102 research outputs found
Wound healing angiogenesis: The clinical implications of a simple mathematical model
Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds
Haplotype frequency inference from pooled genetic data with a latent multinomial model
In genetic studies, haplotype data provide more refined information than data
about separate genetic markers. However, large-scale studies that genotype
hundreds to thousands of individuals may only provide results of pooled data,
where only the total allele counts of each marker in each pool are reported.
Methods for inferring haplotype frequencies from pooled genetic data that scale
well with pool size rely on a normal approximation, which we observe to produce
unreliable inference when applied to real data. We illustrate cases where the
approximation breaks down, due to the normal covariance matrix being
near-singular. As an alternative to approximate methods, in this paper we
propose exact methods to infer haplotype frequencies from pooled genetic data
based on a latent multinomial model, where the observed allele counts are
considered integer combinations of latent, unobserved haplotype counts. One of
our methods, latent count sampling via Markov bases, achieves approximately
linear runtime with respect to pool size. Our exact methods produce more
accurate inference over existing approximate methods for synthetic data and for
data based on haplotype information from the 1000 Genomes Project. We also
demonstrate how our methods can be applied to time-series of pooled genetic
data, as a proof of concept of how our methods are relevant to more complex
hierarchical settings, such as spatiotemporal models.Comment: 35 pages, 16 figures, 3 algorithms, submitted to Biometrics journa
Standardizing the measurement of parasite clearance in falciparum malaria: the parasite clearance estimator
<p>Abstract</p> <p>Background</p> <p>A significant reduction in parasite clearance rates following artesunate treatment of falciparum malaria, and increased failure rates following artemisinin combination treatments (ACT), signaled emergent artemisinin resistance in Western Cambodia. Accurate measurement of parasite clearance is therefore essential to assess the spread of artemisinin resistance in <it>Plasmodium falciparum</it>. The slope of the log-parasitaemia <it>versus </it>time relationship is considered to be the most robust measure of anti-malarial effect. However, an initial lag phase of numerical instability often precedes a steady exponential decline in the parasite count after the start of anti-malarial treatment. This lag complicates the clearance estimation, introduces observer subjectivity, and may influence the accuracy and consistency of reported results.</p> <p>Methods</p> <p>To address this problem, a new approach to modelling clearance of malaria parasites from parasitaemia-time profiles has been explored and validated. The methodology detects when a lag phase is present, selects the most appropriate model (linear, quadratic or cubic) to fit log-transformed parasite data, and calculates estimates of parasite clearance adjusted for this lag phase. Departing from previous approaches, parasite counts below the level of detection are accounted for and not excluded from the calculation.</p> <p>Results</p> <p>Data from large clinical studies with frequent parasite counts were examined. The effect of a lag phase on parasite clearance rate estimates is discussed, using individual patient data examples. As part of the World Wide Antimalarial Resistance Network's (WWARN) efforts to make innovative approaches available to the malaria community, an automated informatics tool: the parasite clearance estimator has been developed.</p> <p>Conclusions</p> <p>The parasite clearance estimator provides a consistent, reliable and accurate method to estimate the lag phase and malaria parasite clearance rate. It could be used to detect early signs of emerging resistance to artemisinin derivatives and other compounds which affect ring-stage clearance.</p
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 âhypnozoitesâ, they reside in the liver following an initial exposure, before activating later to cause further infections, referred to as ârelapsesâ. As around 79â96% 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 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
Bayesian Hierarchical Regression on Clearance Rates in the Presence of Lag and Tail Phases with an Application to Malaria Parasites
We present a principled technique for estimating the effect of covariates on malaria parasite clearance rates in the presence of âlagâ and âtailâ 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\u27s 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
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
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