Modeling Civilian and Militant Casualties in Asymmetric Wars: The Case of Gaza 2024

Lanchester-type models for attritional warfare balance military casualties in two opposing forces. In asymmetric wars such as that in Gaza, by contrast, the dominant military force takes few casualties, and the crucial relationship is between casualties among opposing militants and among innocent civilians. We construct and analyze a simple dynamical model in which the proportion β ∈ [0, 1] of effectively targeted, as opposed to indiscriminate, military actions determines the balance between militant and civilian casualties. We derive a conserved quantity which yields an analogue of Lanchester’s laws for this balance, find the general solution of the model, and quantify the effects of variations in levels of targeting effectiveness on civilian casualties. Important conclusions are that every increase in β results in an approximately 1/β(1−β) times greater proportionate reduction in civilian casualties, and that, when militants are a small fraction of the population, the overall percentage of civilian casualties when the militant force has been eliminated is (1−β)/β times the original percentage of militants in the population. We draw some insights regarding the 2023-2025 war in Gaza.