Contact Adaption During Epidemics: A Multilayer Network Formulation Approach.

People change their physical contacts as a preventive response to infectious disease propagations. Yet, only a few mathematical models consider the coupled dynamics of the disease propagation and the contact adaptation process. This paper presents a model where each agent has a default contact neighborhood set, and switches to a different contact set once she becomes alert about infection among her default contacts. Since each agent can adopt either of two possible neighborhood sets, the overall contact network switches among [Formula: see text] possible configurations. Notably, a two-layer network representation can fully model the underlying adaptive, state-dependent contact network. Contact adaptation influences the size of the disease prevalence and the epidemic threshold-a characteristic measure of a contact network robustness against epidemics-in a nonlinear fashion. Particularly, the epidemic threshold for the presented adaptive contact network belongs to the solution of a nonlinear Perron-Frobenius (NPF) problem, which does not depend on the contact adaptation rate monotonically. Furthermore, the network adaptation model predicts a counter-intuitive scenario where adaptively changing contacts may adversely lead to lower network robustness against epidemic spreading if the contact adaptation is not fast enough. An original result for a class of NPF problems facilitate the analytical developments in this paper.

Quantifying the impact of early-stage contact tracing on controlling Ebola diffusion.

Recent experience of the Ebola outbreak in 2014 highlighted the importance of immediate response measure to impede transmission in the early stage. To this aim, efficient and effective allocation of limited resources is crucial. Among the standard interventions is the practice of following up with the recent physical contacts of the infected individuals -- known as contact tracing. In an effort to understand the effects of contact tracing protocols objectively, we explicitly develop a model of Ebola transmission incorporating contact tracing. Our modeling framework is individual-based, patient-centric, stochastic and parameterizable to suit early-stage Ebola transmission. Notably, we propose an activity driven network approach to contact tracing, and estimate the basic reproductive ratio of the epidemic growth in different scenarios. Exhaustive simulation experiments suggest that early contact tracing paired with rapid hospitalization can effectively impede the epidemic growth. Resource allocation needs to be carefully planned to enable early detection of the contacts and rapid hospitalization of the infected people.

Biologically Informed Individual-Based Network Model for Rift Valley Fever in the US and Evaluation of Mitigation Strategies.

Rift Valley fever (RVF) is a zoonotic disease endemic in sub-Saharan Africa with periodic outbreaks in human and animal populations. Mosquitoes are the primary disease vectors; however, Rift Valley fever virus (RVFV) can also spread by direct contact with infected tissues. The transmission cycle is complex, involving humans, livestock, and multiple species of mosquitoes. The epidemiology of RVFV in endemic areas is strongly affected by climatic conditions and environmental variables. In this research, we adapt and use a network-based modeling framework to simulate the transmission of RVFV among hypothetical cattle operations in Kansas, US. Our model considers geo-located livestock populations at the individual level while incorporating the role of mosquito populations and the environment at a coarse resolution. Extensive simulations show the flexibility of our modeling framework when applied to specific scenarios to quantitatively evaluate the efficacy of mosquito control and livestock movement regulations in reducing the extent and intensity of RVF outbreaks in the United States.

Maximizing algebraic connectivity in interconnected networks.

Algebraic connectivity, the second eigenvalue of the Laplacian matrix, is a measure of node and link connectivity on networks. When studying interconnected networks it is useful to consider a multiplex model, where the component networks operate together with interlayer links among them. In order to have a well-connected multilayer structure, it is necessary to optimally design these interlayer links considering realistic constraints. In this work, we solve the problem of finding an optimal weight distribution for one-to-one interlayer links under budget constraint. We show that for the special multiplex configurations with identical layers, the uniform weight distribution is always optimal. On the other hand, when the two layers are arbitrary, increasing the budget reveals the existence of two different regimes. Up to a certain threshold budget, the second eigenvalue of the supra-Laplacian is simple, the optimal weight distribution is uniform, and the Fiedler vector is constant on each layer. Increasing the budget past the threshold, the optimal weight distribution can be nonuniform. The interesting consequence of this result is that there is no need to solve the optimization problem when the available budget is less than the threshold, which can be easily found analytically.

