Hannah Fry

A mathematical model of the London riots and their policing

In August 2011, several areas of London experienced episodes of large-scale disorder, comprising looting, rioting and violence. Much subsequent discourse has questioned the adequacy of the police response, in terms of the resources available and strategies used. In this article, we present a mathematical model of the spatial development of the disorder, which can be used to examine the effect of varying policing arrangements. The model is capable of simulating the general emergent patterns of the events and focusses on three fundamental aspects: the apparently-contagious nature of participation; the distances travelled to riot locations; and the deterrent effect of policing. We demonstrate that the spatial configuration of London places some areas at naturally higher risk than others, highlighting the importance of spatial considerations when planning for such events. We also investigate the consequences of varying police numbers and reaction time, which has the potential to guide policy in this area.

Spatial methods for infectious disease outbreak investigations: systematic literature review.

Investigations of infectious disease outbreaks are conventionally framed in terms of person, time and place. Although geographic information systems have increased the range of tools available, spatial analyses are used relatively infrequently. We conducted a systematic review of published reports of outbreak investigations worldwide to estimate the prevalence of spatial methods, describe the techniques applied and explore their utility. We identified 80 reports using spatial methods published between 1979 and 2013, ca 0.4% of the total number of published outbreaks. Environmental or waterborne infections were the most commonly investigated, and most reports were from the United Kingdom. A range of techniques were used, including simple dot maps, cluster analyses and modelling approaches. Spatial tools were usefully applied throughout investigations, from initial confirmation of the outbreak to describing and analysing cases and communicating findings. They provided valuable insights that led to public health actions, but there is scope for much wider implementation and development of new methods.

Twenty years and counting: epidemiology of an outbreak of isoniazid-resistant tuberculosis in England and Wales, 1995 to 2014

An outbreak of isoniazid-resistant tuberculosis first identified in London has now been ongoing for 20 years, making it the largest drug-resistant outbreak of tuberculosis documented to date worldwide. We identified culture-confirmed cases with indistinguishable molecular strain types and extracted demographic, clinical, microbiological and social risk factor data from surveillance systems. We summarised changes over time and used kernel-density estimation and k-function analysis to assess geographic clustering. From 1995 to 2014, 508 cases were reported, with a declining trend in recent years. Overall, 70% were male (n = 360), 60% born in the United Kingdom (n = 306), 39% white (n = 199), and 26% black Caribbean (n = 134). Median age increased from 25 years in the first 5 years to 42 in the last 5. Approximately two thirds of cases reported social risk factors: 45% drug use (n = 227), 37% prison link (n = 189), 25% homelessness (n = 125) and 13% alcohol dependence (n = 64). Treatment was completed at 12 months by 52% of cases (n = 206), and was significantly lower for those with social risk factors (p < 0.05), but increased over time for all patients (p < 0.05). The outbreak remained focused in north London throughout. Control of this outbreak requires continued efforts to prevent and treat further active cases through targeted screening and enhanced case management.

Spatio-temporal patterns of IED usage by the Provisional Irish Republican Army

In this paper, a unique dataset of improvised explosive device attacks during “The Troubles” in Northern Ireland (NI) is analysed via a Hawkes process model. It is found that this past dependent model is a good fit to improvised explosive device attacks yielding key insights about the nature of terrorism in NI. We also present a novel approach to quantitatively investigate some of the sociological theory surrounding the Provisional Irish Republican Army which challenges previously held assumptions concerning changes seen in the organisation. Finally, we extend our use of the Hawkes process model by considering a multidimensional version which permits both self and mutual-excitations. This allows us to test how the Provisional Irish Republican Army responded to past improvised explosive device attacks on different geographical scales from which we find evidence for the autonomy of the organisation over the six counties of NI and Belfast. By incorporating a second dataset concerning British Security Force (BSF) interventions, the multidimensional model allows us to test counter-terrorism (CT) operations in NI where we find subsequent increases in violence.

Spatial Targeting for Bovine Tuberculosis Control: Can the Locations of Infected Cattle Be Used to Find Infected Badgers?

Bovine tuberculosis is a disease of historical importance to human health in the UK that remains a major animal health and economic issue. Control of the disease in cattle is complicated by the presence of a reservoir species, the Eurasian badger. In spite of uncertainty in the degree to which cattle disease results from transmission from badgers, and opposition from environmental groups, culling of badgers has been licenced in two large areas in England. Methods to limit culls to smaller areas that target badgers infected with TB whilst minimising the number of uninfected badgers culled is therefore of considerable interest. Here, we use historical data from a large-scale field trial of badger culling to assess two alternative hypothetical methods of targeting TB-infected badgers based on the distribution of cattle TB incidents: (i) a simple circular ‘ring cull’; and (ii) geographic profiling, a novel technique for spatial targeting of infectious disease control that predicts the locations of sources of infection based on the distribution of linked cases. Our results showed that both methods required coverage of very large areas to ensure a substantial proportion of infected badgers were removed, and would result in many uninfected badgers being culled. Geographic profiling, which accounts for clustering of infections in badger and cattle populations, produced a small but non-significant increase in the proportion of setts with TB-infected compared to uninfected badgers included in a cull. It also provided no overall improvement at targeting setts with infected badgers compared to the ring cull. Cattle TB incidents in this study were therefore insufficiently clustered around TB-infected badger setts to design an efficient spatially targeted cull; and this analysis provided no evidence to support a move towards spatially targeted badger culling policies for bovine TB control.

A dynamic spatial model of conflict escalation

In both historical and modern conflicts, space plays a critical role in how interactions occur over time. Despite its importance, the spatial distribution of adversaries has often been neglected in mathematical models of conflict. In this paper, we propose an entropy-maximising spatial interaction method for disaggregating the impact of space, employing a general notion of ‘threat’ between two adversaries. This approach addresses a number of limitations that are associated with partial differential equation approaches to spatial disaggregation. We use this method to spatially disaggregate the Richardson model of conflict escalation, and then explore the resulting model with both analytical and numerical treatments. A bifurcation is identified that dramatically influences the resulting spatial distribution of conflict and is shown to persist under a range of model specifications. Implications of this finding for real-world conflicts are discussed.