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Clusters appear in nature in a diversity of contexts, involving distances as long as the cosmological ones, and down to atoms and molecules and the very small nuclear size. They also appear in several other scenarios, in particular in biological systems as in ants, bees, birds, fishes, gnus and rats, for instance. Here we describe a model composed of a set of female and male individuals that obeys simple rules that rapidly transform an uniform initial state into a single cluster that evolves in time as a stable dynamical structure. We show that the center of mass of the structure moves as a random walk, and that the size of the cluster engenders a power law behavior in terms of the number of individuals in the system. Moreover, we also examine other possibilities, in particular the case of two distinct species that can evolve to form one or two distinct clusters.
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We investigate the problem of the predominance and survival of weak species in the context of the simplest generalization of the spatial stochastic rock-paper-scissors model to four species by considering models in which one, two, or three species have a reduced predation probability. We show, using lattice based spatial stochastic simulations with random initial conditions, that if only one of the four species has its probability reduced then the most abundant species is the prey of the weakest (assuming that the simulations are large enough for coexistence to prevail). Also, among the remaining cases, we present examples in which weak and strong species have similar average abundances and others in which either of them dominates -- the most abundant species being always a prey of a weak species with which it maintains a unidirectional predator-prey interaction. However, in contrast to the three-species model, we find no systematic difference in the global performance of weak and strong species, and we conjecture that the same result will hold if the number of species is further increased. We also determine the probability of single species survival and coexistence as a function of the lattice size, discussing its dependence on initial conditions and on the change to the dynamics of the model which results from the extinction of one of the species.
In this letter, we investigate the population dynamics in a May-Leonard formulation of the rock-paper-scissors game in which one or two species, which we shall refer to as weak, have a reduced predation or reproduction probability. We show that in a nonspatial model the stationary solution where all three species coexist is always unstable, while in a spatial stochastic model coexistence is possible for a wide parameter space. We find, that a reduced predation probability results in a significantly higher abundance of weak species, in models with either one or two weak species, as long as the simulation lattices are sufficiently large for coexistence to prevail. On the other hand, we show that a reduced reproduction probability has a smaller impact on the abundance of weak species, generally leading to a slight decrease of its population size -- the increase of the population size of one of the weak species being more than compensated by the reduction of the other, in the two species case. We further show that the species abundances in models where both predation and reproduction probabilities are simultaneously reduced may be accurately estimated from the results obtained considering only a reduction of either the predation or the reproduction probability.
We present a simple analytical model to describe the fast increase of deaths produced by the corona virus (COVID-19) infections. The D (deaths) model comes from a simplified version of the SIR (susceptible-infected-recovered) model known as SI model. It assumes that there is no recovery. In that case the dynamical equations can be solved analytically and the result is extended to describe the D-function that depends on three parameters that we can fit to the data. Results for the data from Spain, Italy and China are presented. The model is validated by comparing with the data of deaths in China, which are well described. This allows to make predictions for the development of the disease in Spain and Italy.
Reactive oxygen and nitrogen species (ROS and RNS) play important roles in various physiological processes (e.g., phagocytosis) and pathological conditions (e.g., cancer). The primary ROS/RNS, viz., hydrogen peroxide, peroxynitrite ion, nitric oxide, and nitrite ion, can be oxidized at different electrode potentials and therefore detected and quantified by electroanalytical techniques. Nanometer-sized electrochemical probes are especially suitable for measuring ROS/RNS in single cells and cellular organelles. In this article, we survey recent advances in localized measurements of ROS/RNS inside single cells and discuss several methodological issues, including optimization of nanoelectrode geometry, precise positioning of an electrochemical probe inside a cell, and interpretation of electroanalytical data.
An epidemiological model is developed for the spread of COVID-19 in South Africa. A variant of the classical compartmental SEIR model, called the SEIQRDP model, is used. As South Africa is still in the early phases of the global COVID-19 pandemic with the confirmed infectious cases not having peaked, the SEIQRDP model is first parameterized on data for Germany, Italy, and South Korea - countries for which the number of infectious cases are well past their peaks. Good fits are achieved with reasonable predictions of where the number of COVID-19 confirmed cases, deaths, and recovered cases will end up and by when. South African data for the period from 23 March to 8 May 2020 is then used to obtain SEIQRDP model parameters. It is found that the model fits the initial disease progression well, but that the long-term predictive capability of the model is rather poor. The South African SEIQRDP model is subsequently recalculated with the basic reproduction number constrained to reported values. The resulting model fits the data well, and long-term predictions appear to be reasonable. The South African SEIQRDP model predicts that the peak in the number of confirmed infectious individuals will occur at the end of October 2020, and that the total number of deaths will range from about 10,000 to 90,000, with a nominal value of about 22,000. All of these predictions are heavily dependent on the disease control measures in place, and the adherence to these measures. These predictions are further shown to be particularly sensitive to parameters used to determine the basic reproduction number. The future aim is to use a feedback control approach together with the South African SEIQRDP model to determine the epidemiological impact of varying lockdown levels proposed by the South African Government.
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