Phillip Schumm

Epidemic spreading on weighted contact networks

The study of epidemics is a crucial issue to several areas. An epidemic can have devastating economic and social consequences. A single crop disease in Kansas could destroy the yearly income of many farmers. Previous work using graph theory has determined a universal epidemic threshold found in the graph topology for a binary contact network in the compartmental susceptible-infected (SI) analysis. We expand this threshold to a more realistic measure. A binary uniform level of contact within a society is too idealistic and an improved threshold is found in allowing a spectrum of contact within a contact network. The expanded contact network also allows for asymmetric contact such as a mother caring for her child. Further study in this area should lead to improved simulators, disease modeling, policies and control of infectious diseases and viruses.

Characterising the robustness of complex networks

With increasingly ambitious initiatives such as GENI and FIND that seek to design the future Internet, it becomes imperative to define the characteristics of robust topologies, and build future networks optimized for robustness. This paper investigates the characteristics of network topologies that maintain a high level of throughput in spite of multiple attacks. To this end, we select network topologies belonging to the main network models and some real world networks. We consider three types of attacks: removal of random nodes, high degree nodes, and high betweenness nodes. We use elasticity as our robustness measure and, through our analysis, illustrate that different topologies can have different degrees of robustness. In particular, elasticity can fall as low as 0.8% of the upper bound based on the attack employed. This result substantiates the need for optimized network topology design. Furthermore, we implement a tradeoff function that combines elasticity under the three attack strategies and considers the cost of the network. Our extensive simulations show that, for a given network density, regular and semi-regular topologies can have higher degrees of robustness than heterogeneous topologies, and that link redundancy is a sufficient but not necessary condition for robustness.

Efficient mitigation strategies for epidemics in rural regions.

Containing an epidemic at its origin is the most desirable mitigation. Epidemics have often originated in rural areas, with rural communities among the first affected. Disease dynamics in rural regions have received limited attention, and results of general studies cannot be directly applied since population densities and human mobility factors are very different in rural regions from those in cities. We create a network model of a rural community in Kansas, USA, by collecting data on the contact patterns and computing rates of contact among a sampled population. We model the impact of different mitigation strategies detecting closely connected groups of people and frequently visited locations. Within those groups and locations, we compare the effectiveness of random and targeted vaccinations using a Susceptible-Exposed-Infected-Recovered compartmental model on the contact network. Our simulations show that the targeted vaccinations of only 10% of the sampled population reduced the size of the epidemic by 34.5%. Additionally, if 10% of the population visiting one of the most popular locations is randomly vaccinated, the epidemic size is reduced by 19%. Our results suggest a new implementation of a highly effective strategy for targeted vaccinations through the use of popular locations in rural communities.

A network-based approach for resistance transmission in bacterial populations

Horizontal transfer of mobile genetic elements (conjugation) is an important mechanism whereby resistance is spread through bacterial populations. The aim of our work is to develop a mathematical model that quantitatively describes this process, and to use this model to optimize antimicrobial dosage regimens to minimize resistance development. The bacterial population is conceptualized as a compartmental mathematical model to describe changes in susceptible, resistant, and transconjugant bacteria over time. This model is combined with a compartmental pharmacokinetic model to explore the effect of different plasma drug concentration profiles. An agent-based simulation tool is used to account for resistance transfer occurring when two bacteria are adjacent or in close proximity. In addition, a non-linear programming optimal control problem is introduced to minimize bacterial populations as well as the drug dose. Simulation and optimization results suggest that the rapid death of susceptible individuals in the population is pivotal in minimizing the number of transconjugants in a population. This supports the use of potent antimicrobials that rapidly kill susceptible individuals and development of dosage regimens that maintain effective antimicrobial drug concentrations for as long as needed to kill off the susceptible population. Suggestions are made for experiments to test the hypotheses generated by these simulations.

A New Metric for Robustness with Respect to Virus Spread

The robustness of a network is depending on the type of attack we are considering. In this paper we focus on the spread of viruses on networks. It is common practice to use the epidemic threshold as a measure for robustness. Because the epidemic threshold is inversely proportional to the largest eigenvalue of the adjacency matrix, it seems easy to compare the robustness of two networks. We will show in this paper that the comparison of the robustness with respect to virus spread for two networks actually depends on the value of the effective spreading rate *** . For this reason we propose a new metric, the viral conductance, which takes into account the complete range of values *** can obtain. In this paper we determine the viral conductance of regular graphs, complete bi-partite graphs and a number of realistic networks.

