Epidemic spreading in modular time-varying networks

We investigate the effects of modular and temporal connectivity patterns on epidemic spreading. To this end, we introduce and analytically characterise a model of time-varying networks with tunable modularity. Within this framework, we study the epidemic size of Susceptible-Infected-Recovered, SIR, models and the epidemic threshold of Susceptible-Infected-Susceptible, SIS, models. Interestingly, we find that while the presence of tightly connected clusters inhibits SIR processes, it speeds up SIS phenomena. In this case, we observe that modular structures induce a reduction of the threshold with respect to time-varying networks without communities. We confirm the theoretical results by means of extensive numerical simulations both on synthetic graphs as well as on a real modular and temporal networ

Capturing sexual contact patterns in modelling the spread of sexually transmitted infections : evidence using Natsal-3

Background Understanding the spread of sexually transmitted infections (STIs) in a population is of great importance to the planning and delivery of health services globally. The worldwide rise of HIV since the 1980’s, and the recent increase in common STIs (including HPV and Chlamydia) in many countries, means that there is an urgent need to understand transmission dynamics in order to better predict the spread of such infections in the population. Unlike many other infections which can be captured by assumptions of random mixing, STI transmission is intimately linked to the number and pattern of sexual contacts. In fact, it is the huge variation in the number of new sexual partners that gives rise to the extremes of risk within populations which need to be captured in predictive models of STI transmission. Such models are vital in providing the necessary scientific evidence to determine whether a range of controls (from education to screening to vaccination) are cost-effective. Method and results We use probability sample survey data from Britain’s third National Survey of Sexual Attitudes and Lifestyles (Natsal-3) to determine robust distributions for the rate of new partnerships that involve condomless sex and can therefore facilitate the spread of STIs. Different distributions are defined depending on four individual-level characteristics: age, sex, sexual orientation, and previous sexual experience. As individual behaviour patterns can change (e.g. by remaining in a monogamous relationship for a long period) we allow risk-percentiles to be randomly redrawn, to capture longer term behaviour as measured by Natsal-3. We demonstrate how this model formulation interacts with the transmission of infection by constructing an individual-based SIS-P (Susceptible—Infected—Susceptible—Protected) transmission model for the spread of a generic STI, and observing overall population demographics when varying the transmission probability within a partnership, recovery rate and the level of population protection (e.g. from vaccination where applicable)

Design and Analysis of Infectious Disease Studies

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Diffusion in Networks and the Unexpected Virtue of Burstiness

Whether an idea, information, infection, or innovation diffuses throughout a society depends not only on the structure of the network of interactions, but also on the timing of those interactions. Recent studies have shown that diffusion can fail on a network in which people are only active in "bursts", active for a while and then silent for a while, but diffusion could succeed on the same network if people were active in a more random Poisson manner. Those studies generally consider models in which nodes are active according to the same random timing process and then ask which timing is optimal. In reality, people differ widely in their activity patterns -- some are bursty and others are not. Here we show that, if people differ in their activity patterns, bursty behavior does not always hurt the diffusion, and in fact having some (but not all) of the population be bursty significantly helps diffusion. We prove that maximizing diffusion requires heterogeneous activity patterns across agents, and the overall maximizing pattern of agents' activity times does not involve any Poisson behavior

Modern temporal network theory: A colloquium

The power of any kind of network approach lies in the ability to simplify a complex system so that one can better understand its function as a whole. Sometimes it is beneficial, however, to include more information than in a simple graph of only nodes and links. Adding information about times of interactions can make predictions and mechanistic understanding more accurate. The drawback, however, is that there are not so many methods available, partly because temporal networks is a relatively young field, partly because it more difficult to develop such methods compared to for static networks. In this colloquium, we review the methods to analyze and model temporal networks and processes taking place on them, focusing mainly on the last three years. This includes the spreading of infectious disease, opinions, rumors, in social networks; information packets in computer networks; various types of signaling in biology, and more. We also discuss future directions.Comment: Final accepted versio

