Open networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals

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

A Multiscale Mathematical Model of Plasmodium Vivax Transmission

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

Optimal Interruption of P. vivax Malaria Transmission Using Mass Drug Administration

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 elimination under our mathematical model (and choice of model parameters) since the prevalence of infection eventually returns to pre-MDA levels

A scoping review of mathematical models of Plasmodium vivax

Plasmodium vivax is one of the most geographically widespread malaria parasites in the world due to its ability to remain dormant in the human liver as hypnozoites and subsequently reactivate after the initial infection (i.e. relapse infections). More than 80% of P. vivax infections are due to hypnozoite reactivation. Mathematical modelling approaches have been widely applied to understand P. vivax dynamics and predict the impact of intervention outcomes. In this article, we provide a scoping review of mathematical models that capture P. vivax transmission dynamics published between January 1988 and May 2023 to provide a comprehensive summary of the mathematical models and techniques used to model P. vivax dynamics. We aim to assist researchers working on P. vivax transmission and other aspects of P. vivax malaria by highlighting best practices in currently published models and highlighting where future model development is required. 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 focus on refining how key aspects of P. vivax dynamics are modelled, including the accumulation of hypnozoite variation, the interaction between P. falciparum and P. vivax, acquisition of immunity, and recovery under superinfection

Transmission-blocking activities of artesunate, chloroquine, and methylene blue on Plasmodium vivax gametocytes

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

Population heterogeneity in Plasmodium vivax relapse risk

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 ‘popula-tion 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

VIVID: A web application for variant interpretation and visualization in multi-dimensional analyses

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

Aryl amino acetamides prevent Plasmodium falciparum ring development via targeting the lipid-transfer protein PfSTART1.

With resistance to most antimalarials increasing, it is imperative that new drugs are developed. We previously identified an aryl acetamide compound, MMV006833 (M-833), that inhibited the ring-stage development of newly invaded merozoites. Here, we select parasites resistant to M-833 and identify mutations in the START lipid transfer protein (PF3D7_0104200, PfSTART1). Introducing PfSTART1 mutations into wildtype parasites reproduces resistance to M-833 as well as to more potent analogues. PfSTART1 binding to the analogues is validated using organic solvent-based Proteome Integral Solubility Alteration (Solvent PISA) assays. Imaging of invading merozoites shows the inhibitors prevent the development of ring-stage parasites potentially by inhibiting the expansion of the encasing parasitophorous vacuole membrane. The PfSTART1-targeting compounds also block transmission to mosquitoes and with multiple stages of the parasite's lifecycle being affected, PfSTART1 represents a drug target with a new mechanism of action