Stochastic dynamics of dengue epidemics

Souza, David R.; Tomé, Tânia; Pinho, Suani Tavares Rubim de; Barreto, Florisneide Rodrigues; Oliveira, Mário J. de

doi:10.1103/physreve.87.012709

Cited by 19 publications

(36 citation statements)

References 27 publications

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“…The SIR model exhibits a phase transition between non-spreading (NS) and spreading (S) regions7. Later, a variety of other models8910111213 were developed to cope with different specific epidemic conditions. Notable are the so-called contact models, particularly the Susceptible-Infected-Susceptible (SIS) model, whose critical properties have been widely analysed8910111415.…”

Section: Lattice Models For Epidemics and Critical Behaviormentioning

confidence: 99%

Critical behavior in a stochastic model of vector mediated epidemics

Alfinito

Beccaria

Macorini

2016

Sci Rep

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The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.

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Section: Lattice Models For Epidemics and Critical Behaviormentioning

confidence: 99%

Critical behavior in a stochastic model of vector mediated epidemics

Alfinito

Beccaria

Macorini

2016

Sci Rep

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“…On the other hand, stochastic SIR models have been applied to simulate and predict the spatiotemporal diffusion of infectious diseases (Hufnagel et al, 2004;Cressie and Wikle, 2011;Ball and Sirl, 2012;Ji et al, 2012;de Souza et al, 2013;Zhang et al, 2013). This modeling, based on a consideration of stochastic differential equations, characterizes not only the spatiotemporal pattern of disease spread, but also the heteroscedastic variance pattern across space and time.…”

Section: Discussionmentioning

confidence: 99%

An online spatiotemporal prediction model for dengue fever epidemic in Kaohsiung (Taiwan)

Angulo

Cheng

et al. 2014

Biometrical J

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The emergence and re-emergence of disease epidemics is a complex question that may be influenced by diverse factors, including the space-time dynamics of human populations, environmental conditions, and associated uncertainties. This study proposes a stochastic framework to integrate space-time dynamics in the form of a Susceptible-Infected-Recovered (SIR) model, together with uncertain disease observations, into a Bayesian maximum entropy (BME) framework. The resulting model (BME-SIR) can be used to predict space-time disease spread. Specifically, it was applied to obtain a space-time prediction of the dengue fever (DF) epidemic that took place in Kaohsiung City (Taiwan) during 2002. In implementing the model, the SIR parameters were continually updated and information on new cases of infection was incorporated. The results obtained show that the proposed model is rigorous to user-specified initial values of unknown model parameters, that is, transmission and recovery rates. In general, this model provides a good characterization of the spatial diffusion of the DF epidemic, especially in the city districts proximal to the location of the outbreak. Prediction performance may be affected by various factors, such as virus serotypes and human intervention, which can change the space-time dynamics of disease diffusion. The proposed BME-SIR disease prediction model can provide government agencies with a valuable reference for the timely identification, control, and prevention of DF spread in space and time.

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“…For example, the majority-vote model exhibits a similar phase transition between a ferromagnetic phase (ordered) and a paramagnetic phase (disordered), even without any spontaneous opinion change, with the critical parameter given by ω t = 0.135 in a pair mean-field approximation on square lattices (denoted here by the same notation as that used before for the sake of clarity) [12]. Other models describing spreading diseases and prey-predator biological populations can also be put in the same context of comparisons and display a phase transition between an active state and an absorbing state on square lattices with the pair mean-field critical parameter respectively equal to ω t = 0.379 [13,14] and ω t = 0.235 [15], showing results closer to the Sznajd model than the majority-vote model. More comparisons with other important models are made in Table III [16].…”

Section: Critical Behavior Of the Modelmentioning

confidence: 98%

Mean-field approximation for the Sznajd model in complex networks

et al. 2015

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This paper studies the Sznajd model for opinion formation in a population connected through a general network. A master equation describing the time evolution of opinions is presented and solved in a mean-field approximation. Although quite simple, this approximation allows us to capture the most important features regarding the steady states of the model. When spontaneous opinion changes are included, a discontinuous transition from consensus to polarization can be found as the rate of spontaneous change is increased. In this case we show that a hybrid mean-field approach including interactions between second nearest neighbors is necessary to estimate correctly the critical point of the transition. The analytical prediction of the critical point is also compared with numerical simulations in a wide variety of networks, in particular Barabási-Albert networks, finding reasonable agreement despite the strong approximations involved. The same hybrid approach that made it possible to deal with second-order neighbors could just as well be adapted to treat other problems such as epidemic spreading or predator-prey systems.

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Stochastic dynamics of dengue epidemics

Cited by 19 publications

References 27 publications

Critical behavior in a stochastic model of vector mediated epidemics

Critical behavior in a stochastic model of vector mediated epidemics

An online spatiotemporal prediction model for dengue fever epidemic in Kaohsiung (Taiwan)

Mean-field approximation for the Sznajd model in complex networks

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