Rigorous lower bounds for the critical infection rate in the diffusive contact process

2001 ◽  
Vol 38 (4) ◽  
pp. 1074-1078 ◽  
Author(s):  
Aidan Sudbury
Keyword(s):  
Infection Rate ◽  
Lower Bounds ◽  
Particle System ◽  
Infected Individual ◽  
Contact Process ◽  
Interacting Particle ◽  
Lower Infection ◽  
The Individual ◽  
The Relationship ◽  
Lower Infection Rate

The contact process is an interacting particle system which models a spatially restricted infection. In the basic contact process the infection can only spread to an uninfected neighbour, but the diffusive contact process allows an infected individual to move to an uninfected site. If the infection rate is too low, the process will die out. If the individual can move (or diffuse), the disease can spread with a lower infection rate. An idea of the relationship between these rates is obtained by obtaining rigorous lower bounds for the critical infection rate for various values of the diffusion rate. In this paper we also improve the lower bound for the critical infection rate for the basic contact process from 1.539 to 1.5517.

Rigorous lower bounds for the critical infection rate in the diffusive contact process

2001 ◽  
Vol 38 (04) ◽  
pp. 1074-1078 ◽  
Author(s):  
Aidan Sudbury
Keyword(s):  
Infection Rate ◽  
Lower Bounds ◽  
Particle System ◽  
Infected Individual ◽  
Contact Process ◽  
Interacting Particle ◽  
Lower Infection ◽  
The Individual ◽  
The Relationship ◽  
Lower Infection Rate

The contact process is an interacting particle system which models a spatially restricted infection. In the basic contact process the infection can only spread to an uninfected neighbour, but the diffusive contact process allows an infected individual to move to an uninfected site. If the infection rate is too low, the process will die out. If the individual can move (or diffuse), the disease can spread with a lower infection rate. An idea of the relationship between these rates is obtained by obtaining rigorous lower bounds for the critical infection rate for various values of the diffusion rate. In this paper we also improve the lower bound for the critical infection rate for the basic contact process from 1.539 to 1.5517.

scholarly journals The impact of quarantine on Covid-19 infections

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Pablo Marshall
Keyword(s):  
Health System ◽  
Infection Rate ◽  
District Level ◽  
Infection Model ◽  
Social Distancing ◽  
Proposed Model ◽  
Lower Infection ◽  
The Impact ◽  
Lower Infection Rate ◽  
Over Time

Abstract Objectives: Coronavirushas had profound effects on people’s lives and the economy of many countries, generating controversy between the need to establish quarantines and other social distancing measures to protect people’s health and the need to reactivate the economy. This study proposes and applies a modification of the SIR infection model to describe the evolution of coronavirus infections and to measure the effect of quarantine on the number of people infected. Methods: Two hypotheses, not necessarily mutually exclusive, are proposed for the impact of quarantines. According to the first hypothesis, quarantine reduces the infection rate, delaying new infections over time without modifying the total number of people infected at the end of the wave. The second hypothesis establishes that quarantine reduces the population infected in the wave. The two hypotheses are tested with data for a sample of 10 districts in Santiago, Chile. Results: The results of applying the methodology show that the proposed model describes well the evolution of infections at the district level. The data shows evidence in favor of the first hypothesis, quarantine reduces the infection rate; and not in favor of the second hypothesis, that quarantine reduces the population infected. Districts of higher socio-economic levels have a lower infection rate, and quarantine is more effective. Conclusions: Quarantine, in most districts, does not reduce the total number of people infected in the wave; it only reduces the rate at which they are infected. The reduction in the infection rate avoids peaks that may collapse the health system.

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.

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 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.

scholarly journals Space mapping-based optimization with the macroscopic limit of interacting particle systems

2021 ◽  
Author(s):  
Jennifer Weißen ◽  
Simone Göttlich ◽  
Claudia Totzeck
Keyword(s):  
Interacting Particle Systems ◽  
Particle System ◽  
Conveyor Belt ◽  
Space Mapping ◽  
Direct Optimization ◽  
Mapping Algorithm ◽  
Interacting Particle ◽  
The Many ◽  
Relationship Of ◽  
The Relationship

AbstractWe propose a space mapping-based optimization algorithm for microscopic interacting particle dynamics which are infeasible for direct optimization. This is of relevance for example in applications with bounded domains for which the microscopic optimization is difficult. The space mapping algorithm exploits the relationship of the microscopic description of the interacting particle system and a corresponding macroscopic description as partial differential equation in the “many particle limit”. We validate the approach with the help of a toy problem that allows for direct optimization. Then we study the performance of the algorithm in two applications. A pedestrian flow is considered and the transportation of goods on a conveyor belt is optimized. The numerical results underline the feasibility of the proposed algorithm.

