A Mathematical Model of Humanitarian Aid Agencies in Attritional Conflict Environments

• Published in: Operations research 2021-11, Vol.69 (6), p.1696-1714
• Main Authors: McLennan-Smith, Timothy A., Kalloniatis, Alexander C., Jovanoski, Zlatko, Sidhu, Harvinder S., Roberts, Dale O., Watt, Simon, Towers, Isaac N.
• Format: Article
• Language: English
• Subjects: Bifurcations; Charities; combat models and simulation; counterinsurgency; Disaster relief; Ecological effects; Ecological models; Environment models; Humanitarian aid; Lanchester theory; Logistics; Mathematical models; operating environment; Operations research; Populations
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.2021.2130

Traditional combat models, such as Lanchester’s equations, are typically limited to two competing populations and exhibit solutions characterized by exponential decay—and growth if logistics are included. We enrich such models to account for modern and future complexities, particularly around the role of interagency engagement in operations as often displayed in counterinsurgency operations. To address this, we explore incorporation of nontrophic effects from ecological modeling. This provides a global representation of asymmetrical combat between two forces in the modern setting in which noncombatant populations are present. As an example, we set the noncombatant population in our model to be a neutral agency supporting the native population to the extent that they are noncombatants. Correspondingly, the opposing intervention force is under obligations to enable an environment in which the neutral agency may undertake its work. In contrast to the typical behavior seen in the classic Lanchester system, our model gives rise to limit cycles and bifurcations that we interpret through a warfighting application. Finally, through a case study, we highlight the importance of the agility of a force in achieving victory when noncombatant populations are present. Tools from mathematical ecology in a combat model with humanitarian aid agencies Conflict models have a long history of taking inspiration from mathematical ecology. In “A mathematical model of humanitarian aid agencies in attritional conflict environments,” McLennan-Smith et al. seek to enrich counterinsurgency (COIN) warfare models to account for modern and future complexities by incorporating nontrophic effects and the functional response from mathematical ecology. The authors consider the application of these ideas in a COIN scenario in which a humanitarian aid agency is present in the conflict environment to support the local population. In this scenario, the aid agency plays the unwilling role of a “hospital shield” whereby it is forced to, or inadvertently, shield combatants or weapons. In contrast to the typical behavior seen in the classic Lanchester system, this model gives rise to limit cycles and bifurcations that the authors interpret through a warfighting application. Finally, through a case study, the authors highlight the importance of the agility of an intervention force in achieving victory when humanitarian aid agencies are present.