Exact coupling threshold for structural transition reveals diversified behaviors in interconnected networks.

An interconnected network features a structural transition between two regimes [F. Radicchi and A. Arenas, Nat. Phys. 9, 717 (2013)]: one where the network components are structurally distinguishable and one where the interconnected network functions as a whole. Our exact solution for the coupling threshold uncovers network topologies with unexpected behaviors. Specifically, we show conditions that superdiffusion, introduced by Gómez et al. [Phys. Rev. Lett. 110, 028701 (2013)], can occur despite the network components functioning distinctly. Moreover, we find that components of certain interconnected network topologies are indistinguishable despite very weak coupling between them.

Optimal information dissemination strategy to promote preventive behaviors in multilayer epidemic networks.

Launching a prevention campaign to contain the spread of infection requires substantial financial investments; therefore, a trade-off exists between suppressing the epidemic and containing costs. Information exchange among individuals can occur as physical contacts (e.g., word of mouth, gatherings), which provide inherent possibilities of disease transmission, and non-physical contacts (e.g., email, social networks), through which information can be transmitted but the infection cannot be transmitted. Contact network (CN) incorporates physical contacts, and the information dissemination network (IDN) represents non-physical contacts, thereby generating a multilayer network structure. Inherent differences between these two layers cause alerting through CN to be more effective but more expensive than IDN. The constraint for an epidemic to die out derived from a nonlinear Perron-Frobenius problem that was transformed into a semi-definite matrix inequality and served as a constraint for a convex optimization problem. This method guarantees a dying-out epidemic by choosing the best nodes for adopting preventive behaviors with minimum monetary resources. Various numerical simulations with network models and a real-world social network validate our method.

Predicting the impact of biocorona formation kinetics on interspecies extrapolations of nanoparticle biodistribution modeling.

AIM: To assess the impact of biocorona kinetics on expected tissue distribution of nanoparticles (NPs) across species. MATERIALS & METHODS: The potential fate of NPs in vivo is described through a simple and descriptive pharmacokinetic model using rate processes dependent upon basal metabolic rate coupled to dynamics of protein corona. RESULTS: Mismatch of time scales between interspecies allometric scaling and the kinetics of corona formation is potentially a fundamental issue with interspecies extrapolations of NP biodistribution. The impact of corona evolution on NP biodistribution across two species is maximal when corona transition half-life is close to the geometric mean of NP half-lives of the two species. CONCLUSION: While engineered NPs can successfully reach target cells in rodent models, the results may be different in humans due to the fact that the longer circulation time allows for further biocorona evolution.

Robustness surfaces of complex networks.

Despite the robustness of complex networks has been extensively studied in the last decade, there still lacks a unifying framework able to embrace all the proposed metrics. In the literature there are two open issues related to this gap: (a) how to dimension several metrics to allow their summation and (b) how to weight each of the metrics. In this work we propose a solution for the two aforementioned problems by defining the R*-value and introducing the concept of robustness surface (Ω). The rationale of our proposal is to make use of Principal Component Analysis (PCA). We firstly adjust to 1 the initial robustness of a network. Secondly, we find the most informative robustness metric under a specific failure scenario. Then, we repeat the process for several percentage of failures and different realizations of the failure process. Lastly, we join these values to form the robustness surface, which allows the visual assessment of network robustness variability. Results show that a network presents different robustness surfaces (i.e., dissimilar shapes) depending on the failure scenario and the set of metrics. In addition, the robustness surface allows the robustness of different networks to be compared.

Nanoparticle surface characterization and clustering through concentration-dependent surface adsorption modeling.

