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Medical digital twins are computational models of human biology relevant to a given medical condition, which can be tailored to an individual patient, thereby predicting the course of disease and individualized treatments, an important goal of personalized medicine. The immune system, which has a central role in many diseases, is highly heterogeneous between individuals, and thus poses a major challenge for this technology. If medical digital twins are to faithfully capture the characteristics of a patient's immune system, we need to answer many questions, such as: What do we need to know about the immune system to build mathematical models that reflect features of an individual? What data do we need to collect across the different scales of immune system action? What are the right modeling paradigms to properly capture immune system complexity? In February 2023, an international group of experts convened in Lake Nona, FL for two days to discuss these and other questions related to digital twins of the immune system. The group consisted of clinicians, immunologists, biologists, and mathematical modelers, representative of the interdisciplinary nature of medical digital twin development. A video recording of the entire event is available. This paper presents a synopsis of the discussions, brief descriptions of ongoing digital twin projects at different stages of progress. It also proposes a 5-year action plan for further developing this technology. The main recommendations are to identify and pursue a small number of promising use cases, to develop stimulation-specific assays of immune function in a clinical setting, and to develop a database of existing computational immune models, as well as advanced modeling technology and infrastructure.

The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the Moore-Shannon network reliability of that graph in engineering. It is the crucial element for decision-making under uncertainty. Not surprisingly, it is provably hard to compute exactly or even to approximate. Many of these applications are concerned only with a subset of problems for which the solutions are monotonic functions. Here we extend the weak- and strong-coupling methods of statistical physics to heterogeneous satisfiability problems and introduce a novel approach to constructing lower and upper bounds on the approximation error for monotonic problems. These bounds combine information from both perturbative analyses to produce bounds that are tight in the sense that they are saturated by some problem instance that is compatible with all the information contained in either approximation.

Beginning in April 2020, we gathered partial county-level data on non-pharmaceutical interventions (NPIs) implemented in response to the COVID-19 pandemic in the United States, using both volunteer and paid crowdsourcing. In this report, we document the data collection process and summarize our results, to increase the utility of our open data and inform the design of future rapid crowdsourcing data collection efforts., Comment: Includes survey instrument

We view sequential design as a model selection problem to determine which new observation is expected to be the most informative, given the existing set of observations. For estimating a probability distribution on a bounded interval, we use bounds constructed from kernel density estimators along with the estimated density itself to estimate the information gain expected from each observation. We choose Bernstein polynomials for the kernel functions because they provide a complete set of basis functions for polynomials of finite degree and thus have useful convergence properties. We illustrate the method with applications to estimating network reliability polynomials, which give the probability of certain sets of configurations in finite, discrete stochastic systems.

Network reliability is the probability that a dynamical system composed of discrete elements interacting on a network will be found in a configuration that satisfies a particular property. We introduce a new reliability property, Ising feasibility, for which the network reliability is the Ising model s partition function. As shown by Moore and Shannon, the network reliability can be separated into two factors: structural, solely determined by the network topology, and dynamical, determined by the underlying dynamics. In this case, the structural factor is known as the joint density of states. Using methods developed to approximate the structural factor for other reliability properties, we simulate the joint density of states, yielding an approximation for the partition function. Based on a detailed examination of why naive Monte Carlo sampling gives a poor approximation, we introduce a novel parallel scheme for estimating the joint density of states using a Markov chain Monte Carlo method with a spin exchange random walk. This parallel scheme makes simulating the Ising model in the presence of an external field practical on small computer clusters for networks with arbitrary topology with 10 to 6 energy levels and more than 10 to 308 microstates., Comment: Ver.2. 8 pages, 7 figures. Accepted. Phys. Rev. E

West Africa is currently experiencing a severe outbreak of Ebola virus disease (EVD). As part of the international effort to address this outbreak, the United States has committed to building specialized Ebola treatment facilities with 1700 beds. However, the effectiveness of this increase in the available healthcare facilities to treat Ebola is unclear, especially in light of the rapidly increasing number of cases. Adapting a previously validated mathematical model of Ebola in West Africa, we examine the potential impact of an increase in hospital capacity to mitigate the impact of Ebola under several scenarios, ranging from the planned scenario of 1700 beds in 10 weeks to a considerably more aggressive approach of twice the number of beds in 5 weeks. We find that even for the most aggressive scenarios, while increasing the availability of healthcare reduces the number of Ebola cases and slows the outbreak, it is not sufficient to stop the epidemic within the next three months. We find that only a combination of increased hospital beds and a dramatic decrease in the rate of transmission within the community can bring the epidemic under control within the near future.

