The contribution of Sir Alan Wilson to spatial interaction and transport modelling

AbstractCOVID-19, a global pandemic caused by the Severe Acute Respiratory Syndrome Coronavirus 2 virus, has claimed millions of lives worldwide. Amid soaring contagion due to newer strains of the virus, it is imperative to design dynamic, spatiotemporal models to contain the spread of infection during future outbreaks of the same or variants of the virus. The reliance on existing prediction and contact tracing approaches on prior knowledge of inter- or intra-zone mobility renders them impracticable. We present a spatiotemporal approach that employs a network inference approach with sliding time windows solely on the date and number of daily infection numbers of zones within a geographical region to generate temporal networks capturing the influence of each zone on another. It helps analyze the spatial interaction among the hotspot or spreader zones and highly affected zones based on the flow of network contagion traffic. We apply the proposed approach to the daily infection counts of New York State as well as the states of USA to show that it effectively measures the phase shifts in the pandemic timeline. It identifies the spreaders and affected zones at different time points and helps infer the trajectory of the pandemic spread across the country. A small set of zones periodically exhibit a very high outflow of contagion traffic over time, suggesting that they act as the key spreaders of infection. Moreover, the strong influence between the majority of non-neighbor regions suggests that the overall spread of infection is a result of the unavoidable long-distance trips by a large number of people as opposed to the shorter trips at a county level, thereby informing future mitigation measures and public policies.

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Mass Transport Modelling in Porous Media Using Delay Differential Equations

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.258-260.586 ◽

2006 ◽

Vol 258-260 ◽

pp. 586-591

Author(s):

António Martins ◽

Paulo Laranjeira ◽

Madalena Dias ◽

José Lopes

Keyword(s):

Porous Media ◽

Differential Equations ◽

Mass Transport ◽

Delay Differential Equations ◽

Dispersion Model ◽

Flow Characteristics ◽

Convective Transport ◽

Transport Modelling ◽

Flow Field Characteristics ◽

Delay Differential

In this work the application of delay differential equations to the modelling of mass transport in porous media, where the convective transport of mass, is presented and discussed. The differences and advantages when compared with the Dispersion Model are highlighted. Using simplified models of the local structure of a porous media, in particular a network model made up by combining two different types of network elements, channels and chambers, the mass transport under transient conditions is described and related to the local geometrical characteristics. The delay differential equations system that describe the flow, arise from the combination of the mass balance equations for both the network elements, and after taking into account their flow characteristics. The solution is obtained using a time marching method, and the results show that the model is capable of describing the qualitative behaviour observed experimentally, allowing the analysis of the influence of the local geometrical and flow field characteristics on the mass transport.

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On the Relationship between Alonso's Theory of Movement and Wilson's Family of Spatial-Interaction Models

Environment and Planning A Economy and Space ◽

10.1068/a130217 ◽

1981 ◽

Vol 13 (2) ◽

pp. 217-224 ◽

Cited By ~ 15

Author(s):

J Ledent

Keyword(s):

Input Data ◽

Spatial Interaction ◽

System Of Equations ◽

Interaction Models ◽

Spatial Interaction Models ◽

Standard Family ◽

Original Contribution ◽

Standard Models ◽

The Relationship

This paper compares the system of equations underlying Alonso's theory of movement with that of Wilson's standard family of spatial-interaction models. It is shown that the Alonso model is equivalent to one of Wilson's four standard models depending on the assumption at the outset about which of the total outflows and/or inflows are known. This result turns out to supersede earlier findings—inconsistent only in appearance—which were derived independently by Wilson and Ledent. In addition to this, an original contribution of this paper—obtained as a byproduct of the process leading to the aforementioned result—is to provide an exact methodology permitting one to solve the Alonso model for each possible choice of the input data.

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