ABSTRACT: Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.
Project description:Understanding the mechanisms that generate oscillations in the incidence of childhood infectious diseases has preoccupied epidemiologists and population ecologists for nearly two centuries. This body of work has generated simple yet powerful explanations for the epidemics of measles and chickenpox, while the dynamics of other infectious diseases, such as whooping cough, have proved more challenging to decipher. A number of authors have, in recent years, proposed that the noisy and somewhat irregular epidemics of whooping cough may arise due to stochasticity and its interaction with nonlinearity in transmission and seasonal variation in contact rates. The reason underlying the susceptibility of whooping cough dynamics to noise and the precise nature of its transient dynamics remain poorly understood. Here we use household data on the incubation period in order to parametrize more realistic distributions of the latent and infectious periods. We demonstrate that previously reported phenomena result from transients following the interaction between the stable annual attractor and unstable multiennial solutions.
Project description:Theoretical models are typically developed through a deductive process where a researcher formulates a system of dynamic equations from hypothesized mechanisms. Recent advances in algorithmic methods can discover dynamic models inductively-directly from data. Most previous research has tested these methods by rediscovering models from synthetic data generated by the already known model. Here we apply Sparse Identification of Nonlinear Dynamics (SINDy) to discover mechanistic equations for disease dynamics from case notification data for measles, chickenpox, and rubella. The discovered models provide a good qualitative fit to the observed dynamics for all three diseases, However, the SINDy chickenpox model appears to overfit the empirical data, and recovering qualitatively correct rubella dynamics requires using power spectral density in the goodness-of-fit criterion. When SINDy uses a library of second-order functions, the discovered models tend to include mass action incidence and a seasonally varying transmission rate-a common feature of existing epidemiological models for childhood infectious diseases. We also find that the SINDy measles model is capable of out-of-sample prediction of a dynamical regime shift in measles case notification data. These results demonstrate the potential for algorithmic model discovery to enrich scientific understanding by providing a complementary approach to developing theoretical models.
Project description:Cell lineage commitment and differentiation are governed by a complex gene regulatory network. Disruption of these processes by inappropriate regulatory signals and by mutational rewiring of the network can lead to tumorigenesis. Cancer cells often exhibit immature or embryonic traits and dysregulated developmental genes can act as oncogenes. However, the prevailing paradigm of somatic evolution and multi-step tumorigenesis, while useful in many instances, offers no logically coherent reason for why oncogenesis recapitulates ontogenesis. The formal concept of "cancer attractors", derived from an integrative, complex systems approach to gene regulatory network may provide a natural explanation. Here we present the theory of attractors in gene network dynamics and review the concept of cell types as attractors. We argue that cancer cells are trapped in abnormal attractors and discuss this concept in the light of recent ideas in cancer biology, including cancer genomics and cancer stem cells, as well as the implications for differentiation therapy.
Project description:In dissipationless linear media, spatial disorder induces Anderson localization of matter, light, and sound waves. The addition of nonlinearity causes interaction between the eigenmodes, which results in a slow wave diffusion. We go beyond the dissipationless limit of Anderson arrays and consider nonlinear disordered systems that are subjected to the dissipative losses and energy pumping. We show that the Anderson modes of the disordered Ginsburg-Landau lattice possess specific excitation thresholds with respect to the pumping strength. When pumping is increased above the threshold for the band-edge modes, the lattice dynamics yields an attractor in the form of a stable multi-peak pattern. The Anderson attractor is the result of a joint action by the pumping-induced mode excitation, nonlinearity-induced mode interactions, and dissipative stabilization. The regimes of Anderson attractors can be potentially realized with polariton condensates lattices, active waveguide or cavity-QED arrays.
Project description:Developmental dynamics in Boolean models of gene networks self-organize, either into point attractors (stable repeating patterns of gene expression) or limit cycles (stable repeating sequences of patterns), depending on the network interactions specified by a genome of evolvable bits. Genome specifications for dynamics that can map specific gene expression patterns in early development onto specific point attractor patterns in later development are essentially impossible to discover by chance mutation alone, even for small networks. We show that selection for approximate mappings, dynamically maintained in the states comprising limit cycles, can accelerate evolution by at least an order of magnitude. These results suggest that self-organizing dynamics that occur within lifetimes can, in principle, guide natural selection across lifetimes.
