A framework for health care planning and control

Rising expenditures spur health care organizations to organize their processes more efficiently and effectively. Unfortunately, health care planning and control lags far behind manufacturing planning and control. Successful manufacturing planning and control concepts can not be directly copied, because of the unique nature of health care delivery. We analyze existing planning and control concepts or frameworks for health care operations management, and find that they do not properly address various important planning and control problems. We conclude that they only focus on hospitals, and are too narrow, focusing on a single managerial area, such as resource capacity planning, or ignoring hierarchical levels. We propose a modern framework for health care planning and control. Our framework integrates all managerial areas involved in health care delivery operations and all hierarchical levels of control, to ensure completeness and coherence of responsibilities for every managerial area. The framework can be used to structure the various planning and control functions, and their interaction. It is applicable broadly, to an individual department, an entire health care organization, and to a complete supply chain of cure and care providers. The framework can be used to identify and position various types of managerial problems, to demarcate the scope of organization interventions, and to facilitate a dialogue between clinical staff and managers. We illustrate the application of the framework with examples

Optimal Flood Control

A mathematical model for optimal control of the water levels in a chain of reservoirs is studied. Some remarks regarding sensitivity with respect to the time horizon, terminal cost and forecast of inflow are made

Structures in supercritical scale-free percolation

Scale-free percolation is a percolation model on $\mathbb{Z}^d$ which can be used to model real-world networks. We prove bounds for the graph distance in the regime where vertices have infinite degrees. We fully characterize transience vs. recurrence for dimension 1 and 2 and give sufficient conditions for transience in dimension 3 and higher. Finally, we show the existence of a hierarchical structure for parameters where vertices have degrees with infinite variance and obtain bounds on the cluster density.Comment: Revised Definition 2.5 and an argument in Section 6, results are unchanged. Correction of minor typos. 29 pages, 7 figure

Rigorous derivation of the Kuramoto-Sivashinsky equation in a 2D weakly nonlinear Stefan problem

In this paper we are interested in a rigorous derivation of the Kuramoto-Sivashinsky equation (K--S) in a Free Boundary Problem. As a paradigm, we consider a two-dimensional Stefan problem in a strip, a simplified version of a solid-liquid interface model. Near the instability threshold, we introduce a small parameter $\varepsilon$ and define rescaled variables accordingly. At fixed $\varepsilon$, our method is based on: definition of a suitable linear 1D operator, projection with respect to the longitudinal coordinate only, Lyapunov-Schmidt method. As a solvability condition, we derive a self-consistent parabolic equation for the front. We prove that, starting from the same configuration, the latter remains close to the solution of K--S on a fixed time interval, uniformly in $\varepsilon$ sufficiently small

Modeling fungal hypha tip growth via viscous sheet approximation

In this paper we present a new model for single-celled, non-branching hypha tip growth. The growth mechanism of hypha cells consists of transport of cell wall building material to the cell wall and subsequent incorporation of this material in the wall as it arrives. To model the transport of cell wall building material to the cell wall we follow Bartnicki-Garcia et al in assuming that the cell wall building material is transported in straight lines by an isotropic point source. To model the dynamics of the cell wall, including its growth by new material, we use the approach of Campas and Mahadevan, which assumes that the cell wall is a thin viscous sheet sustained by a pressure difference. Furthermore, we include a novel equation which models the hardening of the cell wall as it ages. We present numerical results which give evidence that our model can describe tip growth, and briefly discuss validation aspects

Connectivity Threshold for random subgraphs of the Hamming graph

We study the connectivity of random subgraphs of the $d$-dimensional Hamming graph $H(d, n)$, which is the Cartesian product of $d$ complete graphs on $n$ vertices. We sample the random subgraph with an i.i.d.\ Bernoulli bond percolation on $H(d,n)$ with parameter $p$. We identify the window of the transition: when $np- \log n \to - \infty$ the probability that the graph is connected goes to $0$, while when $np- \log n \to + \infty$ it converges to $1$. We also investigate the connectivity probability inside the critical window, namely when $np- \log n \to t \in \mathbb{R}$. We find that the threshold does not depend on $d$, unlike the phase transition of the giant connected component the Hamming graph (see [Bor et al, 2005]). Within the critical window, the connectivity probability does depend on d. We determine how.Comment: 10 pages, no figure

Analytical models to determine room requirements in outpatient clinics

Outpatient clinics traditionally organize processes such that the doctor remains in a consultation room while patients visit for consultation, we call this the Patient-to-Doctor policy (PtD-policy). A different approach is the Doctor-to-Patient policy (DtP-policy), whereby the doctor travels between multiple consultation rooms, in which patients prepare for their consultation. In the latter approach, the doctor saves time by consulting fully prepared patients. We use a queueing theoretic and a discrete-event simulation approach to provide generic models that enable performance evaluations of the two policies for different parameter settings. These models can be used by managers of outpatient clinics to compare the two policies and choose a particular policy when redesigning the patient process.We use the models to analytically show that the DtP-policy is superior to the PtD-policy under the condition that the doctor’s travel time between rooms is lower than the patient’s preparation time. In addition, to calculate the required number of consultation rooms in the DtP-policy, we provide an expression for the fraction of consultations that are in immediate succession; or, in other words, the fraction of time the next patient is prepared and ready, immediately after a doctor finishes a consultation. We apply our methods for a range of distributions and parameters and to a case study in a medium-sized general hospital that inspired this research

Higher order corrections for anisotropic bootstrap percolation

We study the critical probability for the metastable phase transition of the two-dimensional anisotropic bootstrap percolation model with $(1,2)$-neighbourhood and threshold $r = 3$. The first order asymptotics for the critical probability were recently determined by the first and second authors. Here we determine the following sharp second and third order asymptotics: $$p_c\big( [L]^2,\mathcal{N}_{(1,2)},3 \big) \; = \; \frac{(\log \log L)^2}{12\log L} \, - \, \frac{\log \log L \, \log \log \log L}{ 3\log L} + \frac{\left(\log \frac{9}{2} + 1 \pm o(1) \right)\log \log L}{6\log L}.$$ We note that the second and third order terms are so large that the first order asymptotics fail to approximate $p_c$ even for lattices of size well beyond $10^{10^{1000}}$.Comment: 46 page