Stochastic lattice gas model describing the dynamics of the SIRS epidemic process

We study a stochastic process describing the onset of spreading dynamics of an epidemic in a population composed of individuals of three classes: susceptible (S), infected (I), and recovered (R). The stochastic process is defined by local rules and involves the following cyclic process: S -> I -> R -> S (SIRS). The open process S -> I -> R (SIR) is studied as a particular case of the SIRS process. The epidemic process is analyzed at different levels of description: by a stochastic lattice gas model and by a birth and death process. By means of Monte Carlo simulations and dynamical mean-field approximations we show that the SIRS stochastic lattice gas model exhibit a line of critical points separating the two phases: an absorbing phase where the lattice is completely full of S individuals and an active phase where S, I and R individuals coexist, which may or may not present population cycles. The critical line, that corresponds to the onset of epidemic spreading, is shown to belong in the directed percolation universality class. By considering the birth and death process we analyze the role of noise in stabilizing the oscillations. (C) 2009 Elsevier B.V. All rights reserved.

Susceptible-infected-recovered and susceptible-exposed-infected models

Two stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the disease in the former is found to occur when the infection probability b is larger than b(c) = k/2(k - 1). In the latter, which is equivalent to a dynamic site percolation model, the spreading occurs when the infection probability p is greater than p(c) = 1/(k - 1). We set up and solve the time evolution equations for both models and determine the final and time-dependent properties, including the epidemic curve. We show that the two models are closely related by revealing that their relevant properties are exactly mapped into each other when p = b/[k - (k - 1) b]. These include the cluster size distribution and the density of individuals of each type, quantities that have been determined in closed forms.

Conexão entre as redes complexas e estatística de Kaniadakis e busca eficiente das propriedades críticas do processo epidêmico difusivo 1D

In this work we study a connection between a non-Gaussian statistics, the Kaniadakis statistics, and Complex Networks. We show that the degree distribution P(k)of a scale free-network, can be calculated using a maximization of information entropy in the context of non-gaussian statistics. As an example, a numerical analysis based on the preferential attachment growth model is discussed, as well as a numerical behavior of the Kaniadakis and Tsallis degree distribution is compared. We also analyze the diffusive epidemic process (DEP) on a regular lattice one-dimensional. The model is composed of A (healthy) and B (sick) species that independently diffusive on lattice with diffusion rates DA and DB for which the probabilistic dynamical rule A + B → 2B and B → A. This model belongs to the category of non-equilibrium systems with an absorbing state and a phase transition between active an inactive states. We investigate the critical behavior of the DEP using an auto-adaptive algorithm to find critical points: the method of automatic searching for critical points (MASCP). We compare our results with the literature and we find that the MASCP successfully finds the critical exponents 1/ѵ and 1/zѵ in all the cases DA =DB, DA DB. The simulations show that the DEP has the same critical exponents as are expected from field-theoretical arguments. Moreover, we find that, contrary to a renormalization group prediction, the system does not show a discontinuous phase transition in the regime o DA >DB.

Propriedades críticas do processo epidêmico difusivo com interação de Lévy

The diffusive epidemic process (PED) is a nonequilibrium stochastic model which, exhibits a phase trnasition to an absorbing state. In the model, healthy (A) and sick (B) individuals diffuse on a lattice with diffusion constants DA and DB, respectively. According to a Wilson renormalization calculation, the system presents a first-order phase transition, for the case DA > DB. Several researches performed simulation works for test this is conjecture, but it was not possible to observe this first-order phase transition. The explanation given was that we needed to perform simulation to higher dimensions. In this work had the motivation to investigate the critical behavior of a diffusive epidemic propagation with Lévy interaction(PEDL), in one-dimension. The Lévy distribution has the interaction of diffusion of all sizes taking the one-dimensional system for a higher-dimensional. We try to explain this is controversy that remains unresolved, for the case DA > DB. For this work, we use the Monte Carlo Method with resuscitation. This is method is to add a sick individual in the system when the order parameter (sick density) go to zero. We apply a finite size scalling for estimates the critical point and the exponent critical =, e z, for the case DA > DB

