scholarly journals The SEIS model, or, the contact process with a latent stage

2016 ◽  
Vol 53 (3) ◽  
pp. 783-801 ◽  
Author(s):  
Eric Foxall
Keyword(s):  
Particle System ◽  
Contact Process ◽  
Compartment Model ◽  
Spatial Dimension ◽  
Critical Values ◽  
System Model ◽  
Upper And Lower Bounds ◽  
Latent Stage ◽  
Latent Time ◽  
The Moment

AbstractThe susceptible→exposed→infectious→susceptible (SEIS) model is well known in mathematical epidemiology as a model of infection in which there is a latent period between the moment of infection and the onset of infectiousness. The compartment model is well studied, but the corresponding particle system has so far received no attention. For the particle system model in one spatial dimension, we give upper and lower bounds on the critical values, prove convergence of critical values in the limit of small and large latent time, and identify a limiting process to which the SEIS model converges in the limit of large latent time.

scholarly journals A multitype contact process with frozen sites: a spatial model of allelopathy

2005 ◽  
Vol 42 (04) ◽  
pp. 1109-1119
Author(s):  
Nicolas Lanchier
Keyword(s):  
Phase Transitions ◽  
Spatial Model ◽  
Biological Process ◽  
Particle System ◽  
Contact Process ◽  
Interacting Particle System ◽  
Interacting Particle

In this paper, we introduce a generalization of the two-color multitype contact process intended to mimic a biological process called allelopathy. To be precise, we have two types of particle. Particles of each type give birth to particles of the same type, and die at rate 1. When a particle of type 1 dies, it gives way to a frozen site that blocks particles of type 2 for an exponentially distributed amount of time. Specifically, we investigate in detail the phase transitions and the duality properties of the interacting particle system.

A Multilevel birth-death particle system and its continuous diffusion

1993 ◽  
Vol 25 (03) ◽  
pp. 549-569 ◽  
Author(s):  
Yadong Wu
Keyword(s):  
Diffusion Process ◽  
Unique Solution ◽  
Diffusion Approximation ◽  
Particle System ◽  
Martingale Problem ◽  
The Moment ◽  
Birth Death

In this paper we introduce a multilevel birth-death particle system and consider its diffusion approximation which can be characterized as aM([R+)-valued process. The tightness of rescaled processes is proved and we show that the limitingM(R+)-valued process is the unique solution of theM([R+)-valued martingale problem for the limiting generator. We also study the moment structures of the limiting diffusion process.

scholarly journals SIMULATION OF REFUGE FROM INUNDATED UNDERGROUND SPACE BY PARTICLE-SYSTEM MODEL OF CROWD BEHAVIOR

2005 ◽  
Vol 49 ◽  
pp. 607-612
Author(s):  
Hitoshi GOTOH ◽  
Eiji HARADA ◽  
Yuki KUBO ◽  
Tetsuo SAKAI
Keyword(s):  
Particle System ◽  
System Model ◽  
Underground Space ◽  
Crowd Behavior

Estimation of critical values in interacting particle systems

2000 ◽  
Vol 37 (01) ◽  
pp. 118-125
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Gerardo Sanz
Keyword(s):  
Computer Simulation ◽  
Asymptotic Behaviour ◽  
Interacting Particle Systems ◽  
Particle System ◽  
Particle Systems ◽  
Critical Values ◽  
Interacting Particle System ◽  
Absorption Time ◽  
Interacting Particle ◽  
Absorbing State

The estimation of critical values is one of the most interesting problems in the study of interacting particle systems. The bounds obtained analytically are not usually very tight and, therefore, computer simulation has been proved to be very useful in the estimation of these values. In this paper we present a new method for the estimation of critical values in any interacting particle system with an absorbing state. The method, based on the asymptotic behaviour of the absorption time of the process, is very easy to implement and provides good estimates. It can also be applied to processes different from particle systems.

On the critical infection rate of the one-dimensional basic contact process: numerical results

1988 ◽  
Vol 25 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Herbert Ziezold ◽  
Christian Grillenberger
Keyword(s):  
Markov Process ◽  
Infected Cell ◽  
Infection Rate ◽  
Lower Bounds ◽  
Contact Process ◽  
Critical Value ◽  
Critical Values ◽  
One Dimensional ◽  
The One ◽  
The Right

Instead of the basic contact process on with infection rate λ we consider for m ≧ 0 the Markov process starting with ξ0(k) = 1 for k ≧ 0 and ξ0(k)= 0 for k < 0 and with changing only those k which are at most m places to the right of the left-most infected cell. For m = 0, 1,· ··, 14 direct computations give critical values which are lower bounds for the critical value of the original basic contact process.

scholarly journals PARTICLE-SYSTEM MODEL OF CROWD REFUGE FROM INUNDATED UNDERGROUND SPACE

2006 ◽  
Vol 50 ◽  
pp. 589-594
Author(s):  
Eiji HARADA ◽  
Hitoshi GOTOH ◽  
Tetsuo SAKAI ◽  
Yuki KUBO
Keyword(s):  
Particle System ◽  
System Model ◽  
Underground Space

scholarly journals A multitype contact process with frozen sites: a spatial model of allelopathy

2005 ◽  
Vol 42 (4) ◽  
pp. 1109-1119
Author(s):  
Nicolas Lanchier
Keyword(s):  
Phase Transitions ◽  
Spatial Model ◽  
Biological Process ◽  
Particle System ◽  
Contact Process ◽  
Interacting Particle System ◽  
Interacting Particle

In this paper, we introduce a generalization of the two-color multitype contact process intended to mimic a biological process called allelopathy. To be precise, we have two types of particle. Particles of each type give birth to particles of the same type, and die at rate 1. When a particle of type 1 dies, it gives way to a frozen site that blocks particles of type 2 for an exponentially distributed amount of time. Specifically, we investigate in detail the phase transitions and the duality properties of the interacting particle system.

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