Synchronisation of stochastic oscillators in biochemical systems

A formalism is developed which describes the extent to which stochastic oscillations in biochemical models are synchronised. It is based on the calculation of the complex coherence function within the linear noise approximation. The method is illustrated on a simple example and then applied to study the synchronisation of chemical concentrations in social amoeba. The degree to which variation of rate constants in different cells and the volume of the cells affects synchronisation of the oscillations is explored, and the phase lag calculated. In all cases the analytical results are shown to be in good agreement with those obtained through numerical simulations

Intrinsic noise and two-dimensional maps: Quasicycles, quasiperiodicity, and chaos

We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit of large system sizes is shown to be very well-approximated by a Fokker-Planck-like equation, or equivalently by a set of stochastic difference equations. This formalism is applied to the specific case of two species: one predator species and its prey species. Quasi-cycles --- stochastic cycles sustained and amplified by the demographic noise --- previously found in continuous-time predator-prey models are shown to exist, and their behavior predicted from a linear noise analysis is shown to be in very good agreement with simulations. The effects of the noise on other attractors in the corresponding deterministic map, such as periodic cycles, quasiperiodicity and chaos, are also investigated.Comment: 21 pages, 12 figure

Suppressing escape events in maps of the unit interval with demographic noise

We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the mesoscopic description of the system, the large jumps between successive iterates of the process can result in probability leaking out of the unit interval, despite the fact that the noise is multiplicative and vanishes at the boundaries. By including higher-order terms in the mesoscopic expansion, we are able to capture the non-Gaussian nature of the noise distribution near the boundaries, but this does not preclude the possibility of a trajectory leaving the interval. We propose a number of prescriptions for treating these escape events, and we compare the results with those obtained for the metastable behavior of the microscopic model, where escape events are not possible. We find that, rather than truncating the noise distribution, censoring this distribution to prevent escape events leads to results which are more consistent with the microscopic model. The addition of higher moments to the noise distribution does not increase the accuracy of the final results, and it can be replaced by the simpler Gaussian noise.Comment: 14 pages, 13 figure

Turing instabilities from a limit cycle

The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a consequence, the system evolves towards a stationary, nonhomogeneous attractor. Stable patterns can be also obtained via oscillation quenching of an initially synchronous state of diffusively coupled oscillators. In the literature this is known as the oscillation death phenomenon. Here we show that oscillation death is nothing but a Turing instability for the first return map associated to the excitable system in its synchronous periodic state. In particular we obtain a set of closed conditions for identifying the domain in the parameters space that yields the instability. This is a natural generalisation of the original Turing relations, to the case where the homogeneous solution of the examined system is a periodic function of time. The obtained framework applies to systems embedded in continuum space, as well as those defined on a network-like support. The predictive ability of the theory is tested numerically, using different reaction schemes.Comment: 10 pages, 8 figure

Assessing the impact of imperfect adherence to artemether-lumefantrine on malaria treatment outcomes using within-host modelling.

Artemether-lumefantrine (AL) is the most widely-recommended treatment for uncomplicated Plasmodium falciparum malaria worldwide. Its safety and efficacy have been extensively demonstrated in clinical trials; however, its performance in routine health care settings, where adherence to drug treatment is unsupervised and therefore may be suboptimal, is less well characterised. Here we develop a within-host modelling framework for estimating the effects of sub-optimal adherence to AL treatment on clinical outcomes in malaria patients. Our model incorporates the data on the human immune response to the parasite, and AL's pharmacokinetic and pharmacodynamic properties. Utilising individual-level data of adherence to AL in 482 Tanzanian patients as input for our model predicted higher rates of treatment failure than were obtained when adherence was optimal (9% compared to 4%). Our model estimates that the impact of imperfect adherence was worst in children, highlighting the importance of advice to caregivers

Intrinsic noise and discrete-time processes

A general formalism is developed to construct a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are therefore internal to the system and not externally specified. For finite populations an approximate Gaussian scheme is devised to describe the stochastic fluctuations in the non-chaotic regime. More generally, the stochastic dynamics can be captured using a stochastic difference equation, derived through an approximation to the Markov chain. The scheme is demonstrated using the logistic map as a case study.Comment: Modified version accepted for publication in Phys. Rev. E Rapid Communications. New figures adde

Modelling upper respiratory viral load dynamics of SARS-CoV-2.

Relationships between viral load, severity of illness, and transmissibility of virus are fundamental to understanding pathogenesis and devising better therapeutic and prevention strategies for COVID-19. Here we present within-host modelling of viral load dynamics observed in the upper respiratory tract (URT), drawing upon 2172 serial measurements from 605 subjects, collected from 17 different studies. We developed a mechanistic model to describe viral load dynamics and host response and contrast this with simpler mixed-effects regression analysis of peak viral load and its subsequent decline. We observed wide variation in URT viral load between individuals, over 5 orders of magnitude, at any given point in time since symptom onset. This variation was not explained by age, sex, or severity of illness, and these variables were not associated with the modelled early or late phases of immune-mediated control of viral load. We explored the application of the mechanistic model to identify measured immune responses associated with the control of the viral load. Neutralising antibodies correlated strongly with modelled immune-mediated control of viral load amongst subjects who produced neutralising antibodies. Our models can be used to identify host and viral factors which control URT viral load dynamics, informing future treatment and transmission blocking interventions

Assessing the variability in experimental hut trials evaluating insecticide-treated nets against malaria vectors.

