A mathematical, classical stratification modeling approach to disentangling the impact of weather on infectious diseases: A case study using spatio-temporally disaggregated Campylobacter surveillance data for England and Wales.

Disentangling the impact of the weather on transmission of infectious diseases is crucial for health protection, preparedness and prevention. Because weather factors are co-incidental and partly correlated, we have used geography to separate out the impact of individual weather parameters on other seasonal variables using campylobacteriosis as a case study. Campylobacter infections are found worldwide and are the most common bacterial food-borne disease in developed countries, where they exhibit consistent but country specific seasonality.

A Spatially Resolved Mechanistic Growth Law for Cancer Drug Development Predicting Tumor Growing Fractions.

Unlabelled: Mathematical models used in preclinical drug discovery tend to be empirical growth laws. Such models are well suited to fitting the data available, mostly longitudinal studies of tumor volume; however, they typically have little connection with the underlying physiologic processes. This lack of a mechanistic underpinning restricts their flexibility and potentially inhibits their translation across studies including from animal to human.

Best Practices to Maximize the Use and Reuse of Quantitative and Systems Pharmacology Models: Recommendations From the United Kingdom Quantitative and Systems Pharmacology Network.

The lack of standardization in the way that quantitative and systems pharmacology (QSP) models are developed, tested, and documented hinders their reproducibility, reusability, and expansion or reduction to alternative contexts. This in turn undermines the potential impact of QSP in academic, industrial, and regulatory frameworks. This article presents a minimum set of recommendations from the UK Quantitative and Systems Pharmacology Network (UK QSP Network) to guide QSP practitioners seeking to maximize their impact, and stakeholders considering the use of QSP models in their environment.

A mathematical analysis of rebound in a target-mediated drug disposition model: II. With feedback.

We consider the possibility of free receptor (antigen/cytokine) levels rebounding to higher than the baseline level after the application of an antibody drug using a target-mediated drug disposition model. It is assumed that the receptor synthesis rate experiences homeostatic feedback from the receptor levels. It is shown for a very fast feedback response, that the occurrence of rebound is determined by the ratio of the elimination rates, in a very similar way as for no feedback.

Predicting tyrosinaemia: a mathematical model of 4-hydroxyphenylpyruvate dioxygenase inhibition by nitisinone in rats.

Nitisinone or 2-(2-nitro-4-trifluoromethylbenzoyl)cyclohexane-1,3-dione is a reversible inhibitor of 4-hydroxyphenylpyruvate dioxygenase (HPPD), an enzyme important in tyrosine catabolism. Today, nitisinone is successfully used to treat Hereditary Tyrosinaemia type 1, although its original expected role was as a herbicide. In laboratory animals, treatment with nitisinone leads to the elevation of plasma tyrosine (tyrosinaemia).

Modelling changes in sleep timing and duration across the lifespan: Changes in circadian rhythmicity or sleep homeostasis?

Sleep changes across the lifespan, with a delay in sleep timing and a reduction in slow wave sleep seen in adolescence, followed by further reductions in slow wave sleep but a gradual drift to earlier timing during healthy ageing. The mechanisms underlying changes in sleep timing are unclear: are they primarily related to changes in circadian processes, or to a reduction in the neural activity dependent build up of homeostatic sleep pressure during wake, or both? We review existing studies of age-related changes to sleep and explore how mathematical models can explain observed changes. Model simulations show that typical changes in sleep timing and duration, from adolesence to old age, can be understood in two ways: either as a consequence of a simultaneous reduction in the amplitude of the circadian wake-propensity rhythm and the neural activity dependent build-up of homeostatic sleep pressure during wake; or as a consequence of reduced homeostatic sleep pressure alone.

Mathematical models for sleep-wake dynamics: comparison of the two-process model and a mutual inhibition neuronal model.

Sleep is essential for the maintenance of the brain and the body, yet many features of sleep are poorly understood and mathematical models are an important tool for probing proposed biological mechanisms. The most well-known mathematical model of sleep regulation, the two-process model, models the sleep-wake cycle by two oscillators: a circadian oscillator and a homeostatic oscillator. An alternative, more recent, model considers the mutual inhibition of sleep promoting neurons and the ascending arousal system regulated by homeostatic and circadian processes.

A mathematical analysis of rebound in a target-mediated drug disposition model: I.without feedback.

We consider the possibility of free receptor (antigen/cytokine) levels rebounding to higher than the baseline level after one or more applications of an antibody drug using a target-mediated drug disposition model. Using geometry and dynamical systems analysis, we show that rebound will occur if and only if the elimination rate of the drug-receptor product is slower than the elimination rates of the drug and of the receptor. We also analyse the magnitude of rebound through approximations and simulations and demonstrate that it increases if the drug dose increases or if the difference between the elimination rate of the drug-receptor product and the minimum of the elimination rates of the drug and of the receptor increases.

Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency.

We consider the relationship between the target affinity of a monoclonal antibody and its in vivo potency. The dynamics of the system is described mathematically by a target-mediated drug disposition model. As a measure of potency, we consider the minimum level of the free receptor following a single bolus injection of the ligand into the plasma compartment.