Strategic Planning of a Joint SARS-CoV-2 and Influenza Vaccination Campaign in the UK.

The simultaneous administration of SARS-CoV-2 and influenza vaccines is being carried out for the first time in the UK and around the globe in order to mitigate the health, economic, and societal impacts of these respiratory tract diseases. However, a systematic approach for planning the vaccine distribution and administration aspects of the vaccination campaigns would be beneficial. This work develops a novel multi-product mixed-integer linear programming (MILP) vaccine supply chain model that can be used to plan and optimise the simultaneous distribution and administration of SARS-CoV-2 and influenza vaccines. The outcomes from this study reveal that the total budget required to successfully accomplish the SARS-CoV-2 and influenza vaccination campaigns is equivalent to USD 7.29 billion, of which the procurement costs of SARS-CoV-2 and influenza vaccines correspond to USD 2.1 billion and USD 0.83 billion, respectively. The logistics cost is equivalent to USD 3.45 billion, and the costs of vaccinating individuals, quality control checks, and vaccine shipper and dry ice correspond to USD 1.66, 0.066, and 0.014, respectively. The analysis of the results shows that the choice of rolling out the SARS-CoV-2 vaccine during the vaccination campaign can have a significant impact not only on the total vaccination cost but also on vaccine wastage rate.

Global Sensitivity Analysis in Life-Cycle Assessment of Early-Stage Technology using Detailed Process Simulation: Application to Dialkylimidazolium Ionic Liquid Production.

The ability to assess the environmental performance of early-stage technologies at production scale is critical for sustainable process development. This paper presents a systematic methodology for uncertainty quantification in life-cycle assessment (LCA) of such technologies using global sensitivity analysis (GSA) coupled with a detailed process simulator and LCA database. This methodology accounts for uncertainty in both the background and foreground life-cycle inventories, and is enabled by lumping multiple background flows, either downstream or upstream of the foreground processes, in order to reduce the number of factors in the sensitivity analysis. A case study comparing the life-cycle impacts of two dialkylimidazolium ionic liquids is conducted to illustrate the methodology. Failure to account for the foreground process uncertainty alongside the background uncertainty is shown to underestimate the predicted variance of the end-point environmental impacts by a factor of two. Variance-based GSA furthermore reveals that only few foreground and background uncertain parameters contribute significantly to the total variance in the end-point environmental impacts. As well as emphasizing the need to account for foreground uncertainties in LCA of early-stage technologies, these results illustrate how GSA can empower more reliable decision-making in LCA.

Pandemic-response adenoviral vector and RNA vaccine manufacturing.

Rapid global COVID-19 pandemic response by mass vaccination is currently limited by the rate of vaccine manufacturing. This study presents a techno-economic feasibility assessment and comparison of three vaccine production platform technologies deployed during the COVID-19 pandemic: (1) adenovirus-vectored (AVV) vaccines, (2) messenger RNA (mRNA) vaccines, and (3) the newer self-amplifying RNA (saRNA) vaccines. Besides assessing the baseline performance of the production process, impact of key design and operational uncertainties on the productivity and cost performance of these vaccine platforms is quantified using variance-based global sensitivity analysis. Cost and resource requirement projections are computed for manufacturing multi-billion vaccine doses for covering the current global demand shortage and for providing annual booster immunisations. The model-based assessment provides key insights to policymakers and vaccine manufacturers for risk analysis, asset utilisation, directions for future technology improvements and future epidemic/pandemic preparedness, given the disease-agnostic nature of these vaccine production platforms.

Model-Based Planning and Delivery of Mass Vaccination Campaigns against Infectious Disease: Application to the COVID-19 Pandemic in the UK.

Vaccination plays a key role in reducing morbidity and mortality caused by infectious diseases, including the recent COVID-19 pandemic. However, a comprehensive approach that allows the planning of vaccination campaigns and the estimation of the resources required to deliver and administer COVID-19 vaccines is lacking. This work implements a new framework that supports the planning and delivery of vaccination campaigns. Firstly, the framework segments and priorities target populations, then estimates vaccination timeframe and workforce requirements, and lastly predicts logistics costs and facilitates the distribution of vaccines from manufacturing plants to vaccination centres. The outcomes from this study reveal the necessary resources required and their associated costs ahead of a vaccination campaign. Analysis of results shows that by integrating demand stratification, administration, and the supply chain, the synergy amongst these activities can be exploited to allow planning and cost-effective delivery of a vaccination campaign against COVID-19 and demonstrates how to sustain high rates of vaccination in a resource-efficient fashion.

Global optimization in Hilbert space.

We propose a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an ε -suboptimal global solution within finite run-time for any given termination tolerance ε > 0 . Finally, we illustrate these results for a problem of calculus of variations.

Semi-empirical modeling of microalgae photosynthesis in different acclimation states - Application to N. gaditana.

The development of mathematical models capable of accurate predictions of the photosynthetic productivity of microalgae under variable light conditions is paramount to the development of large-scale production systems. The process of photoacclimation is particularly important in outdoor cultivation systems, whereby seasonal variation of the light irradiance can greatly influence microalgae growth. This paper presents a dynamic model that captures the effect of photoacclimation on the photosynthetic production. It builds upon an existing semi-empirical model describing the processes of photoproduction, photoregulation and photoinhibition via the introduction of acclimation rules for key parameters. The model is calibrated against a dataset comprising pulsed amplitude modulation fluorescence, photosynthesis rate, and antenna size measurements for the microalga Nannochloropsis gaditana in several acclimation states. It is shown that the calibrated model is capable of accurate predictions of fluorescence and respirometry data, both in interpolation and in extrapolation.

