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Table Of Integrals Series And Products

BACKGROUND: Artemisinin resistance in Plasmodium falciparum has emerged in Southeast Asia and now poses a threat to the control and elimination of malaria. Mapping the geographic extent of resistance is essential for planning containment and elimination strategies. METHODS: Between May 2011 and April 2013, we enrolled 1241 adults and children with acute, uncomplicated falciparum malaria in an open-label trial at 15 sites in 10 countries (7 in Asia and 3 in Africa). Patients received artesunate, administered orally at a daily dose of either 2 mg per kilogram of body weight per day or 4 mg per kilogram, for 3 days, followed by a standard 3-day course of artemisinin-based combination therapy. Parasite counts in peripheral-blood samples were measured every 6 hours, and the parasite clearance half-lives were determined. RESULTS: The median parasite clearance half-lives ranged from 1.9 hours in the Democratic Republic of Congo to 7.0 hours at the Thailand-Cambodia border. Slowly clearing infections (parasite clearance half-life >5 hours), strongly associated with single point mutations in the "propeller" region of the P. falciparum kelch protein gene on chromosome 13 (kelch13), were detected throughout mainland Southeast Asia from southern Vietnam to central Myanmar. The incidence of pretreatment and post-treatment gametocytemia was higher among patients with slow parasite clearance, suggesting greater potential for transmission. In western Cambodia, where artemisinin-based combination therapies are failing, the 6-day course of antimalarial therapy was associated with a cure rate of 97.7% (95% confidence interval, 90.9 to 99.4) at 42 days. CONCLUSIONS: Artemisinin resistance to P. falciparum, which is now prevalent across mainland Southeast Asia, is associated with mutations in kelch13. Prolonged courses of artemisinin-based combination therapies are currently efficacious in areas where standard 3-day treatments are failing. (Funded by the U.K. Department of International Development and others; ClinicalTrials.gov number, NCT01350856.).

/pdf/spread-of-artemisinin-resistance-in-plasmodium-falciparum-46uaot49qx.pdf

Spread of Artemisinin Resistance in Plasmodium falciparum Malaria

Plasmodium falciparum resistance to artemisinin derivatives in southeast Asia threatens malaria control and elimination activities worldwide. To monitor the spread of artemisinin resistance, a molecular marker is urgently needed. Here, using whole-genome sequencing of an artemisinin-resistant parasite line from Africa and clinical parasite isolates from Cambodia, we associate mutations in the PF3D7_1343700 kelch propeller domain ('K13-propeller') with artemisinin resistance in vitro and in vivo. Mutant K13-propeller alleles cluster in Cambodian provinces where resistance is prevalent, and the increasing frequency of a dominant mutant K13-propeller allele correlates with the recent spread of resistance in western Cambodia. Strong correlations between the presence of a mutant allele, in vitro parasite survival rates and in vivo parasite clearance rates indicate that K13-propeller mutations are important determinants of artemisinin resistance. K13-propeller polymorphism constitutes a useful molecular marker for large-scale surveillance efforts to contain artemisinin resistance in the Greater Mekong Subregion and prevent its global spread.

/pdf/a-molecular-marker-of-artemisinin-resistant-plasmodium-1t4308ovc0.pdf

A molecular marker of artemisinin-resistant Plasmodium falciparum malaria

The electronic properties and relatively small size of fluorine endow it with considerable versatility as a bioisostere and it has found application as a substitute for lone pairs of electrons, the hydrogen atom, and the methyl group while also acting as a functional mimetic of the carbonyl, carbinol, and nitrile moieties. In this context, fluorine substitution can influence the potency, conformation, metabolism, membrane permeability, and P-gp recognition of a molecule and temper inhibition of the hERG channel by basic amines. However, as a consequence of the unique properties of fluorine, it features prominently in the design of higher order structural metaphors that are more esoteric in their conception and which reflect a more sophisticated molecular construction that broadens biological mimesis. In this Perspective, applications of fluorine in the construction of bioisosteric elements designed to enhance the in vitro and in vivo properties of a molecule are summarized.

Fluorine and Fluorinated Motifs in the Design and Application of Bioisosteres for Drug Design.

The United Nations Children's Fund, or UNICEF, was originally created to provide relief for children in countries devastated by the destruction of World War II. After 1950, UNICEF turned to focus on general programs for the improvement of children's welfare worldwide, and in 1965, it was awarded the Nobel Prize for Peace for its humanitarian efforts. The organization concentrates on areas in which relatively small expenditures can have a significant impact on the lives of the most disadvantaged children in developing countries, such as the prevention and treatment of disease, child healthcare, malnutrition, illiteracy, and other welfare services.