An Ebola outbreak of unparalleled size is currently affecting several countries in West Africa, and international efforts to control the outbreak are underway. However, the efficacy of these interventions, and their likely impact on an Ebola epidemic of this size, is unknown. Forecasting and simulation of these interventions may inform public health efforts. We use existing data from Liberia and Sierra Leone to parameterize a mathematical model of Ebola and use this model to forecast the progression of the epidemic, as well as the efficacy of several interventions, including increased contact tracing, improved infection control practices, the use of a hypothetical pharmaceutical intervention to improve survival in hospitalized patients. Model forecasts until Dec. 31, 2014 show an increasingly severe epidemic with no sign of having reached a peak. Modeling results suggest that increased contact tracing, improved infection control, or a combination of the two can have a substantial impact on the number of Ebola cases, but these interventions are not sufficient to halt the progress of the epidemic. The hypothetical pharmaceutical intervention, while impacting mortality, had a smaller effect on the forecasted trajectory of the epidemic. Near-term, practical interventions to address the ongoing Ebola epidemic may have a beneficial impact on public health, but they will not result in the immediate halting, or even obvious slowing of the epidemic. A long-term commitment of resources and support will be necessary to address the outbreak.

This paper uses the reliability polynomial, introduced by Moore and Shannon in 1956, to analyze the effect of network structure on diffusive dynamics such as the spread of infectious disease. We exhibit a representation for the reliability polynomial in terms of what we call {\em structural motifs} that is well suited for reasoning about the effect of a network's structural properties on diffusion across the network. We illustrate by deriving several general results relating graph structure to dynamical phenomena.

We build an agent-based model of incarceration based on the SIS model of infectious disease propagation. Our central hypothesis is that the observed racial disparities in incarceration rates between Black and White Americans can be explained as the result of differential sentencing between the two demographic groups. We demonstrate that if incarceration can be spread through a social influence network, then even relatively small differences in sentencing can result in the large disparities in incarceration rates. Controlling for effects of transmissibility, susceptibility, and influence network structure, our model reproduces the observed large disparities in incarceration rates given the differences in sentence lengths for White and Black drug offenders in the United States without extensive parameter tuning. We further establish the suitability of the SIS model as applied to incarceration, as the observed structural patterns of recidivism are an emergent property of the model. In fact, our model shows a remarkably close correspondence with California incarceration data, without requiring any parameter tuning. This work advances efforts to combine the theories and methods of epidemiology and criminology.

This paper re-introduces the network reliability polynomial - introduced by Moore and Shannon in 1956 -- for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is well-suited for estimation by distributed simulation. We describe a collection of graphs derived from Erd\H{o}s-R\'enyi and scale-free-like random graphs in which we have manipulated assortativity-by-degree and the number of triangles. We evaluate the network reliability for all these graphs under a reliability rule that is related to the expected size of a connected component. Through these extensive simulations, we show that for positively or neutrally assortative graphs, swapping edges to increase the number of triangles does not increase the network reliability. Also, positively assortative graphs are more reliable than neutral or disassortative graphs with the same number of edges. Moreover, we show the combined effect of both assortativity-by-degree and the presence of triangles on the critical point and the size of the smallest subgraph that is reliable., Comment: 12 pages, 8 figures, 1 table

Large scale simulations of the movements of people in a ``virtual'' city and their analyses are used to generate new insights into understanding the dynamic processes that depend on the interactions between people. Models, based on these interactions, can be used in optimizing traffic flow, slowing the spread of infectious diseases or predicting the change in cell phone usage in a disaster. We analyzed cumulative and aggregated data generated from the simulated movements of 1.6 million individuals in a computer (pseudo agent-based) model during a typical day in Portland, Oregon. This city is mapped into a graph with $181,206$ nodes representing physical locations such as buildings. Connecting edges model individual's flow between nodes. Edge weights are constructed from the daily traffic of individuals moving between locations. The number of edges leaving a node (out-degree), the edge weights (out-traffic), and the edge-weights per location (total out-traffic) are fitted well by power law distributions. The power law distributions also fit subgraphs based on work, school, and social/recreational activities. The resulting weighted graph is a ``small world'' and has scaling laws consistent with an underlying hierarchical structure. We also explore the time evolution of the largest connected component and the distribution of the component sizes. We observe a strong linear correlation between the out-degree and total out-traffic distributions and significant levels of clustering. We discuss how these network features can be used to characterize social networks and their relationship to dynamic processes., Comment: 18 pages, 10 figures

A common first step in time series signal analysis involves digitally filtering the data to remove linear correlations. The residual data is spectrally white (it is ``bleached''), but in principle retains the nonlinear structure of the original time series. It is well known that simple linear autocorrelation can give rise to spurious results in algorithms for estimating nonlinear invariants, such as fractal dimension and Lyapunov exponents. In theory, bleached data avoids these pitfalls. But in practice, bleaching obscures the underlying deterministic structure of a low-dimensional chaotic process. This appears to be a property of the chaos itself, since nonchaotic data are not similarly affected. The adverse effects of bleaching are demonstrated in a series of numerical experiments on known chaotic data. Some theoretical aspects are also discussed., Comment: 12 dense pages (82K) of ordinary LaTeX; uses macro psfig.tex for inclusion of figures in text; figures are uufile'd into a single file of size 306K; the final dvips'd postscript file is about 1.3mb Replaced 9/30/93 to incorporate final changes in the proofs and to make the LaTeX more portable; the paper will appear in CHAOS 4 (Dec, 1993)