Modelling host population support for combat adversaries

TL;DR

This paper presents a nonlinear differential equation model of three populations—Red, Blue, and Green—analyzing how support dynamics influence adversarial combat effectiveness in counter-insurgency scenarios.

Contribution

It introduces a novel model incorporating support dynamics and logistic interactions to study adversarial populations and their influence on combat outcomes.

Findings

Support levels significantly impact combat effectiveness.

Support diminishes when populations exceed local capacity.

Balance between support and size is crucial for victory.

Abstract

We consider a model of adversarial dynamics consisting of three populations, labelled Blue, Green and Red, which evolve under a system of first order nonlinear differential equations. Red and Blue populations are adversaries and interact via a set of Lanchester combat laws. Green is divided into three sub-populations: Red supporters, Blue supporters and Neutral. Green support for Red and Blue leads to more combat effectiveness for either side. From Green's perspective, if either Red or Blue exceed a size according to the capacity of the local population to facilitate or tolerate, then support for that side diminishes; the corresponding Green population reverts to the neutral sub-population, who do not contribute to combat effectiveness of either side. The mechanism for supporters deciding if either Blue or Red are too big is given by a logistic-type interaction term. The intent of the model is to examine the role of influence in complex adversarial situations typical in counter-insurgency, where victory requires a genuine balance between maintaining combat effectiveness and support from a third party whose backing is not always assured.