Agent-Based Modeling – Dr Duncan Robertson

Herd Immunity

I’ve built a model to show the concept of herd immunity. It shows why we need to not leave hard-to-reach parts of the population unvaccinated.

Herd immunity, also called population immunity, is the protection for the population that comes from when a proportion have been vaccinated. With more vaccinations, we move towards this herd immunity threshold. (We’re not there yet, even though some say we are.)

Here’s my model. Imagine a population in a country. People are either susceptible (they may not be vaccinated or have had the virus). We colour these green. People may have had the vaccine. These are blue. And there’s one (near the bottom left in purple) that is infectious.

Now, in my model, they will infect anyone who is susceptible (green) within that little circle surrounding them. And those will infect people surrounding *them*

After a few generations, more and more are infected.

Eventually, almost all (although not all – some are fortunate) are infected. That’s bad. And it’s because we haven’t reached the herd immunity threshold.

So – what happens when we reach the herd immunity threshold (or get close to it)? We have many more vaccinated (they’re blue). Let’s see what happens when the infectious person (this time in the middle) infects others.

Well, in this case, there’s a local infection, but the infection can’t be sustained (that’s good). Herd immunity.

But.

What happens when those vaccines are not spread out equally across the country?

Let’s vaccinate *the same number of people* just in the bottom half of our population.

There we are – lots of vaccinated people in blue. That infection (right middle) doesn’t stand a chance.

Now let’s see what happens when that infectious person is in the top half among the unvaccinated population (remember, we have the same number of vaccinated people in the population as a whole).

Well, that infection spreads…

… and spreads …

until huge numbers of people are infected *even though we have overall reached the herd immunity threshold*

And that is why we need to vaccinate evenly, not leaving pockets where infection can spread.

Simulation Modelling Community Response to COVID-19

Our paper in Journal of Simulation ‘How simulation modelling can help reduce the impact of COVID-19‘ setting out how simulation modelling can help in the fight against COVID-19 and subsequent epidemics and pandemics. Click here to access the paper.

ABSTRACT

Modelling has been used extensively by all national governments and the World Health Organisation in deciding on the best strategies to pursue in mitigating the effects of COVID-19. Principally these have been epidemiological models aimed at understanding the spread of the disease and the impacts of different interventions. But a global pandemic generates a large number of problems and questions, not just those related to disease transmission, and each requires a different model to find the best solution. In this article we identify challenges resulting from the COVID-19 pandemic and discuss how simulation modelling could help to support decision-makers in making the most informed decisions. Modellers should see the article as a call to arms and decision-makers as a guide to what support is available from the simulation community.

Social Distancing using Play-Doh and Matches

There has been much talk about using social distancing as a response to the Coronavirus outbreak. Here’s a video of how social distancing can be used:

Close Contact, where the population is infected very rapidly. This is not A Good Thing – the national health service is overwhelmed, and the death rate goes up as a result
Extreme Distancing, where the viral spread takes too long. This is not A Good Thing – the social and economic costs are huge
Optimal Distancing, where the spread is controlled and the human, social, and economic costs are optimized. This is A Good Thing. It is also very tricky to get right.

Agent-Based Strategizing: New Book Published at Cambridge University Press

My new book, Agent-Based Strategizing, has been published at Cambridge University Press. It is available to download for free until 31 July 2019 at the link below. The book is an overview of how agent-based modelling has been (and can be) used in strategic management.

https://www.cambridge.org/core/elements/agentbased-strategizing/4AD9D0D7416DE46AEB7F1A5478772ACF

Abstract: Strategic management is a system of continual disequilibrium, with firms in a continual struggle for competitive advantage and relative fitness. Models that are dynamic in nature are required if we are to really understand the complex notion of sustainable competitive advantage. New tools are required to tackle challenges of how firms should compete in environments characterized by both exogeneous shocks and intense endogenous competition. Agent-based modelling of firms’ strategies offers an alternative analytical approach, where individual firm or component parts of a firm are modelled, each with their own strategy. Where traditional models can assume homogeneity of actors, agent-based models simulate each firm individually. This allows experimentation of strategic moves, which is particularly important where reactions to strategic moves are non-trivial. This Element introduces agent-based models and their use within management, reviews the influential NK suite of models, and offers an agenda for the development of agent-based models in strategic management.

