Modelling fungus dispersal scenarios using cellular automata

This study focused on representing spatio-temporal patterns of fungal dispersal using cellular automata. Square lattices were used, with each site representing a host for a hypothetical fungus population. Four possible host states were allowed: resistant, permissive, latent or infectious. In this model, the probability of infection for each of the healthy states (permissive or resistant) in a time step was determined as a function of the host's susceptibility, seasonality, and the number of infectious sites and the distance between them. It was also assumed that infected sites become infectious after a pre-specified latency period, and that recovery is not possible. Several scenarios were simulated to understand the contribution of the model's parameters and the spatial structure on the dynamic behaviour of the modelling system. The model showed good capability for representing the spatio-temporal pattern of fungus dispersal over planar surfaces. With a specific problem in mind, the model can be easily modified and used to describe field behaviour, which can contribute to the conservation and development of management strategies for both natural and agricultural systems. © 2012 Elsevier B.V.

The Effect of Spatial Scale on Predicting Time Series: A Study on Epidemiological System Identification

A susceptible-infective-recovered (SIR) epidemiological model based on probabilistic cellular automaton (PCA) is employed for simulating the temporal evolution of the registered cases of chickenpox in Arizona, USA, between 1994 and 2004. At each time step, every individual is in one of the states S, I, or R. The parameters of this model are the probabilities of each individual (each cell forming the PCA lattice ) passing from a state to another state. Here, the values of these probabilities are identified by using a genetic algorithm. If nonrealistic values are allowed to the parameters, the predictions present better agreement with the historical series than if they are forced to present realistic values. A discussion about how the size of the PCA lattice affects the quality of the model predictions is presented. Copyright (C) 2009 L. H. A. Monteiro et al.

System Identification and Prediction of Dengue Fever Incidence in Rio de Janeiro

Identification, prediction, and control of a system are engineering subjects, regardless of the nature of the system. Here, the temporal evolution of the number of individuals with dengue fever weekly recorded in the city of Rio de Janeiro, Brazil, during 2007, is used to identify SIS (susceptible-infective-susceptible) and SIR (susceptible-infective-removed) models formulated in terms of cellular automaton (CA). In the identification process, a genetic algorithm (GA) is utilized to find the probabilities of the state transition S -> I able of reproducing in the CA lattice the historical series of 2007. These probabilities depend on the number of infective neighbors. Time-varying and non-time-varying probabilities, three different sizes of lattices, and two kinds of coupling topology among the cells are taken into consideration. Then, these epidemiological models built by combining CA and GA are employed for predicting the cases of sick persons in 2008. Such models can be useful for forecasting and controlling the spreading of this infectious disease.

Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

Role of noise in population dynamics cycles

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.

Time correlation function in systems with two coexisting biological species

We study a stochastic lattice model describing the dynamics of coexistence of two interacting biological species. The model comprehends the local processes of birth, death, and diffusion of individuals of each species and is grounded on interaction of the predator-prey type. The species coexistence can be of two types: With self-sustained coupled time oscillations of population densities and without oscillations. We perform numerical simulations of the model on a square lattice and analyze the temporal behavior of each species by computing the time correlation functions as well as the spectral densities. This analysis provides an appropriate characterization of the different types of coexistence. It is also used to examine linked population cycles in nature and in experiment.

A vaccination game based on public health actions and personal decisions

Susceptible-infective-removed (SIR) models are commonly used for representing the spread of contagious diseases. A SIR model can be described in terms of a probabilistic cellular automaton (PCA), where each individual (corresponding to a cell of the PCA lattice) is connected to others by a random network favoring local contacts. Here, this framework is employed for investigating the consequences of applying vaccine against the propagation of a contagious infection, by considering vaccination as a game, in the sense of game theory. In this game, the players are the government and the susceptible newborns. In order to maximize their own payoffs, the government attempts to reduce the costs for combating the epidemic, and the newborns may be vaccinated only when infective individuals are found in their neighborhoods and/or the government promotes an immunization program. As a consequence of these strategies supported by cost-benefit analysis and perceived risk, numerical simulations show that the disease is not fully eliminated and the government implements quasi-periodic vaccination campaigns. (C) 2011 Elsevier B.V. All rights reserved.

Modeling of columnar-to-equiaxed transition in solidified Al-Si alloys

A Cellular-Automaton Finite-Volume-Method (CAFVM) algorithm has been developed, coupling with macroscopic model for heat transfer calculation and microscopic models for nucleation and growth. The solution equations have been solved to determine the time-dependent constitutional undercooling and interface retardation during solidification. The constitutional undercooling is then coupled into the CAFVM algorithm to investigate both the effects of thermal and constitutional undercooling on columnar growth and crystal selection in the columnar zone, and formation of equiaxed crystals in the bulk liquid. The model cannot only simulate microstructures of alloys but also investigates nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies.

Numerical simulation of dendrite growth during solidification

A comprehensive probabilistic model for simulating dendrite morphology and investigating dendritic growth kinetics during solidification has been developed, based on a modified Cellular Automaton (mCA) for microscopic modeling of nucleation, growth of crystals and solute diffusion. The mCA model numerically calculated solute redistribution both in the solid and liquid phases, the curvature of dendrite tips and the growth anisotropy. This modeling takes account of thermal, curvature and solute diffusion effects. Therefore, it can simulate microstructure formation both on the scale of the dendrite tip length. This model was then applied for simulating dendritic solidification of an Al-7%Si alloy. Both directional and equiaxed dendritic growth has been performed to investigate the growth anisotropy and cooling rate on dendrite morphology. Furthermore, the competitive growth and selection of dendritic crystals have also investigated.