The effects of population density on the spread of disease

The objective of this study is to identify the relationship between population density and the initial stages of the spread of disease in a local population. This study proposes to concentrate on the question of how population density affects the distribution of the susceptible individuals in a local population and thus affects the spread of the disease, measles. Population density is measured by the average of the number of contacts with susceptible individuals by each individual in the population during a fixed-length time period. The term “contact with susceptible individuals” means sufficient contact between two people for the disease to pass from an infectious person to a susceptible person. The fixed-length time period is taken to be the average length of time an infected person is infectious without symptoms of the disease. For this study of measles, the time period will be seven days. ^ While much attention has been given to modeling the entire epidemic process of measles, attempts have not been made to study the characteristics of contact rates required to initiate an epidemic. This study explores the relationship between population density, given a specific herd immunity rate in the population, and initial rate of the spread of the disease by considering the underlying distribution of contacts with susceptibles by the individuals in the population. ^ This study does not seek to model an entire measles epidemic, but to model the above stated relationship for the local population within which the first infective person is introduced. This study describes the mathematical relationship between population density parameters and contact distribution parameters. ^ The results are displayed in graphs that show the effects of different population densities on the spread of disease. The results support the idea that the number of new infectives is strongly related to the distribution of susceptible contacts. The results also show large differences in the epidemic measures between populations with densities equal to four versus three. ^

PADRÕES DE PRODUTIVIDADE EM PESQUISA NA LITERATURA DE FINANÇAS: UM ESTUDO BIBLIOMÉTRICO NOS PRINCIPAIS PERIÓDICOS CIENTÍFICOS NACIONAIS NO PERÍODO DE 2005 A 2014

A Administração Financeira surge no início do século XIX juntamente com o movimento de consolidação das grandes empresas e a formação dos mercados nacionais americano enquanto que no Brasil os primeiros estudos ocorrem a partir da segunda metade do século XX. Desde entãoo país conseguiu consolidar alguns centros de excelência em pesquisa, formar grupo significativo de pesquisadores seniores e expandir as áreas de pesquisa no campo, contudo, ainda são poucos os trabalhos que buscam retratar as características da produtividade científica em Finanças. Buscando contribuir para a melhor compreensão do comportamento produtivo dessa área a presente pesquisa estuda sua produção científica, materializada na forma de artigos digitais, publicados em 24 conceituados periódicos nacionais classificados nos estratos Qualis/CAPES A2, B1 e B2 da Área de Administração, Ciências Contábeis e Turismo. Para tanto são aplicadas a Lei de Bradford, Lei do Elitismo de Price e Lei de Lotka. Pela Lei de Bradford são identificadas três zonas de produtividade sendo o núcleo formado por três revistas, estando uma delas classificada no estrato Qualis/CAPES B2, o que evidencia a limitação de um recorte tendo como único critério a classificação Qualis/CAPES. Para a Lei do Elitismo de Price, seja pela contagem direta ou completa, não identificamos comportamento de uma elite semelhante ao apontado pela teoria e que conta com grande número de autores com apenas uma publicação.Aplicando-se o modelo do Poder Inverso Generalizado, calculado por Mínimos Quadrados Ordinários (MQO), verificamos que produtividade dos pesquisadores, quando feita pela contagem direta, se adequa àquela definida pela Lei de Lotka ao nível de α = 0,01 de significância, contudo, pela contagem completa não podemos confirmar a hipótese de homogeneidade das distribuições, além do fato de que nas duas contagens a produtividade analisada pelo parâmetro n é maior que 2 e, portanto, a produtividade do pesquisadores de finanças é menor que a defendida pela teoria.

Asymptotic theory of time varying networks with memory and heterogeneous activation pattern

