On the effects of the spatial distribution in an epidemic model based on cellular automaton

Several theoretical studies on disease propagation assume that individuals belonging to different groups regarding their health conditions are homogeneously distributed over the space. This is the well-known homogenous mixing assumption, which supports epidemiological models written in terms of ordinary differential or difference equations. Here, we consider that the host population infected by a contagious pathogen is composed by two groups with distinct traits and habits, which can be homogeneously mixed or not. The pathogen propagation is modeled by using an asynchronous probabilistic cellular automaton. Our main goal is to examine how a heterogeneous spatial distribution of these groups affects the endemic state. We noted that homogeneous distribution favors the occurrence of oscillations in the population composition. Surprisingly, we found out that the propagation dynamics of the heterogeneous distribution can also be described by a set of ordinary difference equations.     

Self-sustained oscillations in epidemic models with infective immigrants

A relevant issue related to eco-epidemiological studies concerns the demographic mechanisms that can lead to self-sustained oscillations in the composition of a host population subject to infection. In particular, why does the prevalence of some contagious diseases oscillate over time? Here, we address this question by using susceptible-infective-recovered-empty models including migration of infective foreigners and variable population size. These models are described in terms of ordinary differential equations (ODE) and also in terms of probabilistic cellular automaton (PCA), in which each cell is connected to others either by a regular lattice or by a random graph favoring local contacts. Each cell in the PCA model can be either empty or occupied by a single individual. The amount of neighbors per cell affects the value of the basic reproduction number R₀, which is, in fact, a bifurcation parameter. We show that, by varying the amount of neighbors per cell (and consequently R₀), the number of infective individuals can start to exhibit periodic behavior, which corresponds to a Hopf bifurcation in the ODE model. This bifurcation gives rise to a self-sustained oscillation and it can only occur if the immigration rate of infective individuals is above a critical value. We also investigate how the sum of new infections, within the considered time window, depends on the number of neighbors per cell.     

Yeast Secretes High Amounts of Human Calreticulin without Cellular Stress

The ER chaperone calreticulin (CALR) also has extracellular functions and can exit the mammalian cell in response to various factors, although the mechanism by which this takes place is unknown. The yeast Saccharomyces cerevisiae efficiently secretes human CALR, and the analysis of this process in yeast could help to clarify how it gets out of eukaryotic cells. We have achieved a secretion titer of about 140 mg/L CALR in our S. cerevisiae system. Here, we present a comparative quantitative whole proteome study in CALR-secreting yeast using non-equilibrium pH gradient electrophoresis (NEPHGE)-based two-dimensional gel electrophoresis (2DE) as well as liquid chromatography mass spectrometry in data-independent analysis mode (LC-MS^E). A reconstructed carrier ampholyte (CA) composition of NEPHGE-based first-dimension separation for 2DE could be used instead of formerly commercially available gels. Using LC-MS^E, we identified 1574 proteins, 20 of which exhibited differential expression. The largest group of differentially expressed proteins were structural ribosomal proteins involved in translation. Interestingly, we did not find any signs of cellular stress which is usually observed in recombinant protein-producing yeast, and we did not identify any secretory pathway proteins that exhibited changes in expression. Taken together, high-level secretion of human recombinant CALR protein in S. cerevisiae does not induce cellular stress and does not burden the cellular secretory machinery. There are only small changes in the cellular proteome of yeast secreting CALR at a high level.     

Modelling the effect of urbanization on the transmission of an infectious disease

This paper models the impact of urbanization on infectious disease transmission by integrating a CA land use development model, population projection matrix model and CA epidemic model in S-Plus. The innovative feature of this model lies in both its explicit treatment of spatial land use development, demographic changes, infectious disease transmission and their combination in a dynamic, stochastic model. Heuristically-defined transition rules in cellular automata (CA) were used to capture the processes of both land use development with urban sprawl and infectious disease transmission. A population surface model and dwelling distribution surface were used to bridge the gap between urbanization and infectious disease transmission. A case study is presented involving modelling influenza transmission in Southampton, a dynamically evolving city in the UK. The simulation results for Southampton over a 30-year period show that the pattern of the average number of infection cases per day can depend on land use and demographic changes. The modelling framework presents a useful tool that may be of use in planning applications.     

