Epidemic variability in complex networks

We study numerically the variability of the outbreak of diseases on complex networks. We use a SI model to simulate the disease spreading at short times, in homogeneous and in scale-free networks. In both cases, we study the effect of initial conditions on the epidemic's dynamics and its variability. The results display a time regime during which the prevalence exhibits a large sensitivity to noise. We also investigate the dependence of the infection time on nodes' degree and distance to the seed. In particular, we show that the infection time of hubs have large fluctuations which limit their reliability as early-detection stations. Finally, we discuss the effect of the multiplicity of shortest paths between two nodes on the infection time. Furthermore, we demonstrate that the existence of even longer paths reduces the average infection time. These different results could be of use for the design of time-dependent containment strategies

Size-structured populations: immigration, (bi)stability and the net growth rate

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the linearised system is governed by a quasicontraction semigroup. We also establish that linear stability of equilibrium solutions is governed by a generalized net reproduction function. In a special case of the model ingredients we discuss the nonlinear dynamics of the system when the spectral bound of the linearised operator equals zero, i.e. when linearisation does not decide stability. This allows us to demonstrate, through a concrete example, how immigration might be beneficial to the population. In particular, we show that from a nonlinearly unstable positive equilibrium a linearly stable and unstable pair of equilibria bifurcates. In fact, the linearised system exhibits bistability, for a certain range of values of the external inflow, induced potentially by All\'{e}e-effect.Comment: to appear in Journal of Applied Mathematics and Computin

Daphnia revisited: Local stability and bifurcation theory for physiologically structured population models explained by way of an example

We consider the interaction between a general size-structured consumer population and an unstructured resource. We show that stability properties and bifurcation phenomena can be understood in terms of solutions of a system of two delay equations (a renewal equation for the consumer population birth rate coupled to a delay differetial equation for the resource concentration). As many results for such systems are available, we can draw rigorous conclusions concerning dynamical behaviour from an analysis of a characteristic equation. We derive the characteristic equation for a fairly general class of population models, including those based on the Kooijman-Metz Daphnia model and a model introduced by Gurney-Nisbet and Jones et al., and next obtain various ecological insights by analytical or numerical studies of special cases

Late Quaternary terrigenous sediment supply in the Drake Passage in response to Patagonian and Antarctic ice dynamics

The Drake Passage, as the narrowest passage around Antarctica, exerts significant influences on the physical, chemical, and biological interactions between the Pacific and Atlantic Ocean. Here, we identify terrigenous sediment sources and transport pathways in the Drake Passage region over the past 140 ka BP (thousand years before present), based on grain size, clay mineral assemblages, geochemistry and mass-specific magnetic susceptibility records. Terrigenous sediment supply in the Drake Passage is mainly derived from the southeast Pacific, southern South America and the Antarctic Peninsula. Our results provide robust evidence that the Antarctic Circumpolar Current (ACC) has served as the key driver for sediment dispersal in the Drake Passage. High glacial mass accumulation rates indicate enhanced detrital input, which was closely linked to a large expansion of ice sheets in southern South America and on the Antarctic Peninsula during the glacial maximum, as significantly advanced glaciers eroded more glaciogenic sediments from the continental hinterlands into the Drake Passage. Moreover, lower glacial sea levels exposed large continental shelves, which together with weakened ACC strength likely amplified the efficiency of sediment supply and deposition in the deep ocean. In contrast, significant glaciers' shrinkage during interglacials, together with higher sea-level conditions and storage of sediment in nearby fjords reduced terrigenous sediment inputs. Furthermore, a stronger ACC may have induced winnowing effects and further lowered the mass accumulation rates. Evolution of ice sheets, sea level changes and climate related ACC dynamic have thus exerted critical influences on the terrigenous sediment supply and deposition in the Drake Passage region over the last glacial-interglacial cycle

