Estimating the numerical strength of insurgents remains a fundamental question in counterinsurgency. This question becomes even more compelling considering that insurgent populations often form networks with varying degrees of centralisation and hierarchy. As there is a tendency for removed and active insurgents to be linked within these networks, a more nuanced understanding of these networks could provide insights into the number of active insurgents based on the ones already removed.
Recent research from academics and counterinsurgency practitioners has demonstrated the potential benefits of applying concepts from complex adaptive systems, network theory, and ecological population models to enhance our understanding of insurgencies. This approach considers the adaptive nature of insurgent groups as they learn and adjust to their evolving operational environment. Similarly, counterinsurgents also gain knowledge from past interactions with insurgents, indicating a coupled dynamical behaviour between the two opposing forces. But how does this learning process manifest for counterinsurgents, and what does their learning curve look like over time?
Expected behaviour of the cumulative detection function 
Erdős–Rényi graph and its degree distribution 
Leader and neighbours in a network 
Cumulative detection function in equilibrating model simulation 
Cumulative delta function in equilibrating model simulation 
Instantaneous detection function in equilibrating model simulation 
Active insurgents and counterinsurgents in equilibrating model simulation 
Cumulative detection function in non-equilibrating model simulation 
Cumulative delta function in non-equilibrating model simulation 
Active insurgents and counterinsurgents in non-equilibrating model simulation
In this report, we address some of these issues by employing computational modelling. Specifically, we introduce a dynamical model to simulate the evolution of insurgent populations, accounting for factors such as recruitment, removal through kinetic and non-kinetic methods, and the rise of new insurgent leaders. This model also adapts the counterinsurgent population based on insurgent recruitment and removal, which, in turn, impacts the rate at which insurgents are removed; the interaction between the two creates feedback effects. Under certain conditions, the model indicates that the ratio of cumulative removed insurgents to cumulative total insurgents can serve as a learning curve for counterinsurgents.
Our modelling insights reveal that the initial stages of an insurgency present the most valuable learning opportunities for counterinsurgents, where rapid gains are likely. However, counterinsurgents must sustain their efforts and pressure, even when there appears to be an improvement in the situation. The learning process in counterinsurgency is cumulative, and the model demonstrates that even under relatively simple conditions, significant gains can be achieved. It also underscores the importance of understanding the structure of insurgent networks and tailoring strategies based on the number of insurgents recruited and removed. Additionally, analysts should recognize that key parameters governing insurgency dynamics can change over time, necessitating suitable adjustments in policy.
The report is organized into three chapters. In the first chapter, we articulate questions concerning insurgent population sizes, discuss the role of learning in counterinsurgency, introduce a cumulative detection function (CDF) as a potential learning curve, and present mathematical expressions relating active and removed insurgent population sizes. In the second chapter of this report, we delve into the specifics of the dynamical network model designed to simulate the evolution of insurgent populations. This model employs an Erdős-Rényi graph to depict the connections within insurgent networks and updates the graph at each time step based on recruitment, leadership removal, and regular insurgent removal rules. Concurrently, the counterinsurgent count is updated with a delay according to changes in the insurgent population. Model simulations reveal alignment with the CDF, illustrating – metaphorically at the very least – conditions for counterinsurgency learning. Our model showcases how understanding insurgent network structure and tailoring strategies based on insurgent recruitment and removal is crucial in counterinsurgency operations. Further exploration of the model’s policy implications and limitations, as well as potential future research avenues, is discussed in the final chapter.
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