A Mathematical Model of Humanitarian Aid Agencies in Attritional Conflict Environments

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.