In this thesis work we develop a new generative model of social networks belonging to the family of Time Varying Networks. The importance of correctly modelling the mechanisms shaping the growth of a network and the dynamics of the edges activation and inactivation are of central importance in network science. Indeed, by means of generative models that mimic the real-world dynamics of contacts in social networks it is possible to forecast the outcome of an epidemic process, optimize the immunization campaign or optimally spread an information among individuals. This task can now be tackled taking advantage of the recent availability of large-scale, high-quality and time-resolved datasets. This wealth of digital data has allowed to deepen our understanding of the structure and properties of many real-world networks. Moreover, the empirical evidence of a temporal dimension in networks prompted the switch of paradigm from a static representation of graphs to a time varying one. In this work we exploit the Activity-Driven paradigm (a modeling tool belonging to the family of Time-Varying-Networks) to develop a general dynamical model that encodes fundamental mechanism shaping the social networks' topology and its temporal structure: social capital allocation and burstiness. The former accounts for the fact that individuals does not randomly invest their time and social interactions but they rather allocate it toward already known nodes of the network. The latter accounts for the heavy-tailed distributions of the inter-event time in social networks. We then empirically measure the properties of these two mechanisms from seven real-world datasets and develop a data-driven model, analytically solving it. We then check the results against numerical simulations and test our predictions with real-world datasets, finding a good agreement between the two. Moreover, we find and characterize a non-trivial interplay between burstiness and social capital allocation in the parameters phase space. Finally, we present a novel approach to the development of a complete generative model of Time-Varying-Networks. This model is inspired by the Kaufman's adjacent possible theory and is based on a generalized version of the Polya's urn. Remarkably, most of the complex and heterogeneous feature of real-world social networks are naturally reproduced by this dynamical model, together with many high-order topological properties (clustering coefficient, community structure etc.).

PADRÕES DE PRODUTIVIDADE EM PESQUISA NA LITERATURA DE FINANÇAS: UM ESTUDO BIBLIOMÉTRICO NOS PRINCIPAIS PERIÓDICOS CIENTÍFICOS NACIONAIS NO PERÍODO DE 2005 A 2014

A Administração Financeira surge no início do século XIX juntamente com o movimento de consolidação das grandes empresas e a formação dos mercados nacionais americano enquanto que no Brasil os primeiros estudos ocorrem a partir da segunda metade do século XX. Desde entãoo país conseguiu consolidar alguns centros de excelência em pesquisa, formar grupo significativo de pesquisadores seniores e expandir as áreas de pesquisa no campo, contudo, ainda são poucos os trabalhos que buscam retratar as características da produtividade científica em Finanças. Buscando contribuir para a melhor compreensão do comportamento produtivo dessa área a presente pesquisa estuda sua produção científica, materializada na forma de artigos digitais, publicados em 24 conceituados periódicos nacionais classificados nos estratos Qualis/CAPES A2, B1 e B2 da Área de Administração, Ciências Contábeis e Turismo. Para tanto são aplicadas a Lei de Bradford, Lei do Elitismo de Price e Lei de Lotka. Pela Lei de Bradford são identificadas três zonas de produtividade sendo o núcleo formado por três revistas, estando uma delas classificada no estrato Qualis/CAPES B2, o que evidencia a limitação de um recorte tendo como único critério a classificação Qualis/CAPES. Para a Lei do Elitismo de Price, seja pela contagem direta ou completa, não identificamos comportamento de uma elite semelhante ao apontado pela teoria e que conta com grande número de autores com apenas uma publicação.Aplicando-se o modelo do Poder Inverso Generalizado, calculado por Mínimos Quadrados Ordinários (MQO), verificamos que produtividade dos pesquisadores, quando feita pela contagem direta, se adequa àquela definida pela Lei de Lotka ao nível de α = 0,01 de significância, contudo, pela contagem completa não podemos confirmar a hipótese de homogeneidade das distribuições, além do fato de que nas duas contagens a produtividade analisada pelo parâmetro n é maior que 2 e, portanto, a produtividade do pesquisadores de finanças é menor que a defendida pela teoria.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

The endemisation of schistosomiasis in Porto de Galinhas, Pernambuco, Brazil, 10 years after the first epidemic outbreak

In 2000, after heavy rains and floods in Porto de Galinhas, Pernambuco, Brazil, an outbreak of schistosomiasis was recorded, of which 62.2% (412 cases) were of the acute clinical form. Between 2001-2009, occasional findings of Biomphalaria snails parasitised by Schistosoma mansoni indicated that disease transmission was still occurring. This motivated a new epidemiological survey between August-December 2010 to provide an update of the occurrence of this health hazard and to investigate the process of disease endemisation at this locality. This survey gathered parasitological, clinical and malacological data. The results of this survey, compared with data from the year 2000 survey, showed the following: (i) over these 10 years, there were declines in the total percentage of cases and the percentage of acute forms, (ii) the acute clinical form now represents 23.3% in contrast with the 62.2% detected in 2000 and (iii) the current prevalence of schistosomiasis is 15.7%, while in 2000 32.1% of the individuals were diagnosed as parasitised. Today, the chronic clinical form represents 76.7% of the total number of cases diagnosed, thus showing that over the 10-year period the occurrences of clinical forms became inverted. These findings, together with visual observation of insalubrious environmental conditions, indicate that schistosomiasis has become endemic in Porto de Galinhas.