A generic C1C^1 map has no absolutely continuous invariant probability measure

Let $M$ be a smooth compact manifold (maybe with boundary, maybe disconnected) of any dimension $d \ge 1$. We consider the set of $C^1$ maps $f:M\to M$ which have no absolutely continuous (with respect to Lebesgue) invariant probability measure. We show that this is a residual (dense $G_\delta) set in the$C^1$ topology. In the course of the proof, we need a generalization of the usual Rokhlin tower lemma to non-invariant measures. That result may be of independent interest.Comment: 12 page

The evolutionary stability of attenuators that mask information about animals that social partners can exploit

Signals and cues are fundamental to social interactions. A well-established concept in the study of animal communication is an amplifier, defined as a trait that does not add extra information to that already present in the original cue or signal, but rather enhances the fidelity with which variation in the original cue or signal is correctly perceived. Attenuators as the logical compliment of amplifiers: attenuators act to reduce the fidelity with which variation in a signal or cue can be reliably evaluated by the perceivers. Where amplifiers reduce the effect of noise on the perception of variation, attenuators add noise. Attenuators have been subject to much less consideration than amplifiers, however they will be the focus of our theoretical study. We utilise an extension of a well-established model incorporated signal or cue inaccuracy and costly investments by emitter and perceiver in sending and attending to the signal or cue. We present broad conditions involving some conflict of interest between emitter and perceiver where it may be advantageous for emitters to invest in costly attenuators to mask cues from potential perceivers, and a subset of these conditions where the perceiver may be willing to invest in costly anti-attentuators to mitigate the loss of information to them. We demonstrate that attenuators can be evolutionary stable even if they are costly, even if they are sometimes disadvantageous, and even if a perceiver can mount counter-measures to them. As such, we feel that attenuators of cues may be deserving of much more research attention.PostprintPeer reviewe

A Network-Based Meta-Population Approach to Model Rift Valley Fever Epidemics

Rift Valley fever virus (RVFV) has been expanding its geographical distribution with important implications for both human and animal health. The emergence of Rift Valley fever (RVF) in the Middle East, and its continuing presence in many areas of Africa, has negatively impacted both medical and veterinary infrastructures and human health. Furthermore, worldwide attention should be directed towards the broader infection dynamics of RVFV. We propose a new compartmentalized model of RVF and the related ordinary differential equations to assess disease spread in both time and space; with the latter driven as a function of contact networks. The model is based on weighted contact networks, where nodes of the networks represent geographical regions and the weights represent the level of contact between regional pairings for each set of species. The inclusion of human, animal, and vector movements among regions is new to RVF modeling. The movement of the infected individuals is not only treated as a possibility, but also an actuality that can be incorporated into the model. We have tested, calibrated, and evaluated the model using data from the recent 2010 RVF outbreak in South Africa as a case study; mapping the epidemic spread within and among three South African provinces. An extensive set of simulation results shows the potential of the proposed approach for accurately modeling the RVF spreading process in additional regions of the world. The benefits of the proposed model are twofold: not only can the model differentiate the maximum number of infected individuals among different provinces, but also it can reproduce the different starting times of the outbreak in multiple locations. Finally, the exact value of the reproduction number is numerically computed and upper and lower bounds for the reproduction number are analytically derived in the case of homogeneous populations.Comment: published on Journal of Theoretical biolog

Dynamics of multi-stage infections on networks

This paper investigates the dynamics of infectious diseases with a nonexponentially distributed infectious period. This is achieved by considering a multistage infection model on networks. Using pairwise approximation with a standard closure, a number of important characteristics of disease dynamics are derived analytically, including the final size of an epidemic and a threshold for epidemic outbreaks, and it is shown how these quantities depend on disease characteristics, as well as the number of disease stages. Stochastic simulations of dynamics on networks are performed and compared to output of pairwise models for several realistic examples of infectious diseases to illustrate the role played by the number of stages in the disease dynamics. These results show that a higher number of disease stages results in faster epidemic outbreaks with a higher peak prevalence and a larger final size of the epidemic. The agreement between the pairwise and simulation models is excellent in the cases we consider