Project description:This paper addresses the problem of finding attractors in biological regulatory networks. We focus here on non-deterministic synchronous and asynchronous multi-valued networks, modeled using automata networks (AN). AN is a general and well-suited formalism to study complex interactions between different components (genes, proteins,...). An attractor is a minimal trap domain, that is, a part of the state-transition graph that cannot be escaped. Such structures are terminal components of the dynamics and take the form of steady states (singleton) or complex compositions of cycles (non-singleton). Studying the effect of a disease or a mutation on an organism requires finding the attractors in the model to understand the long-term behaviors.We present a computational logical method based on answer set programming (ASP) to identify all attractors. Performed without any network reduction, the method can be applied on any dynamical semantics. In this paper, we present the two most widespread non-deterministic semantics: the asynchronous and the synchronous updating modes. The logical approach goes through a complete enumeration of the states of the network in order to find the attractors without the necessity to construct the whole state-transition graph. We realize extensive computational experiments which show good performance and fit the expected theoretical results in the literature.The originality of our approach lies on the exhaustive enumeration of all possible (sets of) states verifying the properties of an attractor thanks to the use of ASP. Our method is applied to non-deterministic semantics in two different schemes (asynchronous and synchronous). The merits of our methods are illustrated by applying them to biological examples of various sizes and comparing the results with some existing approaches. It turns out that our approach succeeds to exhaustively enumerate on a desktop computer, in a large model (100 components), all existing attractors up to a given size (20 states). This size is only limited by memory and computation time.
Project description:The detection of the singleton attractors is of great significance for the systematic study of genetic regulatory network. In this paper, we design an algorithm to compute the singleton attractors and pre-images of the strong-inhibition Boolean networks which is a biophysically plausible gene model. Our algorithm can not only identify accurately the singleton attractors, but also find easily the pre-images of the network. Based on extensive computational experiments, we show that the computational time of the algorithm is proportional to the number of the singleton attractors, which indicates the algorithm has much advantage in finding the singleton attractors for the networks with high average degree and less inhibitory interactions. Our algorithm may shed light on understanding the function and structure of the strong-inhibition Boolean networks.
Project description:Attractors represent the long-term behaviors of Random Boolean Networks. We study how the amount of information propagated between the nodes when on an attractor, as quantified by the average pairwise mutual information (I(A)), relates to the robustness of the attractor to perturbations (R(A)). We find that the dynamical regime of the network affects the relationship between I(A) and R(A). In the ordered and chaotic regimes, I(A) is anti-correlated with R(A), implying that attractors that are highly robust to perturbations have necessarily limited information propagation. Between order and chaos (for so-called "critical" networks) these quantities are uncorrelated. Finite size effects cause this behavior to be visible for a range of networks, from having a sensitivity of 1 to the point where I(A) is maximized. In this region, the two quantities are weakly correlated and attractors can be almost arbitrarily robust to perturbations without restricting the propagation of information in the network.
Project description:BACKGROUND: The rubella vaccine was introduced into the immunization program in 1995 in the Shandong province, China. A series of different rubella vaccination strategies were implemented at different stages of measles control in Shandong province. METHODOLOGY/PRINCIPAL FINDINGS: The average reported incidence rate of rubella cases remained at a low level in Shandong province after 1999. However, rubella epidemics occurred repeatedly in 2001/2002, 2006, and 2008/2009. The age of the onset of rubella cases gradually increased during 1999-2010, which showed that most cases were found among the 10 years old in 1999 and among the 17 years old in 2010. Phylogenetic analysis was performed and a phylogenetic tree was constructed based on the World Health Organization standard sequence window for rubella virus isolates. All rubella viruses isolated in Shandong province were divided into 4 genotypes: 1E, 1F, 2A, and 2B. Genotype 1E viruses accounted for the majority (79%) of all these viruses. The similarity of nucleotide and amino acid sequences among genotype 1E viruses was 98.2-100% and 99.1-100%, respectively. All Shandong genotype 1E strains, differed from international genotype 1E strains, belonged to cluster 1 and interdigitated with the viruses from other provinces in mainland China. The effective number of infections indicated by a bayesian skyline plot remained constant from 2001 to 2009. CONCLUSIONS/SIGNIFICANCE: The gradual shift of disease burden to an older age group occurred after a rubella-containing vaccine was introduced into the childhood immunization schedule in 1995 in Shandong province. Four genotypes, including 1E, 1F, 2A, and 2B, were found in Shandong province during 2000-2009. Genotype 1E, rather than genotype 1F, became the predominant genotype circulating in Shandong province from 2001. All Shandong genotype 1E viruses belong to the genotype 1E/cluster 1; they have constantly circulated, and co-evolved and co-circulated, with those from other provinces.