From Bee Species Aggregation to Models of Disease Avoidance: The Ben-Hur effect

Yong, Kamuela E.; Herrera, Emílio; Castillo‐Chavez, Carlos

doi:10.1007/978-3-319-40413-4_11

Cited by 4 publications

(3 citation statements)

References 40 publications

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“…The limitations of the role of technology in the absence of the public health infrastructure –there is no silver bullet– has been recently addressed in the context of Ebola (( Chowell et al., 2015 , Yong et al., 2016 )) with applications of the Lagrangian approach as presented here in the context of communicable and vector born diseases, including dengue, tuberculosis and Ebola, in settings where health disparities are pervasive (( Bichara et al., 2016 , Espinoza et al., 2016 , p. pp.123)). Further, the use of simplified models, quite often tends to over-estimate the impact of an outbreak (see ( Nishiura et al., 2009 , Nishiura et al., 2011 )) and the model and scenarios used highlight the limitations on the use of simplified settings when the goal is to capture or mimic the dynamics of specific systems–not the goal of this manuscript.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Role of short-term dispersal on the dynamics of Zika virus in an extreme idealized environment

Moreno

Espinoza

Bichara

et al. 2017

Infectious Disease Modelling

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In November 2015, El Salvador reported their first case of Zika virus (ZIKV) infection, an event followed by an explosive outbreak that generated over 6000 suspected cases in a period of two months. National agencies began implementing control measures that included vector control and recommending an increased use of repellents. Further, in response to the alarming and growing number of microcephaly cases in Brazil, the importance of avoiding pregnancies for two years was stressed. In this paper, we explore the role of mobility within communities characterized by extreme poverty, crime and violence. Specifically, the role of short term mobility between two idealized interconnected highly distinct communities is explored in the context of ZIKV outbreaks. We make use of a Lagrangian modeling approach within a two-patch setting in order to highlight the possible effects that short-term mobility, within highly distinct environments, may have on the dynamics of ZIKV outbreak when the overall goal is to reduce the number of cases not just in the most affluent areas but everywhere. Outcomes depend on existing mobility patterns, levels of disease risk, and the ability of federal or state public health services to invest in resource limited areas, particularly in those where violence is systemic. The results of simulations in highly polarized and simplified scenarios are used to assess the role of mobility. It quickly became evident that matching observed patterns of ZIKV outbreaks could not be captured without incorporating increasing levels of heterogeneity. The number of distinct patches and variations on patch connectivity structure required to match ZIKV patterns could not be met within the highly aggregated model that is used in the simulations.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Role of short-term dispersal on the dynamics of Zika virus in an extreme idealized environment

Moreno

Espinoza

Bichara

et al. 2017

Infectious Disease Modelling

View full text Add to dashboard Cite

show abstract

“…The limitations of the role of technology in the absence of the public health infrastructure-there is no silver bullet-have been addressed in the context of Ebola [16,49]. It would be interesting to see the impact of technology in settings where health disparities are pervasive, using a two-patch Lagrangian epidemic model in the context of communicable and vector-borne diseases, including dengue, tuberculosis , and Ebola [5,23,34,35].…”

Section: What Did We Learn From These Single Outbreak Simulations?mentioning

confidence: 99%

Epidemiological Models Incorporating Mobility, Behavior, and Time Scales

Brauer

Castillo‐Chavez

Feng

2019

Texts in Applied Mathematics

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The work of Eubank et al. [24], Sara del Valle et al. [44], Chowell et al. [7, 18], and Castillo-Chavez and Song [13] have highlighted the impact of modified modeling approaches that incorporate heterogeneous modes of mobility within variable environments in order to study their impact on the dynamics of infectious diseases. Castillo-Chavez and Song [13], for example, proceeded to highlight a Lagrangian perspective, that is, the use of models that keep track at all times of the identity of each individual. This approach was used to study the consequences of deliberate efforts to transmit smallpox in a highly populated city, involving transient subpopulations and the availability of massive modes of public transportation. Here, a multi-group epidemic Lagrangian framework where mobility and the risk of infection are functions of patch residence time and local environmental risk is introduced. This Lagrangian approach has been used within classical contact epidemiological (that is, transmission is due to "contacts" between individuals) formulations in the context of a possible deliberate release of biological agents [2, 13]. The Lagrangian approach is introduced here as a modeling approach that explicitly avoids the assignment of heterogeneous contact rates to individuals. The use of contacts or activity levels and the view that transmission is due to collisions between individuals has a long history and it is conceptually consistent with the way we envision disease transmission between susceptible and infectious individuals. However, contacts are hard to define and consequently, at least in the context of communicable diseases, impossible to measure in various settings. Is it possible to capture interactions of individual mathematically in a way different from the notion of contacts? The approach that is proposed focuses on the use of modeling frameworks that involve patches/environments defined or characterized by risks of infection that are functions of the time spent in each environment/patch. These patches/environments may or may not have permanent hosts and they may be used to account for places of "transitory" residence like mass transportation systems or

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“…The inclusion of self-and cross-diffusion terms allow for realistic responses to predator and prey movement and are often incorporated into mathematical models in population biology [8][9][10][11]. Our current efforts consider only a two species model, yet the methods developed herein can by readily extended to more general systems.…”

Section: Introductionmentioning

confidence: 99%

A variable nonlinear splitting algorithm for reaction diffusion systems with self‐ and cross‐ diffusion

Beauregard

Padgett

2018

Numerical Methods Partial

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Self-and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response of one species in light of the concentration of another. In this paper, a novel nonlinear operator splitting method is presented that directly incorporates both self-and cross-diffusion into a computational efficient design. The numerical analysis guarantees the accuracy and demonstrates appropriate criteria for stability. Numerical experiments display its efficiency and accuracy. KEYWORDS cross-diffusion, nonlinear operator splitting, reactiondiffusion equations, self-diffusionHere Ω = [0, L] × [0, L], Δ is the two-dimensional Laplacian operator, and the reactive functions f and g are in C 1 (R 2 ). We define x to be the spatial coordinate vector in two dimensions.Numer Methods Partial Differential Eq. 2019;35:597-614. wileyonlinelibrary.com/journal/num

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From Bee Species Aggregation to Models of Disease Avoidance: The Ben-Hur effect

Cited by 4 publications

References 40 publications

Role of short-term dispersal on the dynamics of Zika virus in an extreme idealized environment

Role of short-term dispersal on the dynamics of Zika virus in an extreme idealized environment

Epidemiological Models Incorporating Mobility, Behavior, and Time Scales

A variable nonlinear splitting algorithm for reaction diffusion systems with self‐ and cross‐ diffusion

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