The United Nations Children's Fund

https://link.springer.com/content/pdf/10.1007/s11538-022-01036-0.pdf

A Multiscale Mathematical Model of Plasmodium Vivax Transmission

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 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. By deriving, rather than assuming parameteric forms, we characterise the transient dynamics of the hypnozoite reservoir following radical cure more accurately than previous approaches. 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.

Hypnozoite dynamics for Plasmodium vivax malaria: the epidemiological effects of radical cure

We present a principled technique for estimating the effect of covariates on malaria parasite clearance rates in the presence of "lag" and "tail" phases through the use of a Bayesian hierarchical linear model. The hierarchical approach enables us to appropriately incorporate the uncertainty in both estimating clearance rates in patients and assessing the potential impact of covariates on these rates into the posterior intervals generated for the parameters associated with each covariate. Furthermore, it permits us to incorporate information about individuals for whom there exists only one observation time before censoring, which alleviates a systematic bias affecting inference when these individuals are excluded. We use a changepoint model to account for both lag and tail phases, and hence base our estimation of the parasite clearance rate only on observations within the decay phase. The Bayesian approach allows us to treat the delineation between lag, decay, and tail phases within an individual's clearance profile as themselves being random variables, thus taking into account the additional uncertainty of boundaries between phases. We compare our method to existing methodology used in the antimalarial research community through a simulation study and show that it possesses desirable frequentist properties for conducting inference. We use our methodology to measure the impact of several covariates on Plasmodium falciparum clearance rate data collected in 2009 and 2010. Though our method was developed with this application in mind, it can be easily applied to any biological system exhibiting these hindrances to estimation.

/pdf/bayesian-hierarchical-regression-on-clearance-rates-in-the-1ytgj3j33w.pdf

Bayesian Hierarchical Regression on Clearance Rates in the Presence of "Lag" and "Tail" Phases with an Application to Malaria Parasites

Chronicwounds fail to proceed through an orderly process to produce anatomic and functional integrity and are a significant socioeconomic problem. There is much debate about the best way to treat these wounds. In this thesis we review earlier mathematical models of angiogenesis and wound healing. Many of these models assume a chemotactic response of endothelial cells, the primary cell type involved in angiogenesis. Modelling this chemotactic response leads to a system of advection-dominated partial differential equations and we review numerical methods to solve these equations and argue that the finite volume method with flux limiting is best-suited to these problems. One treatment of chronic wounds that is shrouded with controversy is hyperbaric oxygen therapy (HBOT). There is currently no conclusive data showing that HBOT can assist chronic wound healing, but there has been some clinical success. In this thesis we use several mathematical models of wound healing to investigate the use of hyperbaric oxygen therapy to assist the healing process - a novel threespecies model and a more complex six-species model. The second model accounts formore of the biological phenomena but does not lend itself tomathematical analysis. Bothmodels are then used tomake predictions about the efficacy of hyperbaric oxygen therapy and the optimal treatment protocol. Based on our modelling, we are able to make several predictions including that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds, treatment should continue until healing is complete and finding the right protocol for an individual patient is crucial if HBOT is to be effective. Analysis of the models allows us to derive constraints for the range of HBOT protocols that will stimulate healing, which enables us to predict which patients are more likely to have a positive response to HBOT and thus has the potential to assist in improving both the success rate and thus the cost-effectiveness of this therapy.

Mathematical modelling of chronic wound healing

In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models Qualitative and quantitative data based around the students' approaches to learning new mathematical models were collected The data revealed that students actively adopt three approaches to understanding a new mathematical model: gathering information for the task of understanding the model, practising with and using the model, and finding interrelationships between elements of the model We found that the students appreciate mathematical models that have a real worl application and that this can be used to engage students in higher level learning approaches

Jennifer A. Flegg

Papers

A Multiscale Mathematical Model of Plasmodium Vivax Transmission

Hypnozoite dynamics for Plasmodium vivax malaria: the epidemiological effects of radical cure

Bayesian Hierarchical Regression on Clearance Rates in the Presence of "Lag" and "Tail" Phases with an Application to Malaria Parasites

Mathematical modelling of chronic wound healing

Students' approaches to learning a new mathematical model