Modular Verification of Biological Systems

Systems of interest in systems biology (such as metabolic pathways, signalling pathways and gene regulatory networks) often consist of a huge number of components interacting in different ways, thus exhibiting very complex behaviours. In biology, such behaviours are usually explored by means of simulation techniques applied to models defined on the basis of system observation and of hypotheses on its functioning. Model checking has also been recently applied to the analysis of biological systems. This analysis technique typically relies on a state space representation whose size, unfortunately, makes the analysis often intractable for realistic models. A method for trying to avoid the state space explosion problem is to consider a decomposition of the system, and to apply a modular verification technique. In particular, properties to be verified often concern only a small portion of the modelled system rather than the system as a whole. Hence, for each property it would be useful to be able to isolate a minimal fragment of the model that is necessary to verify such a property. In this thesis we introduce a modular verification technique in which the system of interest is described by means of an automata-based formalism, called sync-programs, that supports modular construction. Our modular verification technique is based on results of Grumberg et al.~and on their application to the theory of concurrent systems proposed by Attie and Emerson. In particular, we adapt Attie and Emerson's approach to deal with biological systems by allowing automata to synchronise by performing transitions simultaneously. Modular verification allows qualitative aspects of systems to be analysed with the guarantee that properties proved to hold in a suitable model fragment also hold in the whole model. The correctness of the verification technique is proved. The class of properties preserved is ACTL$^{-}$, the universal fragment of temporal logic CTL. The preservation holds only for positive answers and negative answers are not necessarily preserved. In order to verify properties we use the NuSMV model checker, which is a well-established and efficient instrument. We provide a formal translation of sync-programs to simpler automata, which can be given as input to NuSMV. We prove the correspondence of the verification problems. We show the application of our verification technique in some biological case studies. We compare the time required to verify the property on the whole model with the time needed to verify the same property by only considering those modules which are involved in the behaviour of the system related to the property. In order to handle modelling and verification of more realistic biological scenarios, we propose also a dynamic version of our formalism. It allows entities to be created dynamically, in particular by other already running entities, as it often happens in biological systems. Moreover, multiple copies of the same entities can be present at the same time in a system. We show a correspondence of our model with Petri Nets. This has a consequence that tools developed for Petri Nets could be used also for dynamic sync-programs. Modular verification allows properties expressed as DACTL- formulae (dynamic version of ACTL-) to be verified on a portion of the model. The results of analysis of the case study of the MAP kinase cascade activated by surface and internalised EGF receptors, which consists of 143 species and 80 reactions, suggest applicability and scalability of the approach. The results raise the prospect of rendering tractable problems that are currently intractable in the verification of biological systems. In addition, we expect that the techniques developed in the thesis could be applied with profit not only to models of biological systems, but more generally to models of concurrent systems

Strategy evolution on dynamic networks

Models of strategy evolution on static networks help us understand how population structure can promote the spread of traits like cooperation. One key mechanism is the formation of altruistic spatial clusters, where neighbors of a cooperative individual are likely to reciprocate, which protects prosocial traits from exploitation. But most real-world interactions are ephemeral and subject to exogenous restructuring, so that social networks change over time. Strategic behavior on dynamic networks is difficult to study, and much less is known about the resulting evolutionary dynamics. Here, we provide an analytical treatment of cooperation on dynamic networks, allowing for arbitrary spatial and temporal heterogeneity. We show that transitions among a large class of network structures can favor the spread of cooperation, even if each individual social network would inhibit cooperation when static. Furthermore, we show that spatial heterogeneity tends to inhibit cooperation, whereas temporal heterogeneity tends to promote it. Dynamic networks can have profound effects on the evolution of prosocial traits, even when individuals have no agency over network structures.Comment: 45 pages; final versio

Contagion dynamics in time-varying metapopulation networks

The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the migration routes among them. The connections have been so far mostly considered as static, but in general evolve in time. Here we address this case by investigating simple contagion processes on time-varying metapopulation networks. We focus on the SIR process and determine analytically the mobility threshold for the onset of an epidemic spreading in the framework of activity-driven network models. We find profound differences from the case of static networks. The threshold is entirely described by the dynamical parameters defining the average number of instantaneously migrating individuals and does not depend on the properties of the static network representation. Remarkably, the diffusion and contagion processes are slower in time-varying graphs than in their aggregated static counterparts, the mobility threshold being even two orders of magnitude larger in the first case. The presented results confirm the importance of considering the time-varying nature of complex networks