Stability of choice in the honey bee nest-site selection process

We introduce a pair of compartment models for the honey bee nest-site selection process that lend themselves to analytic methods. The first model represents a swarm of bees deciding whether a site is viable, and the second characterizes its ability to select between two viable sites. We find that the one-site assessment process has two equilibrium states: a disinterested equilibrium (DE) in which the bees show no interest in the site and an interested equilibrium (IE) in which bees show interest. In analogy with epidemic models, we define basic and absolute recruitment numbers (R₀ and B₀) as measures of the swarm's sensitivity to dancing by a single bee. If R₀ is less than one then the DE is locally stable, and if B₀ is less than one then it is globally stable. If R₀ is greater than one then the DE is unstable and the IE is stable under realistic conditions. In addition, there exists a critical site quality threshold Q^* above which the site can attract some interest (at equilibrium) and below which it cannot. We also find the existence of a second critical site quality threshold Q^** above which the site can attract a quorum (at equilibrium) and below which it cannot. The two-site discrimination process, in which we examine a swarm's ability to simultaneously consider two sites differing in both site quality and discovery time, has a stable DE if and only if both sites’ individual basic recruitment numbers are less than one. Numerical experiments are performed to study the influences of site quality on quorum time and the outcome of competition between a lower quality site discovered first and a higher quality site discovered second.     

Modelling the potential spread of Solenopsis invicta Buren (Hymenoptera: Formicidae) (red imported fire ant) in Australia

Abstract  Quantifying the potential spread and density of an invading organism enables decision-makers to determine the most appropriate response to incursions. We present two linked models that estimate the spread of Solenopsis invicta Buren (red imported fire ant) in Australia based on limited data gathered after its discovery in Brisbane in 2001. A stochastic cellular automaton determines spread within a location (100 km by 100 km) and this is coupled with a model that simulates human-mediated movement of S. invicta to new locations. In the absence of any control measures, the models predict that S. invicta could cover 763 000–4 066 000 km² by the year 2035 and be found at 200 separate locations around Australia by 2017–2027, depending on the rate of spread. These estimated rates of expansion (assuming no control efforts were in place) are higher than those experienced in the USA in the 1940s during the early invasion phases in that country. Active control efforts and quarantine controls in the USA (including a concerted eradication attempt in the 1960s) may have slowed spread. Further, milder winters, the presence of the polygynous social form, increased trade and human mobility in Australia in 2000s compared with the USA in 1940s could contribute to faster range expansion.     

Spatial pattern analysis in forest dynamics: deviation from power law and direction of regeneration waves

Grid-based models have been used to understand spatial heterogeneity of the vegetation height in forests and to analyze spatio-temporal dynamics of the forest regeneration process. In this report, we present two methods of identifying lattice models when spatio-temporal data are given. The first method detects directionality of regeneration waves based on the timing of local disturbance events. The second evaluates the forest pattern by recording the fraction of high and low vegetation areas at multiple spatial scales. We illustrate these methods by applying them to patterns generated using three simple stochastic lattice models: (1) two-state model, distinguishing sites with high and low vegetation, (2) three-state model, in which sites can be in an additional disturbed state, and (3) Shimagare model, which considers a continuous range of states. The combination of the two methods provides efficient means of distinguishing the models. The first method has a more direct ecological meaning, while the second is useful when forest data are limited in time.     

A Model for Cross-Cultural Reciprocal Interactions through Mass Media

We investigate the problem of cross-cultural interactions through mass media in a model where two populations of social agents, each with its own internal dynamics, get information about each other through reciprocal global interactions. As the agent dynamics, we employ Axelrod''s model for social influence. The global interaction fields correspond to the statistical mode of the states of the agents and represent mass media messages on the cultural trend originating in each population. Several phases are found in the collective behavior of either population depending on parameter values: two homogeneous phases, one having the state of the global field acting on that population, and the other consisting of a state different from that reached by the applied global field; and a disordered phase. In addition, the system displays nontrivial effects: (i) the emergence of a largest minority group of appreciable size sharing a state different from that of the applied global field; (ii) the appearance of localized ordered states for some values of parameters when the entire system is observed, consisting of one population in a homogeneous state and the other in a disordered state. This last situation can be considered as a social analogue to a chimera state arising in globally coupled populations of oscillators.     

