An epidemiological model which incorporates synergistic effects that allow the infectivity and/or susceptibility of hosts to be dependent on the number of infected neighbors is proposed. Constructive synergy induces an exploitative behavior which results in a rapid invasion that infects a large number of hosts. Interfering synergy leads to a slower and sparser explorative foraging strategy that traverses larger distances by infecting fewer hosts. The model can be mapped to a dynamical bond percolation with spatial correlations that affect the mechanism of spread but do not influence the critical behavior of epidemics.
Localization-delocalization transitions occur in problems ranging from semiconductor-device physics to propagation of disease in plants and viruses on the internet. Here, we report calculations of localized electronic and vibrational eigenstates for remarkably different, mostly realistic, disordered systems and point out similar characteristics in the cases studied. We show in each case that the eigenstates may be decomposed into exponentially localized islands which may appear in many different eigenstates. In all cases, the decay length of the islands increases only modestly near the localization-delocalization transition; the eigenstates become extended primarily by proliferation (growth in number) of islands near the transition. Recently, microphotoluminescence experiments (Guillet et al 2003 Phys. Rev. B 68 045319) have imaged exciton states in disordered quantum wires, and these bear a strong qualitative resemblance to the island structure of eigenstates that we have studied theoretically.
The vibrational equivalent of the Anderson tight-binding Hamiltonian has been studied, with particular focus on the properties of the eigenstates at the transition from extended to localized states. The critical energy has been found approximately for several degrees of force-constant disorder using system-size scaling of the multifractal spectra of the eigenmodes, and the spectrum at which there is no system-size dependence has been obtained. This is shown to be in good agreement with the critical spectrum for the electronic problem, which has been derived both numerically and by analytic means. Universality of the critical states is therefore suggested also to hold for the vibrational problem.
There is increasing interest in the use of the percolation paradigm to analyse and predict the progress of disease spreading in spatially structured populations of animals and plants. The wider utility of the approach has been limited, however, by several restrictive assumptions, foremost of which is a strict requirement for simple nearest-neighbour transmission, in which the disease history of an individual is influenced only by that of its neighbours. In a recent paper, the percolation paradigm has been generalized to incorporate synergistic interactions in host infectivity and susceptibility, and the impact of these interactions on the invasive dynamics of an epidemic has been demonstrated. In the current paper, we elicit evidence that such synergistic interactions may underlie transmission dynamics in real-world systems by first formulating a model for the spread of a ubiquitous parasitic and saprotrophic fungus through replicated populations of nutrient sites and subsequently fitting and testing the model using data from experimental microcosms. Using Bayesian computational methods for model fitting, we demonstrate that synergistic interactions are necessary to explain the dynamics observed in the replicate experiments. The broader implications of this work in identifying disease-control strategies that deflect epidemics from invasive to non-invasive regimes are discussed.
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