Bloom: a stochastic growth-based fast method of community detection in networks

Abstract Networks are characterized by a variety of topological features and dynamics. Classifying nodes into communities, community structure, is important when exploring networks. This paper explores the community detection metric called modularity. The theoretical definitions of modularity are connected with intuitive insights into the compositions of communities. Local modularity costs/benefits are explored and an efficient stochastic algorithm, Bloom, is introduced, based on growing communities using local improvement measures. Three extensions of Bloom are presented that build upon the basic version. A numerical analysis compares Bloom with the popular fast-greedy algorithm and demonstrates the successful performance of the three modifications of Bloom.

A network model of successive partitioning-limited solute diffusion through the stratum corneum

As the most exposed point of contact with the external environment, the skin is an important barrier to many chemical exposures, including medications, potentially toxic chemicals and cosmetics. Traditional dermal absorption models treat the stratum corneum lipids as a homogenous medium through which solutes diffuse according to Ficks first law of diffusion. This approach does not explain non-linear absorption and irregular distribution patterns within the stratum corneum lipids as observed in experimental data. A network model, based on successive partitioning-limited solute diffusion through the stratum corneum, where the lipid structure is represented by a large, sparse, and regular network where nodes have variable characteristics, offers an alternative, efficient, and flexible approach to dermal absorption modeling that simulates non-linear absorption data patterns. Four model versions are presented: two linear models, which have unlimited node capacities, and two non-linear models, which have limited node capacities. The non-linear model outputs produce absorption to dose relationships that can be best characterized quantitatively by using power equations, similar to the equations used to describe non-linear experimental data.

Impact of Preventive Responses to Epidemics in Rural Regions

Various epidemics have arisen in rural locations through human-animal interaction, such as the H1N1 outbreak of 2009. Through collaboration with local government officials, we have surveyed a rural county and its communities and collected a dataset characterizing the rural population. From the respondents’ answers, we build a social (face-to-face) contact network. With this network, we explore the potential spread of epidemics through a Susceptible-Latent-Infected-Recovered (SLIR) disease model. We simulate an exact model of a stochastic SLIR Poisson process with disease parameters representing a typical influenza-like illness. We test vaccine distribution strategies under limited resources. We examine global and location-based distribution strategies, as a way to reach critical individuals in the rural setting. We demonstrate that locations can be identified through contact metrics for use in vaccination strategies to control contagious diseases.

An estimation of cattle movement parameters in the Central States of the US

We estimate the movement parameters of cattle across 10 Central States.Large USDA data sets were fed into an optimization procedure to extract parameters.Comparison with other literature suggests a high epidemic risk for US cattle systems. The characterization of cattle demographics and especially movements is an essential component in the modeling of dynamics in cattle systems, yet for cattle systems of the United States (US), this is missing. Through a large-scale maximum entropy optimization formulation, we estimate cattle movement parameters to characterize the movements of cattle across 10 Central States and 1034 counties of the United States. Inputs to the estimation problem are taken from the United States Department of Agriculture National Agricultural Statistics Service database and are pre-processed in a pair of tightly constrained optimization problems to recover non-disclosed elements of data. We compare stochastic subpopulation-based movements generated from the estimated parameters to operation-based movements published by the United States Department of Agriculture. Our novel method to estimate cattle movements across large US regions characterizes county-level stratified subpopulations of cattle for data-driven livestock modeling. Our estimated movement parameters suggest a significant risk of a disease successfully invading the US cattle systems.

Epirur_Cattle: A spatially explicit agent-based simulator of beef cattle movements

We present Epirur_Cattle, a spatially explicit agent-based simulator for synthesizing beef cattle movements and forecasting zoonotic disease spread in the American beef cattle industry. Farm, ranch, and feedlot operators make decisions on cattle trades according to cattle weights and market conditions. Contact networks of cattle are generated by geographical proximity and disease is spread through a simple compartmental model on the dynamic contact structures. An analysis of the network metrics of the contact networks and the aggregated contact networks provides insight into the influence of the network dynamics on the epidemic dynamics. Using farm data based on the Kansas cattle industry, our experiments show a tri-modal distribution of total case counts that becomes bi-modal for weaker diseases. These results are explained by the interaction of the disease and trading processes. We show how simple network metrics, such as the average node degree, can track the complex trading processes which shape the evolution of the disease at an agent level.