Experimental hut trials (EHTs) are used to evaluate indoor vector control interventions against malaria vectors in a controlled setting. The level of variability present in the assay will influence whether a given study is well powered to answer the research question being considered. We utilised disaggregated data from 15 previous EHTs to gain insight into the behaviour typically observed. Using simulations from generalised linear mixed models to obtain power estimates for EHTs, we show how factors such as the number of mosquitoes entering the huts each night and the magnitude of included random effects can influence study power. A wide variation in behaviour is observed in both the mean number of mosquitoes collected per hut per night (ranging from 1.6 to 32.5) and overdispersion in mosquito mortality. This variability in mortality is substantially greater than would be expected by chance and should be included in all statistical analyses to prevent false precision of results. We utilise both superiority and non-inferiority trials to illustrate our methodology, using mosquito mortality as the outcome of interest. The framework allows the measurement error of the assay to be reliably assessed and enables the identification of outlier results which could warrant further investigation. EHTs are increasingly playing an important role in the evaluation and regulation of indoor vector control interventions so it is important to ensure that these studies are adequately powered. [Abstract copyright: © 2023 The Authors.

The Impact of Delayed Treatment of Uncomplicated \u3ci\u3eP. falciparum\u3c/i\u3e Malaria on Progression to Severe Malaria: A Systematic Review and a Pooled Multicentre Individual-Patient Meta-Analysis

BACKGROUND: Delay in receiving treatment for uncomplicated malaria (UM) is often reported to increase the risk of developing severe malaria (SM), but access to treatment remains low in most high-burden areas. Understanding the contribution of treatment delay on progression to severe disease is critical to determine how quickly patients need to receive treatment and to quantify the impact of widely implemented treatment interventions, such as \u27test-and-treat\u27 policies administered by community health workers (CHWs). We conducted a pooled individual-participant meta-analysis to estimate the association between treatment delay and presenting with SM. METHODS AND FINDINGS: A search using Ovid MEDLINE and Embase was initially conducted to identify studies on severe Plasmodium falciparum malaria that included information on treatment delay, such as fever duration (inception to 22nd September 2017). Studies identified included 5 case-control and 8 other observational clinical studies of SM and UM cases. Risk of bias was assessed using the Newcastle-Ottawa scale, and all studies were ranked as \u27Good\u27, scoring ≥7/10. Individual-patient data (IPD) were pooled from 13 studies of 3,989 (94.1% aged \u3c15 years) SM patients and 5,780 (79.6% aged \u3c15 years) UM cases in Benin, Malaysia, Mozambique, Tanzania, The Gambia, Uganda, Yemen, and Zambia. Definitions of SM were standardised across studies to compare treatment delay in patients with UM and different SM phenotypes using age-adjusted mixed-effects regression. The odds of any SM phenotype were significantly higher in children with longer delays between initial symptoms and arrival at the health facility (odds ratio [OR] = 1.33, 95% CI: 1.07-1.64 for a delay of \u3e24 hours versus ≤24 hours; p = 0.009). Reported illness duration was a strong predictor of presenting with severe malarial anaemia (SMA) in children, with an OR of 2.79 (95% CI:1.92-4.06; p \u3c 0.001) for a delay of 2-3 days and 5.46 (95% CI: 3.49-8.53; p \u3c 0.001) for a delay of \u3e7 days, compared with receiving treatment within 24 hours from symptom onset. We estimate that 42.8% of childhood SMA cases and 48.5% of adult SMA cases in the study areas would have been averted if all individuals were able to access treatment within the first day of symptom onset, if the association is fully causal. In studies specifically recording onset of nonsevere symptoms, long treatment delay was moderately associated with other SM phenotypes (OR [95% CI] \u3e3 to ≤4 days versus ≤24 hours: cerebral malaria [CM] = 2.42 [1.24-4.72], p = 0.01; respiratory distress syndrome [RDS] = 4.09 [1.70-9.82], p = 0.002). In addition to unmeasured confounding, which is commonly present in observational studies, a key limitation is that many severe cases and deaths occur outside healthcare facilities in endemic countries, where the effect of delayed or no treatment is difficult to quantify. CONCLUSIONS: Our results quantify the relationship between rapid access to treatment and reduced risk of severe disease, which was particularly strong for SMA. There was some evidence to suggest that progression to other severe phenotypes may also be prevented by prompt treatment, though the association was not as strong, which may be explained by potential selection bias, sample size issues, or a difference in underlying pathology. These findings may help assess the impact of interventions that improve access to treatment