Current Funded Projects:

• Evolution of an outbreak of Tuberculosis disease in a white indigenous population in South Wales
• Examining the process of recruitment to violent extremism through an agent-based model
• UK Immigration Policy Models

Evolution of an outbreak of Tuberculosis disease in a white indigenous population in South Wales

Investigator: Mark Temple (Consultant in Public Health Medicine, NHS, Wales)

Background

In two separate locations in South Wales outbreaks of Tuberculosis have occurred in the white indigenous population, with a locally unique genotype (by genetic fingerprinting) of Mycobacterium Tubercle. In both outbreaks despite full contact tracing and screening of contacts after more than 5 to 10 years new cases linked both epidemiologically and microbiologically continue to be diagnosed and require treatment.

Problem

The natural history of tuberculosis is complex. Whilst most cases of infection do not give rise to overt disease initially some do. Though the incubation period is variable, it is generally held that after 5 years the infection has been contained by the bodies own responses.

In these people who have contained the infection if re-infected subsequently they may develop disease on this or subsequent occasion, hence the importance of continuing to contain tuberculosis. However, to add to the complexity those who have contained the disease may fail to eradicate the infection and after a long period reactivation of the infection can occur with endogenous development of disease after an interval of decades or more. Once reactivation has occurred the patient is infectious and can start a new outbreak.

Thus following a widespread outbreak in a naïve population recurrent cases may occur despite full and effective control measures having been taken, but the concern of the TB control team is; could this new patient be evidence of continuing undiagnosed community transmission?

Aim

To estimate the probability of new cases of a particular frequency occurring after a controlled outbreak: that is one in which all initial infective cases have been successfully identified and treated.

Method

Build and agent based model where each agent represents a patient or contact in the social network derived from the contact tracing work undertaken by the TB control team.

The individual agents will be given the demographic details of the person they represent as we know them and the links to other agents of the type and known to us.

Initially the model will assume no movement of patients takes place but the linkages are fixed (i.e. be configured as a micro simulation).

The Index case will then be infected and using the published literature the spread of TB infection and disease though the network observed until a time representing identification of the first case and control measures are instituted.

At this stage the control measures will be simulated, close contacts screened, those found to have disease treated. For those infected using the evidence of the sensitivity of the test, that proportion will be given preventative treatment.

If this simulation model after verification develops the observed outbreak profile with a reasonable frequency (>5%) then this model will be considered adequate. If as expected this simple model does not adequately describe the observations then patient interaction will be added to the model.

Examining the process of recruitment to violent extremism through an agent-based model

Investigators: Operational Research Analysts, Home Office

Due to the sensitive nature of the project, details cannot be disclosed.

UK Immigration Policy Models

Investigators: Jeremy Franklin (Economist, Migration Advisory Committee Secretariat, Home Office), Kate Mieske (Economist, UK Boarder Agency, Home Office)

1 – Migration flows between two countries

The aim would be to model the flows of people migrating between two countries. Following the KISS (Keep It Simple Stupid) principle the model will begin with a simple stylised characterisation that will be built up to explore more complex ideas.

• Two countries, A and B, will be defined.
• A number of people, agents, will be assigned to each country. Each agent will be part of a 'family' or 'social group' of size n (allocated randomly from a uniform distribution).
• An agent from A will move to B according to a probability p which in turn is determined by the number of family members in B and a random shock component. Similarly for agents moving from B to A.
• Country A and B will be assigned income distributions and each agent a position on that income distribution. Each country will also be assigned an employment rate. The probability that an agent moves country will be updated to include an assessment of their likely earnings in the other country.
• The model will then be calibrated according to the characteristics and experiences of two countries, such as the UK and Poland. For example incorporating the income distributions of each country as well as the employment rate and calibrating the parameters according to recorded flows of individuals between the two nations.

Extensions to this model could include examining the impact of shocks to the income distributions and employment rate as well as introducing an exchange rate. It may also be possible to explore the impact of restricting the flow of migrants by introducing a stylised version of the Points Based System or maximum number to the flow of migrants to one country.

2 – The regional distribution of migrants

This option would explore the spatial distribution of immigrants in the UK. Again, it would begin by setting up a simple stylised model to test more complex ideas later down the line. This model would explore the interaction between migrant stocks and migrant flows and the impact on the regional distribution of migrants. The connection between migrantclusters and flows is well-documented in econometric papers such as Card and DiNardo (2000) and Lemos and Portes (2008). In our proposed agent-based model:

• There are x regions and a constant flow of immigrants, agents, from y countries. • Each agent decides on which x to settle in based on a probability function defined
• by the number of agents from the same country who are located in that region.
• Each agent is assigned a position in the income distribution and a probability of being employed based on the region’s employment rate.
• Each period the agent can opt to move region based on a function relating to the number of people from the same in that region and the employment rate and income available of that region.
• This model would be calibrated based on data pertaining to the UK.

An extension to this model could be to examine the implications of randomly locating migrants to regions and analysing the spatial patterns that emerge. The model could be calibrated using information on the distribution of asylum seeker accommodation support in the UK.

3 – An employer search model

This model would explore employers’ decisions whether to recruit immigrant or native labour.

• There are x employers. Each employer needs to hire y employees (taken from a uniform distribution) of skill level z for £z.
• Employees are fired according to a firing probability ?. If an employee is unemployed, they search for jobs until meeting an employer that will hire them. An employer will only hire an employee if their skill level is z or above.
• Each employee is assigned a skill level (z denoted by a random probability distribution). If an employee meets an employer with a vacancy and has the right skill level, they will be employed.
• Two types of employees are introduced, natives and immigrants. Immigrants of skill level z must be paid £z+i, reflecting the additional costs to an employer from having to pay for a certificate of sponsorship.
• An employer will increase the wage offered after a period p without finding a native to employ.

There are a number of potential expansions to this model. The firing probability, α, would initially be exogenous but could be made endogenous to the unemployment rate. Skill levels of migrants and natives could be modelled according to the observed probability distributions in the UK. The model could then be expanded to analyse the impact of native and immigrant unemployment as a result of increasing the costs to an employer from hiring an immigrant and examine the presence of shortage of labour.