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Register a new userRegularity underlies erratic population abundances in marine ecosystems
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The abundance of a species population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a well-defined double-exponential (Laplace) distribution. This striking regularity allows us to devise a stochastic model despite seemingly irregular variations in population abundances. The model identifies the effect of reduced growth at low population density as a key factor missed in current approaches of population variability analysis and without which extinction risks are severely underestimated. The model also allows us to separate the effect of demographic stochasticity and show that single-species growth rates are dominantly determined by stochasticity common to all species. This dominance---and the implications it has for interspecies correlations, including co-extinctions---emphasizes the need of ecosystem-level management approaches to reduce the extinction risk of the individual species themselves.
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Behavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized--and thus homogeneous--across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.
We present a generic epidemic model with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective reproduction rate fluctuates close to the critical value one, as observed for different epidemics. The main assumptions underlying the model are that the rate at which each individual becomes infected changes stochastically in time with a heavy-tailed steady state. The critical regime is characterized by an extremely long duration of the epidemic. Its stability is analyzed both numerically and analytically.
Dengue viral infections show unique infection patterns arising from its four serot- ypes, (DENV-1,2,3,4). Its effects range from simple fever in primary infections to potentially fatal secondary infections. We analytically and numerically analyse virus dynamics and humoral response in a host during primary and secondary dengue infection for long periods using micro-epidemic models. The models presented here incorporate time delays, antibody dependent enhancement (ADE), a dynamic switch and a correlation factor between different DENV serotypes. We find that the viral load goes down to undetectable levels within 7-14 days as is observed for dengue infection, in both cases. For primary infection, the stability analysis of steady states shows interesting dependence on the time delay involved in the production of antibodies from plasma cells. We demonstrate the existence of a critical value for the immune response parameter, beyond which the infection gets completely cured. For secondary infections with a different serotype, the homologous antibody production is enhanced due to the influence of heterologous antibodies. The antibody production is also controlled by the correlation factor, which is a measure of similarities between the different DENV serotypes involved. Our results agree with clinically observed humoral responses for primary and secondary infections.
We discuss several models of the dynamics of interacting populations. The models are constructed by nonlinear differential equations and have two sets of parameters: growth rates and coefficients of interaction between populations. We assume that the parameters depend on the densities of the populations. In addition the parameters can be influenced by different factors of the environment. This influence is modelled by noise terms in the equations for the growth rates and interaction coefficients. Thus the model differential equations become stochastic. In some particular cases these equations can be reduced to a Foker-Plancnk equation for the probability density function of the densities of the interacting populations.
The network of 5823 cities of Mexico with a population more than 5000 inhabitants is studied. Our analysis is focused to the spectral properties of the adjacency matrix, the small-world properties of the network, the distribution of the clustering coefficients and the degree distribution of the vertices. The connection of these features with the spread of epidemics on this network is also discussed.
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