Most mathematical models for the spread of disease use differential equations based on uniform mixing assumptions or ad hoc models for the contact process. Here we explore the use of dynamic bipartite graphs to model the physical contact patterns that result from movements of individuals between specific locations. The graphs are generated by large-scale individual-based urban traffic simulations built on actual census, land-use and population-mobility data. We find that the contact network among people is a strongly connected small-world-like graph with a well-defined scale for the degree distribution. However, the locations graph is scale-free, which allows highly efficient outbreak detection by placing sensors in the hubs of the locations network. Within this large-scale simulation framework, we then analyse the relative merits of several proposed mitigation strategies for smallpox spread. Our results suggest that outbreaks can be contained by a strategy of targeted vaccination combined with early detection without resorting to mass vaccination of a population.

A recent manuscript (Ferguson et al. in Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, Imperial College COVID-19 Response Team, London, 2020. https://www.imperial.ac.uk/media/ imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf) from Imperial College modelers examining ways to mitigate and control the spread of COVID-19 has attracted much attention. In this paper, we will discuss a coarse taxonomy of models and explore the context and significance of the Imperial College and other models in contributing to the analysis of COVID-19.

Abstract3G networks are currently overloaded, due to the increasing popularity of various applications for smartphones. Offloading mobile data traffic through opportunistic communications is a promising solution to partially solve this problem, because there is almost no monetary cost for it. We propose to exploit opportunistic communications to facilitate information dissemination in the emerging Mobile Social Networks (MoSoNets) and thus reduce the amount of mobile data traffic. As a case study, we investigate the target-set selection problem for information delivery. In particular, we study how to select the target set with only k users, such that we can minimize the mobile data traffic over cellular networks. We propose three algorithms, called Greedy, Heuristic, and Random, for this problem and evaluate their performance through an extensive trace-driven simulation study. Our simulation results verify the efficiency of these algorithms for both synthetic and real-world mobility traces. For example, the Heuristic algorithm can offload mobile data traffic by up to 73.66% for a real-world mobility trace. Moreover, to investigate the feasibility of opportunistic communications for mobile phones, we implement a proof-of-concept prototype, called Opp-Off, on Nokia N900 smartphones, which utilizes their Bluetooth interface for device/service discovery and content transfer.

Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominating set. We also present an on-line coloring heuristic which achieves a competitive ratio of 6 for unit disk graphs. Our heuristics do not need a geometric representation of unit disk graphs. Geometric representations are used only in establishing the performance guarantees of the heuristics. Several of our approximation algorithms can be extended to intersection graphs of circles of arbitrary radii in the plane, intersection graphs of regular polygons, and to intersection graphs of higher dimensional regular objects.

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Preventing and controlling outbreaks of infectious diseases such as pandemic influenza is a top public health priority. We describe EpiSimdemics -a scalable parallel algorithm to simulate the spread of contagion in large, realistic social contact networks using individual-based models. EpiSimdemics is an interaction-based simulation of a certain class of stochastic reaction-diffusion processes. Straightforward simulations of such process do not scale well, limiting the use of individual-based models to very small populations. EpiSimdemics is specifically designed to scale to social networks with 100 million individuals. The scaling is obtained by exploiting the semantics of disease evolution and disease propagation in large networks. We evaluate an MPI-based parallel implementation of EpiSimdemics on a mid-sized HPC system, demonstrating that EpiSimdemics scales well. EpiSimdemics has been used in numerous sponsor defined case studies targeted at policy planning and course of action analysis, demonstrating the usefulness of EpiSimdemics in practical situations.

Forecasting the dynamics of influenza outbreaks could be useful for decision-making regarding the allocation of public health resources. Reliable forecasts could also aid in the selection and implementation of interventions to reduce morbidity and mortality due to influenza illness. This paper reviews methods for influenza forecasting proposed during previous influenza outbreaks and those evaluated in hindsight. We discuss the various approaches, in addition to the variability in measures of accuracy and precision of predicted measures. PubMed and Google Scholar searches for articles on influenza forecasting retrieved sixteen studies that matched the study criteria. We focused on studies that aimed at forecasting influenza outbreaks at the local, regional, national, or global level. The selected studies spanned a wide range of regions including USA, Sweden, Hong Kong, Japan, Singapore, United Kingdom, Canada, France, and Cuba. The methods were also applied to forecast a single measure or multiple measures. Typical measures predicted included peak timing, peak height, daily/weekly case counts, and outbreak magnitude. Due to differences in measures used to assess accuracy, a single estimate of predictive error for each of the measures was difficult to obtain. However, collectively, the results suggest that these diverse approaches to influenza forecasting are capable of capturing specific outbreak measures with some degree of accuracy given reliable data and correct disease assumptions. Nonetheless, several of these approaches need to be evaluated and their performance quantified in real-time predictions.

Background: 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. Methods: 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. Findings: 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. Interpretation: 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.