Microbial electrolysis cells (MECs) are a promising new technology for producing hydrogen cheaply, efficiently, and sustainably. However, to scale up this technology, we need a better understanding of the processes in the devices. In this effort, we present a differential-algebraic equation (DAE) model of a microbial electrolysis cell with an algebraic constraint on current. We then perform sensitivity and bifurcation analysis for the DAE system. The model can be applied either to batch-cycle MECs or to continuous-flow MECs. We conduct differential-algebraic sensitivity analysis after fitting simulations to current density data for a batch-cycle MEC. The sensitivity analysis suggests which parameters have the greatest influence on the current density at particular times during the experiment. In particular, growth and consumption parameters for exoelectrogenic bacteria have a strong effect prior to the peak current density. An alternative strategy to maximizing peak current density is maintaining a long term stable equilibrium with non-zero current density in a continuous-flow MEC. We characterize the minimum dilution rate required for a stable nonzero current equilibrium and demonstrate transcritical bifurcations in the dilution rate parameter that exchange stability between several curves of equilibria. Specifically, increasing the dilution rate transitions the system through three regimes where the stable equilibrium exhibits (i) competitive exclusion by methanogens, (ii) coexistence, and (iii) competitive exclusion by exolectrogens. Positive long term current production is only feasible in the final two regimes. These results suggest how to modify system parameters to increase peak current density in a batch-cycle MEC or to increase the long term current density equilibrium value in a continuous-flow MEC.

BackgroundMalaria is a mosquito-borne, lethal disease that affects millions and kills hundreds of thousands of people each year, mostly children. There is an increasing need for models of malaria control. In this paper, a model is developed for allocating malaria interventions across geographic regions and time, subject to budget constraints, with the aim of minimizing the number of person-days of malaria infection.MethodsThe model considers a range of several conditions: climatic characteristics, treatment efficacy, distribution costs, and treatment coverage. An expanded susceptible-infected-recovered compartment model for the disease dynamics is coupled with an integer linear programming model for selecting the disease interventions. The model produces an intervention plan for all regions, identifying which combination of interventions, with which level of coverage, to use in each region and year in a 5-year planning horizon.ResultsSimulations using the model yield high-level, qualitative insights on optimal intervention policies: The optimal intervention policy is different when considering a 5-year time horizon than when considering only a single year, due to the effects that interventions have on the disease transmission dynamics. The vaccine intervention is rarely selected, except if its assumed cost is significantly lower than that predicted in the literature. Increasing the available budget causes the number of person-days of malaria infection to decrease linearly up to a point, after which the benefit of increased budget starts to taper. The optimal policy is highly dependent on assumptions about mosquito density, selecting different interventions for wet climates with high density than for dry climates with low density, and the interventions are found to be less effective at controlling malaria in the wet climates when attainable intervention coverage is 60 % or lower. However, when intervention coverage of 80 % is attainable, then malaria prevalence drops quickly in all geographic regions, even when factoring in the greater expense of the higher coverage against a constant budget.ConclusionsThe model provides a qualitative decision-making tool to weigh alternatives and guide malaria eradication efforts. A one-size-fits-all campaign is found not to be cost-effective; it is better to consider geographic variations and changes in malaria transmission over time when determining intervention strategies.

Microbial electrolysis cells (MECs) are devices that employ electroactive bacteria to perform extracellular electron transfer, enabling hydrogen generation from biodegradable substrates. Previously we analyzed a regular, semi-explicit, index 1 differential-algebraic equation (DAE) model for MECs. The model consists of ordinary differential equations (ODE) resembling chemostats or continuous stirred tank reactors (CSTRs), an ODE for a mediator involved in electron transfer, and an algebraic constraint for electric current and hydrogen production. This work characterizes asymptotic stability of equilibria in two biologically relevant versions of the model. Our goal is to determine the outcome of competition between methanogenic archaea and electroactive bacteria, because only the latter contribute to electric current and hydrogen production. We investigate global asymptotic stability in a model with finitely many species, Monod kinetics, different removal rates, and a constraint based on the Nernst and Butler-Volmer equations. If methanogens can grow at the lowest substrate concentration, then the equilibrium corresponding to competitive exclusion by methanogens is globally asymptotically stable. Establishing the analogous result for electroactive bacteria has proven challenging. As a first step towards characterizing stability of an electroactive-only equilibrium, we consider local asymptotic stability in a model with three types of microbes, general monotone kinetics, equal removal rates, and a general constraint. In this model, even if electroactive bacteria can grow at the lowest substrate concentration, a few additional conditions are required to guarantee local asymptotic stability. We also provide numerical simulations supporting these arguments. Our results suggest operating conditions that are most conducive to success of electroactive bacteria and current or hydrogen production in MECs.

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