A complete convergence theorem for an epidemic model

1996 ◽  
Vol 33 (3) ◽  
pp. 741-748 ◽  
Author(s):  
Enrique Andjel ◽  
Rinaldo Schinazi
Keyword(s):  
Healthy Individual ◽  
Particle System ◽  
Infected Individual ◽  
Nearest Neighbors ◽  
Healthy Individuals ◽  
Interacting Particle ◽  
Healthy State ◽  
Finite Set ◽  
Dimension 2 ◽  
Complete Convergence Theorem

We use an interacting particle system on ℤ to model an epidemic. Each site of ℤ can be in either one of three states: empty, healthy or infected. An empty site x gets occupied by a healthy individual at a rate βn1(x) where n1(x) is the number of healthy nearest neighbors of x. A healthy individual at x gets infected at rate αn2(x) where n2(x) is the number of infected nearest neighbors of x. An infected individual dies at rate δ independently of everything else. We show that for all α, β and δ> 0 and all initial configurations, all the sites of a fixed finite set remain either all empty or all healthy after an almost surely finite time. Moreover, if the initial configuration has infinitely many healthy individuals then the process converges almost surely (in the sense described above) to the all healthy state. We also consider a model introduced by Durrett and Neuhauser where healthy individuals appear spontaneously at rate β > 0 and for which coexistence of 1's and 2's was proved in dimension 2 for some values of α and β. We prove that coexistence may occur in any dimension.

A complete convergence theorem for an epidemic model

1996 ◽  
Vol 33 (03) ◽  
pp. 741-748 ◽  
Author(s):  
Enrique Andjel ◽  
Rinaldo Schinazi
Keyword(s):  
Healthy Individual ◽  
Particle System ◽  
Infected Individual ◽  
Nearest Neighbors ◽  
Healthy Individuals ◽  
Interacting Particle ◽  
Healthy State ◽  
Finite Set ◽  
Dimension 2 ◽  
Complete Convergence Theorem

We use an interacting particle system on ℤ to model an epidemic. Each site of ℤ can be in either one of three states: empty, healthy or infected. An empty site x gets occupied by a healthy individual at a rate βn 1(x) where n 1(x) is the number of healthy nearest neighbors of x. A healthy individual at x gets infected at rate αn 2(x) where n 2(x) is the number of infected nearest neighbors of x. An infected individual dies at rate δ independently of everything else. We show that for all α, β and δ&gt; 0 and all initial configurations, all the sites of a fixed finite set remain either all empty or all healthy after an almost surely finite time. Moreover, if the initial configuration has infinitely many healthy individuals then the process converges almost surely (in the sense described above) to the all healthy state. We also consider a model introduced by Durrett and Neuhauser where healthy individuals appear spontaneously at rate β &gt; 0 and for which coexistence of 1's and 2's was proved in dimension 2 for some values of α and β. We prove that coexistence may occur in any dimension.

Influence of shell size ofLymnaea columellaon infectivity and development ofFasciola hepatica

2008 ◽  
Vol 82 (1) ◽  
pp. 77-80 ◽  
Author(s):  
L.H.L. Coelho ◽  
M.P. Guimarães ◽  
W.S. Lima
Keyword(s):  
Infection Rate ◽  
Post Infection ◽  
Fasciola Hepatica ◽  
Negative Association ◽  
Shell Size ◽  
Experimental Infections ◽  
Non Linear ◽  
Lower Infection ◽  
Lower Infection Rate

AbstractExperimental infections ofLymnaea columellawithFasciola hepaticawere carried out to determine the influence of shell size on the infection rate and on the outcome of rediae and cercariae. Snails were divided into seven groups according to shell size: 2–4 mm, 5–6 mm, 7–8 mm, 9–10 mm, 11–12 mm, 13–14 mm and 15 mm or more. One hundred snails in each group were infected by using four miracidia for each snail. Snails with larger shell size showed a lower infection rate, the groups presenting the highest (79%) and lowest (2%) proportions of positives being those of 5–6 mm and 15 mm or more, respectively. Cercariae were present in 21% of them at 31 days post-infection, and cercarial shedding was observed 61 days post-infection. It was concluded that there is a non-linear negative association between shell size and infection rate.

scholarly journals More Active Internet-Search on Google and Twitter Posting for COVID-19 Corresponds with Lower Infection Rate in the 50 U.S. States

2020 ◽  
Author(s):  
Jiachen Sun ◽  
Peter Gloor
Keyword(s):  
Infection Rate ◽  
Predictive Accuracy ◽  
State Level ◽  
The United States ◽  
The Novel ◽  
Internet Search ◽  
Online Social Media ◽  
Lower Infection ◽  
Novel Coronavirus ◽  
Lower Infection Rate

Abstract As the novel coronavirus disease 2019 (COVID-19) continues to rage worldwide, the United States has become the most affected country with more than 2.5 million total confirmed cases up to now (June 2, 2020). In this work, we investigate the predictive power of online social media and Internet search for the COVID-19 pandemic among 50 U.S. states. By collecting the state-level daily trends through both Twitter and Google Trends, we observe a high but state-different lag correlation with the number of daily confirmed cases. We further find that the predictive accuracy measured by the correlation coefficient is positively correlated to a state’s demographic, air traffic volume and GDP development. Most importantly, we show that a state’s early infection rate is negatively correlated with the lag to the previous peak in Internet search and tweeting about COVID-19, indicating that the earlier the collective awareness on Twitter/Google in a state, the lower is the infection rate.

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