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The techniques of optimal control are applied to a validated blood circulation model of cardiopulmonary resuscitation (CPR), consisting of a system of seven difference equations. In this system, the non-homogeneous forcing terms are chest and abdominal pressures acting as the 'controls'. We seek to maximize the blood flow, as measured by the pressure difference between the thoracic aorta and the right atrium. By applying optimal control methods, we characterize the optimal waveforms for external chest and abdominal compression during cardiac arrest and CPR in terms of the solutions of the circulation model and of the corresponding adjoint system. Numerical results are given for various scenarios. The optimal waveforms confirm the previously discovered positive effects of active decompression and interposed abdominal compression. These waveforms can be implemented with manual (Lifestick-like) and mechanical (vest-like) devices to achieve levels of blood flow substantially higher than those provided by standard CPR, a technique which, despite its long history, is far from optimal.

ABSTRACT. We develop a metapopulation harvesting model that includes density‐dependent immigration and emigration and apply Pontryagin's maximum principle to derive an optimal harvesting and reserve design strategy. The model is designed to mimic the black bear population of eastern Tennessee and western North Carolina. Model results suggest that a forest region's population can be maintained despite high harvest levels due to emigration from a connected, un‐harvested park region. The amount of shared border between the park and forest region is important in determining the optimal harvesting strategy. This technique offers new insight on the spatial control of protected populations.

Queueing theory studies the properties of waiting queues and has been applied to investigate direct host-to-host transmitted disease dynamics, but its potential in modelling environmentally transmitted pathogens has not been fully explored. In this study, we provide a flexible and customizable queueing theory modelling framework with three major subroutines to study the in-hospital contact processes between environments and hosts and potential nosocomial pathogen transfer, where environments are servers and hosts are customers. Two types of servers with different parameters but the same utilization are investigated. We consider various forms of transfer functions that map contact duration to the amount of pathogen transfer based on existing literature. We propose a case study of simulated in-hospital contact processes and apply stochastic queues to analyse the amount of pathogen transfer under different transfer functions, and assume that pathogen amount decreases during the inter-arrival time. Different host behaviour (feedback and non-feedback) as well as initial pathogen distribution (whether in environment and/or in hosts) are also considered and simulated. We assess pathogen transfer and circulation under these various conditions and highlight the importance of the nonlinear interactions among contact processes, transfer functions and pathogen demography during the contact process. Our modelling framework can be readily extended to more complicated queueing networks to simulate more realistic situations by adjusting parameters such as the number and type of servers and customers, and adding extra subroutines.

As many ecosystems worldwide are in peril, efforts to manage them sustainably require scientific advice. While numerous researchers around the world use a great variety of models to understand ecological dynamics and their responses to disturbances, only a small fraction of these models are ever used to inform ecosystem management. There seems to be a perception that ecological models are not useful for management, even though mathematical models are indispensable in many other fields. We were curious about this mismatch, its roots, and potential ways to overcome it. We searched the literature on recommendations and best practices for how to make ecological models useful to the management of ecosystems and we searched for ‘success stories’ from the past. We selected and examined several cases where models were instrumental in ecosystem management. We documented their success and asked whether and to what extent they followed recommended best practices. We found that there is not a unique way to conduct a research project that is useful in management decisions. While research is more likely to have impact when conducted with many stakeholders involved and specific to a situation for which data are available, there are great examples of small groups or individuals conducting highly influential research even in the absence of detailed data. We put the question of modelling for ecosystem management into a socio-economic and national context and give our perspectives on how the discipline could move forward.

Background The development of public health policy is inextricably linked with governance structure. In our increasingly globalized world, human migration and infectious diseases often span multiple administrative jurisdictions that might have different systems of government and divergent management objectives. However, few studies have considered how the allocation of regulatory authority among jurisdictions can affect disease management outcomes. Methods Here we evaluate the relative merits of decentralized and centralized management by developing and numerically analyzing a two-jurisdiction SIRS model that explicitly incorporates migration. In our model, managers choose between vaccination, isolation, medication, border closure, and a travel ban on infected individuals while aiming to minimize either the number of cases or the number of deaths. Results We consider a variety of scenarios and show how optimal strategies differ for decentralized and centralized management levels. We demonstrate that policies formed in the best interest of individual jurisdictions may not achieve global objectives, and identify situations where locally applied interventions can lead to an overall increase in the numbers of cases and deaths. Conclusions Our approach underscores the importance of tailoring disease management plans to existing regulatory structures as part of an evidence-based decision framework. Most importantly, we demonstrate that there needs to be a greater consideration of the degree to which governance structure impacts disease outcomes.