Connectivity,reproduction number,and mobility interact to determine communities’ epidemiological superspreader potential in a metapopulation network

Disease epidemic outbreaks on human metapopulation networks are often driven by a small number of superspreader nodes, which are primarily responsible for spreading the disease throughout the network. Superspreader nodes typically are characterized either by their locations within the network, by their degree of connectivity and centrality, or by their habitat suitability for the disease, described by their reproduction number (R). Here we introduce a model that considers simultaneously the effects of network properties and R on superspreaders, as opposed to previous research which considered each factor separately. This type of model is applicable to diseases for which habitat suitability varies by climate or land cover, and for direct transmitted diseases for which population density and mitigation practices influences R. We present analytical models that quantify the superspreader capacity of a population node by two measures: probability-dependent superspreader capacity, the expected number of neighboring nodes to which the node in consideration will randomly spread the disease per epidemic generation, and time-dependent superspreader capacity, the rate at which the node spreads the disease to each of its neighbors. We validate our analytical models with a Monte Carlo analysis of repeated stochastic Susceptible-Infected-Recovered (SIR) simulations on randomly generated human population networks, and we use a random forest statistical model to relate superspreader risk to connectivity, R, centrality, clustering, and diffusion. We demonstrate that either degree of connectivity or R above a certain threshold are sufficient conditions for a node to have a moderate superspreader risk factor, but both are necessary for a node to have a high-risk factor. The statistical model presented in this article can be used to predict the location of superspreader events in future epidemics, and to predict the effectiveness of mitigation strategies that seek to reduce the value of R, alter host movements, or both.     

Patch size and distance: modelling habitat structure from the perspective of clonal growth

Background and Aims

This study considers the spatial structure of patchy habitats from the perspective of plants that forage for resources by clonal growth. Modelling is used in order to compare two basic strategies, which differ in the response of the plant to a patch boundary. The ‘avoiding plant’ (A) never grows out of a good (resource-rich) patch into a bad (resource-poor) region, because the parent ramet withdraws its subsidy from the offspring. The ‘entering plant’ (E) always crosses the boundary, as the offspring is subsidized at the expense of the parent. In addition to these two extreme scenarios, an intermediate mixed strategy (M) will also be tested. The model is used to compare the efficiency of foraging in various habitats in which the proportion of resource-rich areas (p) is varied.

Methods

A stochastic cellular automata (CA) model is developed in which habitat space is represented by a honeycomb lattice. Each cell within the lattice can accommodate a single ramet, and colonization can occur from a parent ramet''s cell into six neighbouring cells. The CA consists of two layers: the population layer and the habitat. In the population layer, a cell can be empty or occupied by a ramet; in the habitat layer, a cell can be good (resource-rich) or bad (resource-poor). The habitat layer is constant; the population layer changes over time, according to the birth and death of ramets.

Key Results

Strategies M and E are primarily limited by patch distance, whereas A is more sensitive to patch size. At a critical threshold of the proportion of resource-rich areas, p = 0·5, the mean patch size increases abruptly. Below the threshold, E is more efficient than A, whilst above the threshold the opposite is true. The mixed strategy (M) is more efficient than either of the pure strategies across a broad range of p values.

Conclusions

The model predicts more species/genotypes with the ‘entering’ strategy, E, in habitats where resource-rich patches are scattered, and more plants with the ‘avoiding’ strategy, A, in habitats where the connectivity of resource-rich patches is high. The results suggest that the degree of physiological integration between a parent and an offspring ramet is important even across a very short distance because it can strongly influence the efficiency of foraging.     

Modeling the effects of vasculature evolution on early brain tumor growth

Mathematical modeling of both tumor growth and angiogenesis have been active areas of research for the past several decades. Such models can be classified into one of two categories: those that analyze the remodeling of the vasculature while ignoring changes in the tumor mass, and those that predict tumor expansion in the presence of a non-evolving vasculature. However, it is well accepted that vasculature remodeling and tumor growth strongly depend on one another. For this reason, we have developed a two-dimensional hybrid cellular automaton model of early brain tumor growth that couples the remodeling of the microvasculature with the evolution of the tumor mass. A system of reaction-diffusion equations has been developed to track the concentration of vascular endothelial growth factor (VEGF), Ang-1, Ang-2, their receptors and their complexes in space and time. The properties of the vasculature and hence of each cell are determined by the relative concentrations of these key angiogenic factors. The model exhibits an angiogenic switch consistent with experimental observations on the upregulation of angiogenesis. Particularly, we show that if the pathways that produce and respond to VEGF and the angiopoietins are properly functioning, angiogenesis is initiated and a tumor can grow to a macroscopic size. However, if the VEGF pathway is inhibited, angiogenesis does not occur and tumor growth is thwarted beyond 1-2mm in size. Furthermore, we show that tumor expansion can occur in well-vascularized environments even when angiogenesis is inhibited, suggesting that anti-angiogenic therapies may not be sufficient to eliminate a population of actively dividing malignant cells.     

