Conference Agenda

In Japan, due to the shortage of healthcare workers, there has been a growing need to effectively allocate patients to different medical diagnoses or treatments according to the severity of their illness and the capabilities of medical institutions. However, since these rules have often been created manually by Japanese local municipalities, whether the resulting rule is reasonable is unclear, and creating a rule requires a lot of effort. In this talk, we propose a data-driven approach for designing a patient allocation rule for medical diagnoses. Since patient allocation rules can be expressed as a flowchart-style diagram, our task of designing an allocation rule is similar to a machine-learning problem of tree-based classification models. Due to its modeling capabilities, mixed-integer optimization has recently attracted attention for learning such tree-based models. Thus, we propose a mixed-integer optimization approach to obtain an effective decision diagram for allocating patients to medical diagnoses with practical constraints on medical resources. Specifically. this study focuses on chronic kidney disease (CKD) and allocating patients into three diagnostic classes: "See a diabetologist," "See a nephrologist," and "Do nothing." We first show that the current allocation rules can be summarized as a decision diagram. We then introduce practical constraints to consider (e.g., healthcare institutions' capacity or medical cost constraints). Finally, we give a mixed-integer optimization formulation to find a decision diagram with high diagnosis effects and low medical costs. Our numerical experiments with synthetic data demonstrated that the proposed method could provide effective medical diagnosis allocations at a low cost.

In epidemics, waning immunity is common after infection or vaccination of individuals. Immunity levels are highly heterogeneous and dynamic. This work presents an immuno-epidemiological model that captures the fundamental dynamic features of immunity acquisition and wane after infection or vaccination and analyzes mathematically its dynamical properties. The model consists of a system of first order partial differential equations, involving nonlinear integral terms and different transfer velocities. Structurally, the equation may be interpreted as a Fokker-Planck equation for a piecewise deterministic process. However, unlike the usual models, our equation involves nonlocal effects, representing the infectivity of the whole environment. In addition, the asymptotic behavior of the model is analyzed based on the obtained qualitative properties of the solution.Finally, an optimal control problem with objective function including the total number of deaths and costs of vaccination is explored, with applications in public health in view.

Abstract

An Intensive Care Unit – Medium Care Unit (IC-MC) system in a hospital can be regarded as a finite tandem queue with a finite Intensive Care (ICU) and a finite Medium Care unit (MCU) (also known as Step-Down Unit). Finite tandem queues are known to be widely applicable but also hard to solve analytically. Particularly by the Covid-19 pandemic it revived as of societal and solvability interest.The presentation is independent from [2,3].

An ICU patient standardly needs to pass both stages for recovery and observation. A key-indicator to evaluate the performance of this system is the ICU congestion probability. The presentation aims to highlight:

• a first-order if not reasonably accurate bound by a simple Erlang loss expression

• numerical support and an IC-MC application

• a formal proof as a lower bound.

The Erlang bound seems trivial. Yet counter-intuitive examples at sample path basis are easily constructed. For the average case a technical formal proof can be given related to Markov Dynamic Programming (MDP) ([1]). Numerical support is provided for natural IC-MC situations. These also capture nón-exponential (realistically: lognormal) recovery times. Accordingly, it might well be practical for real-life IC-MC dimensioning.

[1] MDP in Practice, 2017, Springer (with R.J. Boucherie)

[2] On the corona effect for OT-ICU systems, Proceedings SOR ’21, 2021 (with L.N. Bulder)

[3] On flexible capacity allocation with ICU-SDU application, Int. J. Production Economics, 2024 (with H.J. van der Sluis, L.N. Bulder and Y. Cui)