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This special issue of the European journal of applied mathematics features research articles that involve the application of mathematical methodologies to the modelling of a broad range of problems related to crime and security. Some specific topics in this issue include recent developments in mathematical models of residential burglary, a dynamical model for the spatial spread of riots initiated by some triggering event, the analysis and development of game-theoretic models of crime and conflict, the study of statistically based models of insurgent activity and terrorism using real-world data sets, models for the optimal strategy of police deployment under realistic constraints, and a model of cyber crime as related to the study of spiking behaviour in social network cyberspace communications. Overall, the mathematical and computational methodologies employed in these studies are as diverse as the specific applications themselves and the scales (spatial or otherwise) to which they are applied. These methodologies range from statistical and stochastic methods based on maximum likelihood methods, Bayesian equilibria, regression analysis, self-excited Hawkes point processes, agent-based random walk models on networks, to more traditional applied mathematical methods such as dynamical systems and stability theory, the theory of Nash equilibria, rigorous methods in partial differential equations and travelling wave theory, and asymptotic methods that exploit disparate space and time scales.

Anti-Wolbachia therapy delivers safe macrofilaricidal activity with superior therapeutic outcomes compared to all standard anti-filarial treatments, with the added benefit of substantial improvements in clinical pathology. These outcomes can be achieved, in principle, with existing registered drugs, e.g. doxycycline, that are affordable, available to endemic communities and have well known, albeit population-limiting, safety profiles. The key barriers to using doxycycline as an mass drug administration (MDA) strategy for widespread community-based control are the logistics of a relatively lengthy course of treatment (4–6 weeks) and contraindications in children under eight years and pregnancy. Therefore, the primary goal of the anti-Wolbachia (A·WOL) consortium is to find drugs and regimens that reduce the period of treatment from weeks to days (7 days or less), and to find drugs which would be safe in excluded target populations (pregnancy and children). A secondary goal is to refine regimens of existing antibiotics suitable for a more restricted use, prior to the availability of a regimen that is compatible with MDA usage. For example, for use in the event of the emergence of drug-resistance, in individuals with high loiasis co-infection and at risk of severe adverse events (SAE) to ivermectin, or in post-MDA ‘endgame scenarios’, where test and treat strategies become more cost effective and deliverable.