Spatial Transmission Models Paper Available

The full text of the Spatial Transmissions Models: A Taxonomy and Framework paper can be found on the Risk Analysis journal website or here.

Spatial Transmission Models: A Taxonomy and Framework

This paper , published in the journal Risk Analysis, sets out a review of the different methods used for modelling the spread of an idea, disease, etc. over space.

ABSTRACT

Within risk analysis and more broadly, the decision behind the choice of which modelling technique to use to study the spread of disease, epidemics, fires, technology, rumors, or more generally spatial dynamics, is not well documented.

While individual models are well defined and the modeling techniques are well understood by practitioners, there is little deliberate choice made as to the type of model to be used, with modelers using techniques that are well accepted in the field, sometimes with little thought as to whether alternative modelling techniques could or should be used.

In this paper, we divide modelling techniques for spatial transmission into four main categories: population-level models, where a macro-level estimate of the infected population is required; cellular models, where the transmission takes place between connected domains, but is restricted to a fixed topology of neighboring cells; network models, where host-to-host transmission routes are modelled, either as planar spatial graphs or where short cuts can take place as in social networks; and finally agent-based models which model the local transmission between agents, either as host-to-host geographical contacts, or by modelling the movement of the disease vector, with dynamic movement of hosts and vectors possible, on a Euclidian space or a more complex space deformed by the existence of information about the topology of the landscape using GIS techniques. We summarize these techniques by introducing a taxonomy classifying these modeling approaches.

Finally, we present a framework for choosing the most appropriate spatial modelling method, highlighting the links between seemingly disparate methodologies, bearing in mind that the choice of technique rests with the subject expert.

PhD Studentship in Modelling Dynamic Responses to Dynamic Threats at Loughborough University [applications now closed]

I am co-supervising the following PhD project – the application link and further details can be found here: http://www.lboro.ac.uk/study/postgraduate/research-degrees/funded/modelling-dynamic-responses/ . The closing date is 14 December 2017. Please get in touch if you would like to discuss this opportunity.

One of the most challenging issues for policy makers dealing with bio-security threats is their dynamic nature: diseases may spread quickly and deadly among vulnerable populations and pandemics may cause many casualties.

Finding the appropriate response to threats is a major challenge. Whilst models exist for understanding of the dynamics of the threats themselves, responses can be largely ad-hoc or ‘firefighting’. The aim of this research is to produce robust responses for dynamic threats.

The research will build up as follows, from low to high complexity: static responses to static threats; static responses to dynamic threats; dynamic responses to static threats; and dynamic responses to dynamic threats.

We will use a variety of methods to define the best response: cellular automata, network analysis, spatial modelling, agent-based modelling, and the generation of dynamic fitness landscapes.

This PhD studentship is most suitable for candidates with a background in a quantitative discipline such as management science, operations research, engineering, physics and other natural sciences.

Two Funded PhD Studentships in Agent-Based Modelling at Loughborough University School of Business and Economics [applications now closed]

I am looking for high quality, numerate, candidates to fill these exciting PhD studentships with me as a (co-) supervisor at Loughborough’s School of Business and Economics. Please note that this post has been updated with new links (in blue, below).

The first is modelling dynamic responses to dynamic threats; the second is using analytics in traditional industries. Please see the links below for further details and how to apply. Note that for further information, you will need to click on the blue links below.

Modelling Dynamic Responses to Dynamic Threats (with Professor Gilberto Montibeller)

We will use a variety of methods to define the best response: cellular automata, network analysis, spatial modelling, agent-based modelling, and the generation of dynamic fitness landscapes.

This PhD studentship is most suitable for candidates with a background in a quantitative discipline such as management science, operations research, engineering, physics and other natural sciences.

Business Analytics for Public Services and Regulated Industries: New Techniques for Analytics-Driven Decision Making in Traditional Industries (with Dr Maria Neiswand and Professor David Saal)

The rise of business analytics has given rise to enormous opportunities within the private sector, but these benefits have yet to be fully realized in public services and regulated industries such as energy, water, and transportation networks. Conversely, governments are mandating collection of data by installing smart metering devices. This gives rise to the need for innovative ways of thinking in industries that are still largely based on traditional economic thinking involving conventional assumptions on optimization and behaviour.