Design of ant-inspired stochastic control policies for collective transport by robotic swarms

In this paper, we present an approach to designing decentralized robot control policies that mimic certain microscopic and macroscopic behaviors of ants performing collective transport tasks. In prior work, we used a stochastic hybrid system model to characterize the observed team dynamics of ant group retrieval of a rigid load. We have also used macroscopic population dynamic models to design enzyme-inspired stochastic control policies that allocate a robotic swarm around multiple boundaries in a way that is robust to environmental variations. Here, we build on this prior work to synthesize stochastic robot attachment–detachment policies for tasks in which a robotic swarm must achieve non-uniform spatial distributions around multiple loads and transport them at a constant velocity. Three methods are presented for designing robot control policies that replicate the steady-state distributions, transient dynamics, and fluxes between states that we have observed in ant populations during group retrieval. The equilibrium population matching method can be used to achieve a desired transport team composition as quickly as possible; the transient matching method can control the transient population dynamics of the team while driving it to the desired composition; and the rate matching method regulates the rates at which robots join and leave a load during transport. We validate our model predictions in an agent-based simulation, verify that each controller design method produces successful transport of a load at a regulated velocity, and compare the advantages and disadvantages of each method.     

A mathematical model for Chagas disease with infection-age-dependent infectivity

In this paper we develop a mathematical model for Chagas disease with infection-age-dependent infectivity. The effects of vector and blood transfusion transmission are considered, and the infected population is structured by the infection age (the time elapsed from infection). The authors identify the basic reproduction ratio R0 and show that the disease can invade into the susceptible population and unique endemic steady state exists if R0 > 1, whereas the disease dies out if R0 is small enough. We show that depending on parameters, backward bifurcation of endemic steady state can occur, so even if R0 < 1, there could exist endemic steady states. We also discuss local and global stability of steady states.     

Clustered Desynchronization from High-Frequency Deep Brain Stimulation

While high-frequency deep brain stimulation is a well established treatment for Parkinson’s disease, its underlying mechanisms remain elusive. Here, we show that two competing hypotheses, desynchronization and entrainment in a population of model neurons, may not be mutually exclusive. We find that in a noisy group of phase oscillators, high frequency perturbations can separate the population into multiple clusters, each with a nearly identical proportion of the overall population. This phenomenon can be understood by studying maps of the underlying deterministic system and is guaranteed to be observed for small noise strengths. When we apply this framework to populations of Type I and Type II neurons, we observe clustered desynchronization at many pulsing frequencies.     

Detection and first characterization of an uncommon haptoglobin in porcine saliva of pigs with rectal prolapse by using boronic acid sample enrichment

Salivary glycoprotein profiles, obtained after boronic acid enrichment, were studied for the first time in pigs in order to search for specific overall alterations related to acute inflammatory condition. Five healthy pigs and five pigs suffering from rectal prolapse were used, and the levels of acute phase proteins were measured to determine the degree of inflammation of the animals. The enriched glycoprotein profiles, achieved by two-dimensional gel electrophoresis (2DE) were statistically evaluated and spots that appeared differentially regulated between states were subjected to MS analysis for protein identification. Spots from three unique proteins were identified: carbonic anhydrase VI (CA VI), α-1-antichymotrypsin and haptoglobin (Hp). CA VI appeared as two adjacent horizontal spot trains in the glycoprotein profile of healthy animals in its regular isoelectric points (pI). One spot of α-1-antichymotrypsin was found in saliva from pigs with rectal prolapse in an unusual basic pI, and was considered as a breakdown product. Hp was identified as several spot trains in saliva from pigs with rectal prolapse in an unusual alkaline pI and was consequently further investigated. SDS-PAGE and 2DE of paired serum and saliva samples combined with Western blot analysis showed that the unusual Hp position observed in saliva samples was absent in serum. Furthermore, N-glycans from serum and saliva Hp glycopatterns were evaluated from SDS-PAGE Hp bands and showed that the serum N-glycan distribution in Hp β-chain was comparable in quantity and quality in both groups of animals. In saliva, no Hp β-chain derived N-glycans could unambiguously be identified from this sample set, thus needing further detailed investigations in the future.     