Chebyshev model arithmetic for factorable functions.

This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden.

Correction: High-Fidelity Modelling Methodology of Light-Limited Photosynthetic Production in Microalgae.

[This corrects the article DOI: 10.1371/journal.pone.0152387.].

High-Fidelity Modelling Methodology of Light-Limited Photosynthetic Production in Microalgae.

Reliable quantitative description of light-limited growth in microalgae is key to improving the design and operation of industrial production systems. This article shows how the capability to predict photosynthetic processes can benefit from a synergy between mathematical modelling and lab-scale experiments using systematic design of experiment techniques. A model of chlorophyll fluorescence developed by the authors [Nikolaou et al., J Biotechnol 194:91-99, 2015] is used as starting point, whereby the representation of non-photochemical-quenching (NPQ) process is refined for biological consistency. This model spans multiple time scales ranging from milliseconds to hours, thus calling for a combination of various experimental techniques in order to arrive at a sufficiently rich data set and determine statistically meaningful estimates for the model parameters. The methodology is demonstrated for the microalga Nannochloropsis gaditana by combining pulse amplitude modulation (PAM) fluorescence, photosynthesis rate and antenna size measurements. The results show that the calibrated model is capable of accurate quantitative predictions under a wide range of transient light conditions. Moreover, this work provides an experimental validation of the link between fluorescence and photosynthesis-irradiance (PI) curves which had been theoricized.

Dynamic coupling of photoacclimation and photoinhibition in a model of microalgae growth.

The development of mathematical models that can predict photosynthetic productivity of microalgae under transient conditions is crucial for enhancing large-scale industrial culturing systems. Particularly important in outdoor culture systems, where the light irradiance varies greatly, are the processes of photoinhibition and photoacclimation, which can affect photoproduction significantly. The former is caused by an excess of light and occurs on a fast time scale of minutes, whereas the latter results from the adjustment of the light harvesting capacity to the incoming irradiance and takes place on a slow time scale of days. In this paper, we develop a dynamic model of microalgae growth that simultaneously accounts for the processes of photoinhibition and photoacclimation, thereby spanning multiple time scales. The properties of the model are analyzed in connection to PI-response curves, under a quasi steady-state assumption for the slow processes and by neglecting the fast dynamics. For validation purposes, the model is calibrated and compared against multiple experimental data sets from the literature for several species. The results show that the model can describe the difference in photosynthetic unit acclimation strategies between Dunaliella tertiolecta (n-strategy) and Skeletonema costatum (s-strategy).

Modelling of Microalgae Culture Systems with Applications to Control and Optimization.

Mathematical modeling is becoming ever more important to assess the potential, guide the design, and enable the efficient operation and control of industrial-scale microalgae culture systems (MCS). The development of overall, inherently multiphysics, models involves coupling separate submodels of (i) the intrinsic biological properties, including growth, decay, and biosynthesis as well as the effect of light and temperature on these processes, and (ii) the physical properties, such as the hydrodynamics, light attenuation, and temperature in the culture medium. When considering high-density microalgae culture, in particular, the coupling between biology and physics becomes critical. This chapter reviews existing models, with a particular focus on the Droop model, which is a precursor model, and it highlights the structure common to many microalgae growth models. It summarizes the main developments and difficulties towards multiphysics models of MCS as well as applications of these models for monitoring, control, and optimization purposes.

A model of chlorophyll fluorescence in microalgae integrating photoproduction, photoinhibition and photoregulation.

This paper presents a mathematical model capable of quantitative prediction of the state of the photosynthetic apparatus of microalgae in terms of their open, closed and damaged reaction centers under variable light conditions. This model combines the processes of photoproduction and photoinhibition in the Han model with a novel mathematical representation of photoprotective mechanisms, including qE-quenching and qI-quenching. For calibration and validation purposes, the model can be used to simulate fluorescence fluxes, such as those measured in PAM fluorometry, as well as classical fluorescence indexes. A calibration is carried out for the microalga Nannochloropsis gaditana, whereby 9 out of the 13 model parameters are estimated with good statistical significance using the realized, minimal and maximal fluorescence fluxes measured from a typical PAM protocol. The model is further validated by considering a more challenging PAM protocol alternating periods of intense light and dark, showing a good ability to provide quantitative predictions of the fluorescence fluxes even though it was calibrated for a different and somewhat simpler PAM protocol. A promising application of the model is for the prediction of PI-response curves based on PAM fluorometry, together with the long-term prospect of combining it with hydrodynamic and light attenuation models for high-fidelity simulation and optimization of full-scale microalgae production systems.

Three-reaction model for the anaerobic digestion of microalgae.

Coupling an anaerobic digester to a microalgal culture has received increasing attention as an alternative process for combined bioenergy production and depollution. In this article, a dynamic model for anaerobic digestion of microalgae is developed with the aim of improving the management of such a coupled system. This model describes the dynamics of inorganic nitrogen and volatile fatty acids since both can lead to inhibition and therefore process instability. Three reactions are considered: Two hydrolysis-acidogenesis steps in parallel for sugars/lipids and for proteins, followed by a methanogenesis step. The proposed model accurately reproduces experimental data for anaerobic digestion of the freshwater microalgae Chlorella vulgaris with an organic loading rate of 1 gCOD L(-1) d(-1). In particular, the three-reaction pathway allows to adequately represent the observed decoupling between biogas production and nitrogen release. The reduced complexity of this model makes it suitable for developing advanced, model-based control and monitoring strategies.