Daphnias: from the individual based model to the large population equation

The class of deterministic 'Daphnia' models treated by Diekmann et al. (J Math Biol 61: 277-318, 2010) has a long history going back to Nisbet and Gurney (Theor Pop Biol 23: 114-135, 1983) and Diekmann et al. (Nieuw Archief voor Wiskunde 4: 82-109, 1984). In this note, we formulate the individual based models (IBM) supposedly underlying those deterministic models. The models treat the interaction between a general size-structured consumer population ('Daphnia') and an unstructured resource ('algae'). The discrete, size and age-structured Daphnia population changes through births and deaths of its individuals and throught their aging and growth. The birth and death rates depend on the sizes of the individuals and on the concentration of the algae. The latter is supposed to be a continuous variable with a deterministic dynamics that depends on the Daphnia population. In this model setting we prove that when the Daphnia population is large, the stochastic differential equation describing the IBM can be approximated by the delay equation featured in (Diekmann et al., l.c.)

On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed for different sources of heterogeneity. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from a heterogeneous model with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which mimics reality very well, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the model.Comment: 23 pages, 2 figure

Effects of aging and links removal on epidemic dynamics in scale-free networks

We study the combined effects of aging and links removal on epidemic dynamics in the Barab\'{a}si-Albert scale-free networks. The epidemic is described by a susceptible-infected-refractory (SIR) model. The aging effect of a node introduced at time $t_{i}$ is described by an aging factor of the form $(t-t_{i})^{-\beta}$ in the probability of being connected to newly added nodes in a growing network under the preferential attachment scheme based on popularity of the existing nodes. SIR dynamics is studied in networks with a fraction $1-p$ of the links removed. Extensive numerical simulations reveal that there exists a threshold $p_{c}$ such that for $p \geq p_{c}$, epidemic breaks out in the network. For $p < p_{c}$, only a local spread results. The dependence of $p_{c}$ on $\beta$ is studied in detail. The function $p_{c}(\beta)$ separates the space formed by $\beta$ and $p$ into regions corresponding to local and global spreads, respectively.Comment: 8 pages, 3 figures, revtex, corrected Ref.[11

Особенности попередельного способа калькуляции себестоимости продукции в перерабатывающем производстве

We are interested in the asymptotic stability of equilibria of structured populations modelled in terms of systems of Volterra functional equations coupled with delay differential equations. The standard approach based on studying the characteristic equation of the linearized system is often involved or even unattainable. Therefore, we propose and investigate a numerical method to compute the eigenvalues of the associated infinitesimal generator. The latter is discretized by using a pseudospectral approach, and the eigenvalues of the resulting matrix are the sought approximations. An algorithm is presented to explicitly construct the matrix from the model coefficients and parameters. The method is tested first on academic examples, showing its suitability also for a class of mathematical models much larger than that mentioned above, including neutral- and mixed-type equations. Applications to cannibalism and consumer\u2013resource models are then provided in order to illustrate the efficacy of the proposed technique, especially for studying bifurcations

Experimental pig-to-pig transmission dynamics for African swine fever virus, Georgia 2007/1 strain

African swine fever virus (ASFV) continues to cause outbreaks in domestic pigs and wild boar in Eastern European countries. To gain insights into its transmission dynamics, we estimated the pig-to-pig basic reproduction number (R 0) for the Georgia 2007/1 ASFV strain using a stochastic susceptible-exposed-infectious-recovered (SEIR) model with parameters estimated from transmission experiments. Models showed that R 0 is 2·8 [95% confidence interval (CI) 1·3–4·8] within a pen and 1·4 (95% CI 0·6–2·4) between pens. The results furthermore suggest that ASFV genome detection in oronasal samples is an effective diagnostic tool for early detection of infection. This study provides quantitative information on transmission parameters for ASFV in domestic pigs, which are required to more effectively assess the potential impact of strategies for the control of between-farm epidemic spread in European countries.ISSN:0950-2688ISSN:1469-440

