasmodium falciparum, have focused on a handful of well-known antigens, while several others have never been studied. Here we examine the global diversity and population structure of leading vaccine candidate antigens of P. falciparum using the MalariaGEN Pf3K (version 5.1) resource, comprising more than 2600 genomes from 15 malaria endemic countries. A stringent variant calling pipeline was used to extract high quality antigen gene 'haplotypes' from the global dataset and a new R-package named VaxPack was used to streamline population genetic analyses. In addition, a newly developed algorithm that enables spatial averaging of selection pressure on 3D protein structures was applied to the dataset. We analysed the genes encoding 23 leading and novel candidate malaria vaccine antigens including csp, trap, eba175, ama1, rh5, and CelTOS. Our analysis shows that current malaria vaccine formulations are based on rare haplotypes and thus may have limited efficacy against natural parasite populations. High levels of diversity with evidence of balancing selection was detected for most of the erythrocytic and pre-erythrocytic antigens. Measures of natural selection were then mapped to 3D protein structures to predict targets of functional antibodies. For some antigens, geographical variation in the intensity and distribution of these signals on the 3D structure suggests adaptation to different human host or mosquito vector populations. This study provides an essential framework for the diversity of P. falciparum antigens to be considered in the design of the next generation of malaria vaccines.

Malaria is caused by Plasmodium parasites which are transmitted to humans by the bite of an infected Anopheles mosquito. Plasmodium vivax is distinct from other malaria species in its ability to remain dormant in the liver (as hypnozoites) and activate later to cause further infections (referred to as relapses). Mathematical models to describe the transmission dynamics of P. vivax have been developed, but most of them fail to capture realistic dynamics of hypnozoites. Models that do capture the complexity tend to involve many governing equations, making them difficult to extend to incorporate other important factors for P. vivax, such as treatment status, age and pregnancy. In this paper, we have developed a multiscale model (a system of integro-differential equations) that involves a minimal set of equations at the population scale, with an embedded within-host model that can capture the dynamics of the hypnozoite reservoir. In this way, we can gain key insights into dynamics of P. vivax transmission with a minimum number of equations at the population scale, making this framework readily scalable to incorporate more complexity. We performed a sensitivity analysis of our multiscale model over key parameters and found that prevalence of P. vivax blood-stage infection increases with both bite rate and number of mosquitoes but decreases with hypnozoite death rate. Since our mathematical model captures the complex dynamics of P. vivax and the hypnozoite reservoir, it has the potential to become a key tool to inform elimination strategies for P. vivax.

A key characteristic of Plasmodium vivax parasites is their ability to adopt a latent liver-stage form called hypnozoites, able to cause relapse of infection months or years after a primary infection. Relapses of infection through hypnozoite activation are a major contributor to blood-stage infections in P vivax endemic regions and are thought to be influenced by factors such as febrile infections which may cause temporary changes in hypnozoite activation leading to 'temporal heterogeneity' in reactivation risk. In addition, immunity and variation in exposure to infection may be longer-term characteristics of individuals that lead to 'population heterogeneity' in hypnozoite activation. We analyze data on risk of P vivax in two previously published data sets from Papua New Guinea and the Thailand-Myanmar border region. Modeling different mechanisms of reactivation risk, we find strong evidence for population heterogeneity, with 30% of patients having almost 70% of all P vivax infections. Model fitting and data analysis indicates that individual variation in relapse risk is a primary source of heterogeneity of P vivax risk of recurrences. Trial Registration: ClinicalTrials.gov NCT01640574, NCT01074905, NCT02143934.

Malaria is a mosquito-borne disease with a devastating global impact. Plasmodium vivax is a major cause of human malaria beyond sub-Saharan Africa. Relapsing infections, driven by a reservoir of liver-stage parasites known as hypnozoites, present unique challenges for the control of P. vivax malaria. Following indeterminate dormancy periods, hypnozoites may activate to trigger relapses. Clearance of the hypnozoite reservoir through drug treatment (radical cure) has been proposed as a potential tool for the elimination of P. vivax malaria. Here, we introduce a stochastic, within-host model to jointly characterise hypnozoite and infection dynamics for an individual in a general transmission setting, allowing for radical cure. We begin by extending an existing activation-clearance model for a single hypnozoite, adapted to both short- and long-latency strains, to include drug treatment. We then embed this activation-clearance model in an epidemiological framework accounting for repeated mosquito inoculation and the administration of radical cure. By constructing an open network of infinite server queues, we derive analytic expressions for several quantities of epidemiological significance, including the size of the hypnozoite reservoir; the relapse rate; the relative contribution of relapses to the infection burden; the distribution of multiple infections; the cumulative number of recurrences over time, and the time to first recurrence following drug treatment. We derive from first principles the functional dependence between within-host and transmission parameters and patterns of blood- and liver-stage infection, whilst allowing for treatment under a mass drug administration regime. To yield population-level insights, our analytic within-host distributions can be embedded in multiscale models. Our work thus contributes to the epidemiological understanding of the effects of radical cure on P. vivax malaria.

Large-scale comparative genomics- and population genetic studies generate enormous amounts of polymorphism data in the form of DNA variants. Ultimately, the goal of many of these studies is to associate genetic variants to phenotypes or fitness. We introduce VIVID, an interactive, user-friendly web application that integrates a wide range of approaches for encoding genotypic to phenotypic information in any organism or disease, from an individual or population, in three-dimensional (3D) space. It allows mutation mapping and annotation, calculation of interactions and conservation scores, prediction of harmful effects, analysis of diversity and selection, and 3D visualization of genotypic information encoded in Variant Call Format on AlphaFold2 protein models. VIVID enables the rapid assessment of genes of interest in the study of adaptive evolution and the genetic load, and it helps prioritizing targets for experimental validation. We demonstrate the utility of VIVID by exploring the evolutionary genetics of the parasitic protist Plasmodium falciparum, revealing geographic variation in the signature of balancing selection in potential targets of functional antibodies.