Dynamics of interacting diseases

Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place on a single level (be it a single population, a meta-population system or a network of contacts). In particular, interdependent contagion phenomena can only be addressed if we go beyond the scheme one pathogen-one network. In this paper, we propose a framework that allows describing the spreading dynamics of two concurrent diseases. Specifically, we characterize analytically the epidemic thresholds of the two diseases for different scenarios and also compute the temporal evolution characterizing the unfolding dynamics. Results show that there are regions of the parameter space in which the onset of a disease's outbreak is conditioned to the prevalence levels of the other disease. Moreover, we show, for the SIS scheme, that under certain circumstances, finite and not vanishing epidemic thresholds are found even at the thermodynamic limit for scale-free networks. For the SIR scenario, the phenomenology is richer and additional interdependencies show up. We also find that the secondary thresholds for the SIS and SIR models are different, which results directly from the interaction between both diseases. Our work thus solve an important problem and pave the way towards a more comprehensive description of the dynamics of interacting diseases.Comment: 24 pages, 9 figures, 4 tables, 3 appendices. Final version accepted for publication in Physical Review

Interacting Spreading Processes in Multilayer Networks: A Systematic Review

© 2013 IEEE. The world of network science is fascinating and filled with complex phenomena that we aspire to understand. One of them is the dynamics of spreading processes over complex networked structures. Building the knowledge-base in the field where we can face more than one spreading process propagating over a network that has more than one layer is a challenging task, as the complexity comes both from the environment in which the spread happens and from characteristics and interplay of spreads' propagation. As this cross-disciplinary field bringing together computer science, network science, biology and physics has rapidly grown over the last decade, there is a need to comprehensively review the current state-of-the-art and offer to the research community a roadmap that helps to organise the future research in this area. Thus, this survey is a first attempt to present the current landscape of the multi-processes spread over multilayer networks and to suggest the potential ways forward

Multilayer Networks

In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include multiple subsystems and layers of connectivity, and it is important to take such "multilayer" features into account to try to improve our understanding of complex systems. Consequently, it is necessary to generalize "traditional" network theory by developing (and validating) a framework and associated tools to study multilayer systems in a comprehensive fashion. The origins of such efforts date back several decades and arose in multiple disciplines, and now the study of multilayer networks has become one of the most important directions in network science. In this paper, we discuss the history of multilayer networks (and related concepts) and review the exploding body of work on such networks. To unify the disparate terminology in the large body of recent work, we discuss a general framework for multilayer networks, construct a dictionary of terminology to relate the numerous existing concepts to each other, and provide a thorough discussion that compares, contrasts, and translates between related notions such as multilayer networks, multiplex networks, interdependent networks, networks of networks, and many others. We also survey and discuss existing data sets that can be represented as multilayer networks. We review attempts to generalize single-layer-network diagnostics to multilayer networks. We also discuss the rapidly expanding research on multilayer-network models and notions like community structure, connected components, tensor decompositions, and various types of dynamical processes on multilayer networks. We conclude with a summary and an outlook.Comment: Working paper; 59 pages, 8 figure

New algorithms for solving high-dimensional time-dependent optimal control problems and their applications in infectious disease models

Doctor of PhilosophyDepartment of Industrial & Manufacturing Systems EngineeringChih-Hang 'John' WuInfectious diseases have been the primary cause of human death worldwide nowadays. The optimal control strategy for infectious disease has attracted increasing attention, becoming a significant issue in the healthcare domain. Optimal control of diseases can affect the progression of diseases and achieve high-quality healthcare. In previous studies, massive efforts on the optimal control of diseases have been made. However, some infectious diseases' mortality is still high and even developed into the second highest cause of mortality in the US. According to the limitations in existing research, this research aims to study the optimal control strategy via some industrial engineering techniques such as mathematical modeling, optimization algorithm, analysis, and numerical simulation. To better understand the optimal control strategy, two infectious disease models (epidemic disease, sepsis) are studied. Complex nonlinear time-series and high-dimensional infectious disease control models are developed to study the transmission and optimal control of deterministic SEIR or stochastic SIS epidemic diseases. In addition, a stochastic sepsis control model is introduced to study the progression and optimal control for sepsis system considering possible medical measurement errors or system uncertainty. Moreover, an improved complex nonlinear sepsis model is presented to more accurately study the sepsis progression and optimal control for sepsis system. In this dissertation, some analysis methods such as stability analysis, bifurcation analysis, and sensitivity analysis are utilized to help reader better understand the model behavior and the effectiveness of the optimal control. The significant contributions of this dissertation are developing or improving nonlinear complex disease optimal control models and proposing several effective and efficient optimization algorithms to solve the optimal control in those researched disease models, such as an optimization algorithm combining machine learning (EBOC), an improved Bayesian Optimization algorithm (IBO algorithm), a novel high-dimensional Bayesian Optimization algorithm combining dimension reduction and dimension fill-in (DR-DF BO algorithm), and a high-dimensional Bayesian Optimization algorithm combining Recurrent Neural Network (RNN-BO algorithm). Those algorithms can solve the optimal control solution for complex nonlinear time-series and high-dimensional systems. On top of that, numerical simulation is used to demonstrate the effectiveness and efficiency of the proposed algorithms