Escherichia coli low-copy-number plasmid R1 centromere parC forms a U-shaped complex with its binding protein ParR

The Escherichia coli low-copy-number plasmid R1 contains a segregation machinery composed of parC, ParR and parM. The R1 centromere-like site parC contains two separate sets of repeats. By atomic force microscopy (AFM) we show here that ParR molecules bind to each of the 5-fold repeated iterons separately with the intervening sequence unbound by ParR. The two ParR protein complexes on parC do not complex with each other. ParR binds with a stoichiometry of about one ParR dimer per each single iteron. The measured DNA fragment lengths agreed with B-form DNA and each of the two parC 5-fold interon DNA stretches adopts a linear path in its complex with ParR. However, the overall parC/ParR complex with both iteron repeats bound by ParR forms an overall U-shaped structure: the DNA folds back on itself nearly completely, including an angle of ∼150°. Analysing linear DNA fragments, we never observed dimerized ParR complexes on one parC DNA molecule (intramolecular) nor a dimerization between ParR complexes bound to two different parC DNA molecules (intermolecular). This bacterial segrosome is compared to other bacterial segregation complexes. We speculate that partition complexes might have a similar overall structural organization and, at least in part, common functional properties

Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation

We investigate saturation effects in susceptible-infected-susceptible (SIS) models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity distribution $P(k)$,including scale-free(SF) networks with power law distributions $P(k)\sim k^{-\gamma}$. Considering cases where the transmission of infection between nodes depends on their connectivity, we introduce a saturation function $C(k)$ which reduces the infection transmission rate $\lambda$ across an edge going from a node with high connectivity $k$. A mean field approximation with the neglect of degree-degree correlation then leads to a finite threshold $\lambda_{c}>0$ for SF networks with $2<\gamma \leq 3$. We also find, in this approximation, the fraction of infected individuals among those with degree $k$ for $\lambda$ close to $\lambda_{c}$. We investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean field theory with and without neglect of degree-degree correlations.Comment: 6 figure

Unconventional feeds for small ruminants in dry areas have a minor effect on manure nitrogen flow in the soil-plant system

In dry areas, unconventional feeds are increasingly used for mitigating feed shortages and rangeland degradation. We evaluated how feeding sheep diets containing olive leaves, saltbush leaves and olive cake affects manure quality compared to a barley straw based diet. Soil incubation and plant growth experiments were carried out to measure soil nitrogen (N) mineralization and N uptake by barley plants and to calculate N flow through the feed-animal-soil-plant system. Fresh feces, composts consisting of feces, urine and straw, and ammonium sulfate fertilizer were mixed with soil at rate of 90mgNkg−1 soil dry matter. Comparisons were made with non-amended soils (control) and soils amended with fresh olive cake applied at 90 and 22.5mgNkg−1 soil dry matter, respectively. The latter treatment enabled investigation of the effect of passage of olive cake through the digestive tract of sheep on N availability and phenol transformation. Applying fresh olive cake and feces, except the saltbush leaf derived feces, resulted in a net N immobilization. All composts resulted in net N mineralization, although not significantly different from the 0N control soil. Barley growing in soils with amendment that caused N immobilization took up less N than barley growing on the 0N treatment. Reduction in N uptake was most pronounced after amendment with fresh-olive cake. Treatments with net mineralization increased barley N uptake over the 0N treatment with 2-16% of N applied being taken up. Dietary composition had a minor effect on N fertilizer value of either feces or compost, but feces N alone was not an efficient N sourc

On the net reproduction rate of continuous structured populations with distributed states at birth

We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least!) in three different ways. One approach is to study spectral properties of a parametrized family of unbounded operators. The alternative approach, on which we focus here, is based on the reformulation of the problem as an integral equation. In this context we introduce a density dependent net reproduction rate and discuss its relationship to a biologically meaningful quantity. Finally, we briefly discuss a third approach, which is based on the finite rank approximation of the recruitment operator.Comment: To appear in Computers and Mathematics with Application