Theory of the Transmission of Infection in the Spread of Epidemics: Interacting Random Walkers with and Without Confinement

Kenkre, V. M.; Sugaya, Satomi

doi:10.1007/s11538-014-0042-8

Cited by 18 publications

(32 citation statements)

References 37 publications

(38 reference statements)

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“…Though we do not propose that our formalism is necessarily applicable to the study of motion of excitations in doped molecular crystals, the quantum yield style calculations outlined above have found recent use in other systems. For example, in the context of Smoluchowski random walkers [23] and in the transmission of infectious epidemics [24], it was demonstrated that the interplay between diffusion, confinement and absorption at site x may bring about non-monotonic dependencies of the quantum yield. We explore below such non-monotonic dependencies in our formalism.…”

Section: Traps Impartial Detection and Yieldmentioning

confidence: 99%

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Comparison of two models of tethered motion

Giuggioli¹,

Gupta²,

Chase³

2019

J. Phys. A: Math. Theor.

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We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic bias towards the focal point, while in the other case, it resets its position to the focal point at random times. The deterministic tendency of the biased walker makes the forays away from the focal point more unlikely when compared to the random nature of the returns of the resetting walker. This difference has consequences on the spatio-temporal dynamics at intermediate times. To show the differences in the two models, we analyze their probability distribution and their dynamics in presence and absence of partially or fully absorbing traps. We derive analytically various quantities: (i) mean first-passage times to one target, where we recover results obtained earlier by a different technique, (ii) splitting probabilities to either of two targets as well as survival probabilities when one or either target is partially absorbing. The interplay between confinement, diffusion and absorbing traps produces interesting non-monotonic effects in various quantities, all potentially accessible in experiments. The formalism developed here may have a diverse range of applications, from study of animals roaming within home ranges and of electronic excitations moving in organic crystals to developing efficient search algorithms for locating targets in a crowded environment.

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Section: Traps Impartial Detection and Yieldmentioning

confidence: 99%

“…In the absence of traps or guest molecule and the associated probability decay, that is respectively with C e → 0 and τ e → +∞ or C → 0 and τ → +∞, the form of the propagator reduces to the one found in Eq. (24).…”

Section: Appendix Amentioning

confidence: 99%

Comparison of two models of tethered motion

Giuggioli¹,

Gupta²,

Chase³

2019

J. Phys. A: Math. Theor.

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“…V.M. Kenkre et al have studied the effect of confinement on the spread of epidemics in a system of random walkers who move in n dimensions [56]. They have found that the spread of the epidemic has a nonmonotonic dependence on the extent of the home range of the individuals.…”

Section: Introductionmentioning

confidence: 99%

Coupled effects of local movement and global interaction on contagion

Liu

Chen

et al. 2015

Physica A: Statistical Mechanics and its Applications

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By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we propose a generalized epidemic model which can change from the territorial epidemic model to the networked epidemic model. The role of the individual-based linkage between different spatial domains is investigated. As we adjust the timescale parameter τ from 0 to unity, which represents the degree of activation of the individual-based linkage, three regions are found. Within the region of 0 < τ < 0.02, the epidemic is determined by local movement and is sensitive to the timescale τ . Within the region of 0.02 < τ < 0.5, the epidemic is insensitive to the timescale τ . Within the region of 0.5 < τ < 1, the outbreak of the epidemic is determined by the structure of the individualbased linkage. As we keep an eye on the first region, the role of activating the individual-based linkage in the present model is similar to the role of the shortcuts in the two-dimensional small world network. Only activating a small number of the individual-based linkage can prompt the outbreak of the epidemic globally. The role of narrowing segregated spatial domain and reducing mobility in epidemic control is checked. These two measures are found to be conducive to curbing the spread of infectious disease only when the global interaction is suppressed. A log-log relation between the change in the number of infected individuals and the timescale τ is found.By calculating the epidemic threshold and the mean first encounter time, we heuristically analyze the microscopic characteristics of the propagation of the epidemic in the present model.

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“…We present below analysis and practically usable results for random walkers moving under a confinement potential and interacting when they arrive within the influence of one another. We develop the theory as an extension of work we have published recently [3] where we have provided a general formalism and illustrated it explicitly for a specific 1-dimensional case. The application in mind here, as in ref.…”

mentioning

confidence: 99%

“…The application in mind here, as in ref. [3], is to the description of transmission of epidemics such as the Hantavirus [4], wherein rodents moving randomly on the terrain pass on infection on encounter.…”

mentioning

confidence: 99%

Confined Random Walkers in Dimensions Higher Than One and Analysis of Transmission of Infection in Epidemics

Sugaya¹,

Kenkre²

2016

Preprint

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A pair of random walkers, the motion of each of which in two dimensions is confined spatially by the action of a quadratic potential centered at different locations for the two walks, are analyzed in the context of reaction-diffusion. The application sought is to the process of transmission of infection in epidemics. The walkers are animals such as rodents in considerations of the Hantavirus epidemic, infected or susceptible, the reaction is the transmission of infection, and the confining potential represents the tendency of the animals to stay in the neighborhood of their home range centers. Calculations are based on a recently developed formalism (Kenkre and Sugaya, Bull. Math. Bio. 76, 3016 (2014)) structured around analytic solutions of a Smoluchowski equation and one of its aims is the resolution of peculiar but well-known problems of reaction-diffusion theory in 2-dimensions. In the present analysis, reaction occurs not at points but in spatial regions of dimensions larger than 0. The analysis uncovers interesting nonintuitive phenomena one of which is similar to that encountered in the 1-dimensional analysis given in the quoted article, and another specific to the fact that the reaction region is spatially extended. The analysis additionally provides a realistic description of observations on animals transmitting infection while moving on what is effectively a 2-dimensional landscape. Along with the general formalism and explicit 1-dimensional analysis given in Bull. Math. Bio. 76, 3016 (2014), the present work forms a model calculational tool for the analysis for the transmission of infection in dilute systems.

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Theory of the Transmission of Infection in the Spread of Epidemics: Interacting Random Walkers with and Without Confinement

Cited by 18 publications

References 37 publications

Comparison of two models of tethered motion

Comparison of two models of tethered motion

Coupled effects of local movement and global interaction on contagion

Confined Random Walkers in Dimensions Higher Than One and Analysis of Transmission of Infection in Epidemics

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