A Method for Reducing the Severity of Epidemics by Allocating Vaccines According to Centrality

One long-standing question in epidemiological research is how best to allocate limited amounts of vaccine or similar preventative measures in order to minimize the severity of an epidemic. Much of the literature on the problem of vaccine allocation has focused on influenza epidemics and used mathematical models of epidemic spread to determine the effectiveness of proposed methods. Our work applies computational models of epidemics to the problem of geographically allocating a limited number of vaccines within several Texas counties. We developed a graph-based, stochastic model for epidemics that is based on the SEIR model, and tested vaccine allocation methods based on multiple centrality measures. This approach provides an alternative method for addressing the vaccine allocation problem, which can be combined with more conventional approaches to yield more effective epidemic suppression strategies. We found that allocation methods based on in-degree and inverse betweenness centralities tended to be the most effective at containing epidemics.Comment: 10 pages, accepted to ACM BCB 201

A Cellular Automata Model for Citrus Variagated Chlorosis

A cellular automata model is proposed to analyze the progress of Citrus Variegated Chlorosis epidemics in S\~ao Paulo oranges plantation. In this model epidemiological and environmental features, such as motility of sharpshooter vectors which perform L\'evy flights, hydric and nutritional level of plant stress and seasonal climatic effects, are included. The observed epidemics data were quantitatively reproduced by the proposed model varying the parameters controlling vectors motility, plant stress and initial population of diseased plants.Comment: 10 pages, 10 figures, Scheduled tentatively for the issue of: 01Nov0

Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend maximum. This is opposite with present results obtained in spatial explicit models that infection rate is limited by upper bound. We observe the emergence of trade-offs of extinction and persistence on the parameters of the infection period and infection rate and show the extinction time having a linear relationship with respect to system size. We further find that the higher mobility can pronouncedly promote the persistence of spread of epidemics, i.e., the phase transition occurs from extinction domain to persistence domain, and the spirals' wavelength increases as the mobility increasing and ultimately, it will saturate at a certain value. Furthermore, for multi-patches case, we find that the lower coupling strength leads to anti-phase oscillation of infected fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page

Epidemic modelling by ripple-spreading network and genetic algorithm

Mathematical analysis and modelling is central to infectious disease epidemiology. This paper, inspired by the natural ripple-spreading phenomenon, proposes a novel ripple-spreading network model for the study of infectious disease transmission. The new epidemic model naturally has good potential for capturing many spatial and temporal features observed in the outbreak of plagues. In particular, using a stochastic ripple-spreading process simulates the effect of random contacts and movements of individuals on the probability of infection well, which is usually a challenging issue in epidemic modeling. Some ripple-spreading related parameters such as threshold and amplifying factor of nodes are ideal to describe the importance of individuals’ physical fitness and immunity. The new model is rich in parameters to incorporate many real factors such as public health service and policies, and it is highly flexible to modifications. A genetic algorithm is used to tune the parameters of the model by referring to historic data of an epidemic. The well-tuned model can then be used for analyzing and forecasting purposes. The effectiveness of the proposed method is illustrated by simulation results

Dynamics of urban sprawl

This paper introduces a framework for understanding the dynamics of urban growth,particularly the continuing problem of urban sprawl. The models we present are based on transitions from vacant land to established development. We propose that the essential mechanism of transition is analogous to the way an epidemic is generated within a susceptible population, with waves of development being generated from the conversion of available land to new development and redevelopment through the aging process. We first outline the standard aggregate model in differential equation form, showing how different variants (including logistic, exponential, predator-prey models) can be derived for various urban growth situations. We then generalize the model to a spatial system and show how sprawl can be conceived as a process of both interaction/reaction and diffusion. We operationalize the model as a cellular automata (CA) which implies that diffusion is entirely local, and we then illustrate how waves of development and redevelopment characterizing both sprawl and aging of the existing urban stock, can be simulated.Finally we show how the model can be adapted to a real urban situation - the AnnArbor area in Eastern Michigan - where we demonstrate how waves of development are absorbed and modified by particular historical contingencies associated with the re-existing urban structure

Addressing population heterogeneity and distribution in epidemics models using a cellular automata approach

BACKGROUND: The spread of an infectious disease is determined by biological and social factors. Models based on cellular automata are adequate to describe such natural systems consisting of a massive collection of simple interacting objects. They characterize the time evolution of the global system as the emergent behaviour resulting from the interaction of the objects, whose behaviour is defined through a set of simple rules that encode the individual behaviour and the transmission dynamic. METHODS: An epidemic is characterized trough an individual–based–model built upon cellular automata. In the proposed model, each individual of the population is represented by a cell of the automata. This way of modeling an epidemic situation allows to individually define the characteristic of each individual, establish different scenarios and implement control strategies. RESULTS: A cellular automata model to study the time evolution of a heterogeneous populations through the various stages of disease was proposed, allowing the inclusion of individual heterogeneity, geographical characteristics and social factors that determine the dynamic of the desease. Different assumptions made to built the classical model were evaluated, leading to following results: i) for low contact rate (like in quarantine process or low density population areas) the number of infective individuals is lower than other areas where the contact rate is higher, and ii) for different initial spacial distributions of infected individuals different epidemic dynamics are obtained due to its influence on the transition rate and the reproductive ratio of disease. CONCLUSIONS: The contact rate and spatial distributions have a central role in the spread of a disease. For low density populations the spread is very low and the number of infected individuals is lower than in highly populated areas. The spacial distribution of the population and the disease focus as well as the geographical characteristic of the area play a central role in the dynamics of the deseaseFil: López, Leonardo Rafael. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación En Señales, Sistemas E Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hidricas. Instituto de Investigación En Señales, Sistemas E Inteligencia Computacional; ArgentinaFil: Burguerner, Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación En Señales, Sistemas E Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hidricas. Instituto de Investigación En Señales, Sistemas E Inteligencia Computacional; ArgentinaFil: Giovanini, Leonardo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación En Señales, Sistemas E Inteligencia Computacional. Universidad Nacional del Litoral. Facultad de Ingeniería y Ciencias Hidricas. Instituto de Investigación En Señales, Sistemas E Inteligencia Computacional; Argentin