As an example, the energy sector is characterised by strongly defined market structures with incumbents and an ultimate need for energy network security, which not only prevents the quick adoption of technical changes but also translates into regulatory outcomes, such as price caps.

This exciting PhD opportunity will integrate theoretical and empirical approaches and spans two strengths of Loughborough’s School of Business and Economics: microeconomics and particularly rigorous analysis of the determinants of productivity and performance (including cost modelling) and management science (including simulation and network analysis).

We are therefore seeking a student with a quantitative background (whether in economics, management science, engineering, physics or other natural sciences). A willingness to learn new techniques such as, cost modelling, performance measurement, agent-based modelling and network analysis is desired.

Agent-Based Models for Simulating Human Behavior: IFORS Conference 2017

This presentation including joint work with Alberto Franco, was presented at the IFORS (International Federation of Operational Research Societies) conference in Quebec City, QC, Canada. We present two different agent-based models for simulating human behavior.

We use the example of group decision making.

The first model uses a cognitive fitness landscape to model the quality of a decision, where participants compare their decision with their nearest neighbor. The decision is based on an external comparison.

The second model uses an internal comparison of a decision with the next best alternative. The model is based on the psychological concept of hidden profiles, where participants only make the best decision by sharing information with the group.

Eight Mile and the Emergence of Segregation

Eight Mile, epitomized by Eminem in the film of the same name, is a street in Detroit that marks the boundary between the majority white northern suburbs and the majority black neighborhoods closer to the inner city.

But what causes this segregation in the first place?

Hypothesis 1: The Central Planner

Zoning Map, 1930s, showing HOLC zoning, source: http://www.urbanoasis.org/projects/holc-fha/digital-holc-maps/

In Detroit’s case, as with many cities across the USA, it was, in part, due to the zoning of the city by the federal Home Owners’ Loan Corporation, which zoned the city into areas of risk, meaning that banks were indirectly encouraged to develop outer suburbs while not offering mortgages to inner city properties. This lead to wealthier, generally white, residents moving to the suburbs.

Indeed, physical barriers, such at the Detroit Wall, also known as the Eight Mile Wall, were built to separate majority black and majority white neighborhoods.

Detroit Today

The legacy of these zones live on today, as seen in the map below from the 2010 US Census. The dividing line between the green (black) areas and the blue (white) areas is Eight Mile Road.

DotMap http://demographics.virginia.edu/DotMap/ based on 2010 US Census

So, segregation exists, and is caused by a central actor. But is there an alternative explanation?

Alternative Hypothesis: Emergence

In 1971, Thomas Schelling set out to model the phenomenon, not by assuming a central planner, but by modelling the interactions of individuals.

Thomas Schelling’s model was this. Assume individuals are placed in a grid, similar to being located on a chess board. Allow individuals who are in a local minority to move. In the example below, the blue circle is in a minority (with 5 out of its 6 neighbors being a different color), and according to the rules of the model, is unhappy. It could decide to move to the vacant square to the north-west, but it would still be in a local minority (with 4 out of 6 neighbors being a different color) and would remain unhappy. So instead, it chooses the space to the south west where 3 out of its 6 neighbors are of the same color, and not being in a minority, it settles there.

Agent Movement © Duncan Robertson after Thomas Schelling (1971)

Schelling, perhaps without knowing it, introduced agent-based modelling, where, instead of modelling the system as a whole, the modelling of individual agents enables us to see the emergence of macro-level properties, in this case segregation, via the modelling of micro-level (local) interactions.

We can see the effect of micro-level interactions causing macro-level segregation in the model below (developed by Duncan Robertson after Wilensky after Schelling). Each individual, or agent, decides whether they are unhappy or happy; if they are unhappy, they search until they find a vacant location where they will become happy. This continues until all individuals attain happiness.

Three Class Segregation Model © Duncan Robertson after Wilensky after Schelling

So, perhaps segregation is not imposed, but is down to us. Or maybe, in reality, it’s a little bit of both.

Please do get in touch if you would like to discuss building or working with agent-based models.