Habitat fragmentation and extinction thresholds on fractal landscapes

Habitat fragmentation is a potentially critical factor in determining population persistence. In this paper, we explore the effect of fragmentation when the fragmentation follows a fractal pattern. The habitat is divided into patches, each of which is suitable or unsuitable. Suitable patches are either occupied or unoccupied, and change state depending on rates of colonization and local extinction. We compare the behaviour of two models: a spatially implicit patch-occupancy (PO) model and a spatially explicit cellular automaton (CA) model. The PO model has two fixed points: extinction, and a stable equilibrium with a fixed proportion of occupied patches. Global extinction results when habitat destruction reduces the proportion of suitable patches below a critical threshold. The PO model successfully recreates the extinction patterns found in other models. We translated the PO model into a stochastic cellular automaton. Fractal arrangements of suitable and unsuitable patches were used to simulate habitat fragmentation. We found that: (i) a population on a fractal landscape can tolerate more habitat destruction than predicted by the patch-occupancy model, and (ii) the extinction threshold decreases as the fractal dimension of the landscape decreases. These effects cannot be seen in spatially implicit models. Landscape struc-ture plays a vital role in mediating the effects of habitat fragmentation on persistence.     

Spatial Dynamics and the Evolution of Enzyme Production

We re-examine the problem of the evolution of protein synthesis or enzyme production using a stochastic cellular automaton model, where the replicators are fixed in the sites of a two-dimensional square lattice. In contrast with the classical chemical kinetics or mean-field predictions, we show that a small colony of mutant, protein-mediated (enzymatic) replicators has an appreciable probability to take over a resident population of simpler, direct-template replicators. In addition, we argue that the threshold phenomenon corresponding to the onset of invasion can be described quantitatively within the physics framework of nonequilibrium phase transitions. We study also the invasion of a resident population of enzymatic replicators by more efficient replicators of the same kind, and show that although slightly more efficient mutants cannot invade, invasion is a likely event if the productivity advantage of the mutants is large. In this sense, the establishment of a population of enzymatic replicators is not a `once-forever' evolutionary decision.     

Nutrient-responsive O-GlcNAcylation dynamically modulates the secretion of glycan-binding protein galectin 3

Endomembrane glycosylation and cytoplasmic O-GlcNAcylation each play essential roles in nutrient sensing, and characteristic changes in glycan patterns have been described in disease states such as diabetes and cancer. These changes in glycosylation have important functional roles and can drive disease progression. However, little is known about the molecular mechanisms underlying how these signals are integrated and transduced into biological effects. Galectins are proteins that bind glycans and that are secreted by a poorly characterized nonclassical secretory mechanism. Once outside the cell, galectins bind to the terminal galactose residues of cell surface glycans and modulate numerous extracellular functions, such as clathrin-independent endocytosis (CIE). Originating in the cytoplasm, galectins are predicted substrates for O-GlcNAc addition and removal; and as we have shown, galectin 3 is a substrate for O-GlcNAc transferase. In this study, we also show that galectin 3 secretion is sensitive to changes in O-GlcNAc levels. We determined using immunoprecipitation and Western blotting that there is a significant difference in O-GlcNAcylation status between cytoplasmic and secreted galectin 3. We observed dramatic alterations in galectin 3 secretion in response to nutrient conditions, which were dependent on dynamic O-GlcNAcylation. Importantly, we showed that these O-GlcNAc-driven alterations in galectin 3 secretion also facilitated changes in CIE. These results indicate that dynamic O-GlcNAcylation of galectin 3 plays a role in modulating its secretion and can tune its function in transducing nutrient-sensing information coded in cell surface glycosylation into biological effects.     

The cost of stabilising the German lapwing population: A bioeconomic study on lapwing population development and distribution using a cellular automaton

The populations of farmland birds such as the lapwing (Vanellus vanellus) are declining sharply. These populations suffer from frequent cultivation measures and degraded habitat quality on arable land. An effective conservation measure is the lapwing plot, an agriculturally unused section within an arable field. We address German lapwing population development and dispersal if different shares of the population are safeguarded by the use of lapwing plots. We adapted a matrix projection model and extended it by projecting population development in three different habitat types (arable land, grassland and optimal habitat) and in varying scenarios. We introduced a cellular automaton and developed a new algorithm to simulate dispersal dynamics. The results show that without further conservation measures, the population could decline from 70 000 breeding pairs in 2006 to 12 000 or 23 000 pairs in 2055, depending on the underlying assumptions. Our model can be used to set environmental goals and then simulate the necessary implementation levels of conservation measures, such as the lapwing plot, and estimate the corresponding costs. For the goal of at least stabilising the population, 60% of the pairs in the normal agricultural landscape need to be safeguarded. For the population on arable land the corresponding costs range between 1.6 and 2.8 million € per year.