Modelling of microstructure formation and evolution during solidification

A comprehensive probabilistic model for simulating microstructure formation and evolution during solidification has been developed, based on coupling a Finite Differential Method (FDM) for macroscopic modelling of heat diffusion to a modified Cellular Automaton (mCA) for microscopic modelling of nucleation, growth of microstructures and solute diffusion. The mCA model is similar to Nastac's model for handling solute redistribution in the liquid and solid phases, curvature and growth anisotropy, but differs in the treatment of nucleation and growth. The aim is to improve understanding of the relationship between the solidification conditions and microstructure formation and evolution. A numerical algorithm used for FDM and mCA was developed. At each coarse scale, temperatures at FDM nodes were calculated while nucleation-growth simulation was done at a finer scale, with the temperature at the cell locations being interpolated from those at the coarser volumes. This model takes account of thermal, curvature and solute diffusion effects. Therefore, it can not only simulate microstructures of alloys both on the scale of grain size (macroscopic level) and the dendrite tip length (mesoscopic level), but also investigate nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies. The calculated results are compared with values of grain sizes and solidification morphologies of microstructures obtained from a set of casting experiments of Al-Si alloys in graphite crucibles.

Stress correlation function evolution in lattice solid elasto-dynamic models of shear and fracture zones and earthquake prediction

It has been argued that power-law time-to-failure fits for cumulative Benioff strain and an evolution in size-frequency statistics in the lead-up to large earthquakes are evidence that the crust behaves as a Critical Point (CP) system. If so, intermediate-term earthquake prediction is possible. However, this hypothesis has not been proven. If the crust does behave as a CP system, stress correlation lengths should grow in the lead-up to large events through the action of small to moderate ruptures and drop sharply once a large event occurs. However this evolution in stress correlation lengths cannot be observed directly. Here we show, using the lattice solid model to describe discontinuous elasto-dynamic systems subjected to shear and compression, that it is for possible correlation lengths to exhibit CP-type evolution. In the case of a granular system subjected to shear, this evolution occurs in the lead-up to the largest event and is accompanied by an increasing rate of moderate-sized events and power-law acceleration of Benioff strain release. In the case of an intact sample system subjected to compression, the evolution occurs only after a mature fracture system has developed. The results support the existence of a physical mechanism for intermediate-term earthquake forecasting and suggest this mechanism is fault-system dependent. This offers an explanation of why accelerating Benioff strain release is not observed prior to all large earthquakes. The results prove the existence of an underlying evolution in discontinuous elasto-dynamic, systems which is capable of providing a basis for forecasting catastrophic failure and earthquakes.

A Model to Evaluate Vertical Handovers on JRRM

In a heterogeneous cellular networks environment, users behaviour and network deployment configuration parameters have an impact on the overall Quality of Service. This paper proposes a new and simple model that, on the one hand, explores the users behaviour impact on the network by having mobility, multi-service usage and traffic generation profiles as inputs, and on the other, enables the network setup configuration evaluation impact on the Joint Radio Resource Management (JRRM), assessing some basic JRRM performance indicators, like Vertical Handover (VHO) probabilities, average bit rates, and number of active users, among others. VHO plays an important role in fulfilling seamless users sessions transfer when mobile terminals cross different Radio Access Technologies (RATs) boundaries. Results show that high bit rate RATs suffer and generate more influence from/on other RATs, by producing additional signalling traffic to a JRRM entity. Results also show that the VHOs probability can range from 5 up to 65%, depending on RATs cluster radius and users mobility profile.

Initiation of primary cell cultures from embryos of the mosquitoes Anopheles albimanus and Aedes taeniorhynchus (Diptera: Culicidae)

Primary cell cultures were obtained from eggs of Anopheles albimanus and Aedes taeniorhynchus mosquitoes, vectors of human malaria and of Venezuelan equine encephalitis virus, respectively. The cellular growth of the An. albimanus cells began four weeks after explanting the embryonic tissues in MK/VP12 medium, supplemented with 15% fetal bovine serum. The culture showed heterogeneous cellular morphology. With regard to the Ae. taeniorhynchus culture, growth occurred three weeks after initiating the culture in MM/VP12 medium. The majority of cells were small and round. Karyotypes were examined in the latter species.

The MIGCLIM R package - seamless integration of dispersal constraints into projections of species distribution models

The MIGCLIM R package is a function library for the open source R software that enables the implementation of species-specific dispersal constraints into projections of species distribution models under environmental change and/or landscape fragmentation scenarios. The model is based on a cellular automaton and the basic modeling unit is a cell that is inhabited or not. Model parameters include dispersal distance and kernel, long distance dispersal, barriers to dispersal, propagule production potential and habitat invasibility. The MIGCLIM R package has been designed to be highly flexible in the parameter values it accepts, and to offer good compatibility with existing species distribution modeling software. Possible applications include the projection of future species distributions under environmental change conditions and modeling the spread of invasive species.

Long-tailed trapping times and Lévy flights in a self-organized critical granular system

We present a continuous time random walk model for the scale-invariant transport found in a self-organized critical rice pile [K. Christensen et al., Phys. Rev. Lett. 77, 107 (1996)]. From our analytical results it is shown that the dynamics of the experiment can be explained in terms of Lvy flights for the grains and a long-tailed distribution of trapping times. Scaling relations for the exponents of these distributions are obtained. The predicted microscopic behavior is confirmed by means of a cellular automaton model.