Optimal control strategy for fed-batch enzymatic hydrolysis of lignocellulosic biomass based on epidemic modeling

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A stochastic spatially structured epidemic model with diffusive processes

We developed a stochastic lattice model to describe the vector-borne disease (like yellow fever or dengue). The model is spatially structured and its dynamical rules take into account the diffusion of vectors. We consider a bipartite lattice, forming a sub-lattice of human and another occupied by mosquitoes. At each site of lattice we associate a stochastic variable that describes the occupation and the health state of a single individual (mosquito or human). The process of disease transmission in the human population follows a similar dynamic of the Susceptible-Infected-Recovered model (SIR), while the disease transmission in the mosquito population has an analogous dynamic of the Susceptible-Infected-Susceptible model (SIS) with mosquitos diffusion. The occurrence of an epidemic is directly related to the conditional probability of occurrence of infected mosquitoes (human) in the presence of susceptible human (mosquitoes) on neighborhood. The probability of diffusion of mosquitoes can facilitate the formation of pairs Susceptible-Infected enabling an increase in the size of the epidemic. Using an asynchronous dynamic update, we study the disease transmission in a population initially formed by susceptible individuals due to the introduction of a single mosquito (human) infected. We find that this model exhibits a continuous phase transition related to the existence or non-existence of an epidemic. By means of mean field approximations and Monte Carlo simulations we investigate the epidemic threshold and the phase diagram in terms of the diffusion probability and the infection probability.

Payone : incentive for epidemic protocol-based anonymity system

Anonymity systems maintain the anonymity of communicating nodes by camouflaging them, either with peer nodes generating dummy traffic or with peer nodes participating in the actual communication process. The probability of any adversary breaking down the anonymity of the communicating nodes is inversely proportional to the number of peer nodes participating in the network. Hence to maintain the anonymity of the communicating nodes, a large number of peer nodes are needed. Lack of peer availability weakens the anonymity of any large scale anonymity system. This work proposes PayOne, an incentive based scheme for promoting peer availability. PayOne aims to increase the peer availability by encouraging nodes to participate in the anonymity system by awarding them with incentives and thereby promoting the anonymity strength. Existing incentive schemes are designed for single path based approaches. There is no incentive scheme for multipath based or epidemic based anonymity systems. This work has been specifically designed for epidemic protocols and has been implemented over MuON, one of the latest entries to the area of multicasting based anonymity systems. MuON is a peer-to-peer based anonymity system which uses epidemic protocol for data dissemination. Existing incentive schemes involve paying every intermediate node that is involved in the communication between the initiator and the receiver. These schemes are not appropriate for epidemic based anonymity systems due to the incurred overhead. PayOne differs from the existing schemes because it involves paying a single intermediate node that participates in the network. The intermediate node can be any random node that participates in the communication and does not necessarily need to lie in the communication path between the initiator and the receiver. The light-weight characteristics of PayOne make it viable for large-scale epidemic based anonymity systems.

On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.

Threshold behaviour and final outcome of an epidemic on a random network with household structure

This paper considers a stochastic SIR (susceptible-infective-removed) epidemic model in which individuals may make infectious contacts in two ways, both within 'households' (which for ease of exposition are assumed to have equal size) and along the edges of a random graph describing additional social contacts. Heuristically-motivated branching process approximations are described, which lead to a threshold parameter for the model and methods for calculating the probability of a major outbreak, given few initial infectives, and the expected proportion of the population who are ultimately infected by such a major outbreak. These approximate results are shown to be exact as the number of households tends to infinity by proving associated limit theorems. Moreover, simulation studies indicate that these asymptotic results provide good approximations for modestly-sized finite populations. The extension to unequal sized households is discussed briefly.