Quantitative characterization of nanoparticle interactions with their surrounding environment is vital for safe nanotechnological development and standardization. A recent quantitative measure, the biological surface adsorption index (BSAI), has demonstrated promising applications in nanomaterial surface characterization and biological/environmental prediction. This paper further advances the approach beyond the application of five descriptors in the original BSAI to address the concentration dependence of the descriptors, enabling better prediction of the adsorption profile and more accurate categorization of nanomaterials based on their surface properties. Statistical analysis on the obtained adsorption data was performed based on three different models: the original BSAI, a concentration-dependent polynomial model, and an infinite dilution model. These advancements in BSAI modeling showed a promising development in the application of quantitative predictive modeling in biological applications, nanomedicine, and environmental safety assessment of nanomaterials.

Competitive epidemic spreading over arbitrary multilayer networks.

This study extends the Susceptible-Infected-Susceptible (SIS) epidemic model for single-virus propagation over an arbitrary graph to an Susceptible-Infected by virus 1-Susceptible-Infected by virus 2-Susceptible (SI_{1}SI_{2}S) epidemic model of two exclusive, competitive viruses over a two-layer network with generic structure, where network layers represent the distinct transmission routes of the viruses. We find analytical expressions determining extinction, coexistence, and absolute dominance of the viruses after we introduce the concepts of survival threshold and absolute-dominance threshold. The main outcome of our analysis is the discovery and proof of a region for long-term coexistence of competitive viruses in nontrivial multilayer networks. We show coexistence is impossible if network layers are identical yet possible if network layers are distinct. Not only do we rigorously prove a region of coexistence, but we can quantitate it via interrelation of central nodes across the network layers. Little to no overlapping of the layers' central nodes is the key determinant of coexistence. For example, we show both analytically and numerically that positive correlation of network layers makes it difficult for a virus to survive, while in a network with negatively correlated layers, survival is easier, but total removal of the other virus is more difficult.

Dynamics of nanoparticle-protein corona complex formation: analytical results from population balance equations.

BACKGROUND: Nanoparticle-protein corona complex formation involves absorption of protein molecules onto nanoparticle surfaces in a physiological environment. Understanding the corona formation process is crucial in predicting nanoparticle behavior in biological systems, including applications of nanotoxicology and development of nano drug delivery platforms. METHOD: This paper extends the modeling work in to derive a mathematical model describing the dynamics of nanoparticle corona complex formation from population balance equations. We apply nonlinear dynamics techniques to derive analytical results for the composition of nanoparticle-protein corona complex, and validate our results through numerical simulations. RESULTS: The model presented in this paper exhibits two phases of corona complex dynamics. In the first phase, proteins rapidly bind to the free surface of nanoparticles, leading to a metastable composition. During the second phase, continuous association and dissociation of protein molecules with nanoparticles slowly changes the composition of the corona complex. Given sufficient time, composition of the corona complex reaches an equilibrium state of stable composition. We find analytical approximate formulae for metastable and stable compositions of corona complex. Our formulae are very well-structured to clearly identify important parameters determining corona composition. CONCLUSION: The dynamics of biocorona formation constitute vital aspect of interactions between nanoparticles and living organisms. Our results further understanding of these dynamics through quantitation of experimental conditions, modeling results for in vitro systems to better predict behavior for in vivo systems. One potential application would involve a single cell culture medium related to a complex protein medium, such as blood or tissue fluid.

On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading.

The spontaneous behavioral responses of individuals to the progress of an epidemic are recognized to have a significant impact on how the infection spreads. One observation is that, even if the infection strength is larger than the classical epidemic threshold, the initially growing infection can diminish as the result of preventive behavioral patterns adopted by the individuals. In order to investigate such dynamics of the epidemic spreading, we use a simple behavioral model coupled with the individual-based SIS epidemic model where susceptible individuals adopt a preventive behavior when sensing infection. We show that, given any infection strength and contact topology, there exists a region in the behavior-related parameter space such that infection cannot survive in long run and is completely contained. Several simulation results, including a spreading scenario in a realistic contact network from a rural district in the State of Kansas, are presented to support our analytical arguments.