A Model of 21^st Century Counterinsurgency Warfare

Abstract

The insurgency warfare being practiced by global terrorists in the 21st Century is put in a historical context and modeled mathematically. The most widely known insurgency model is the “fish in the sea” formulation attributed to Mao Tse-tung. Fundamentally, it is a phased attrition model that can be described by variations of the Lanchester equations. In a collective sense, much of the Vietnam War fits that formulation. However, the 21st Century has featured a different type of insurgency where attrition is not the decisive factor on either side. Today's insurgencies are psychological wars of political endurance, not attrition. They require different mathematics. The mathematical formulation of 21st Century counterinsurgency warfare contains two stochastic time series, the first dealing with defeat and the second success. The defeat portion deals with the likelihood of precipitous troop withdrawals permitting terrorist insurgents to declare victory in a de facto sense. The defeat probability roughly mirrors public opinion polls. Public opinion polls are probabilistic because they are heavily influenced by short-term unpredictable events, some detrimental to the war effort and some supporting it. In a sense, this is similar to the fluctuations of the stock market or exchange rate variations. They are also influenced by the duration of the war and accumulated casualties, both in a negative sense. Consequently, the defeat probability trends upward asymptotically toward unity over time although the instantaneous values cluster above and below the trend curve. In a democracy, decision makers or funding bodies can resist adverse polls but not indefinitely. If war support polls are heavily negative, it is probable that decision makers will eventually move to cut their losses and pull out. The second portion of the model independently deals with success by counterinsurgency forces; i.e., a level of stability and security that permits at least a partial, phased troop draw down. It is based on estimates of the strength and quality of the host country military and police forces, the level of insurgent-initiated violence, the state of the host country economy, the services provided by the host government, and the willingness of the host government to address the insurgency in an even-handed manner. The success model resembles the Hamlet Evaluation System used during the Vietnam War. The instantaneous measures of success fluctuate above and below the trend curve with a variance that can be small, approaching determinacy. The success model has fixed, predetermined benchmarks that can but may not be achieved depending on the level of effort relative to the insurgent opposition. Both parts of the model deal with counterinsurgent troop withdrawals, one precipitous and one gradual and phased. In neither of the cases considered, de facto defeat or phased withdrawal, does the model deal with “military” defeat or victory. If the type of insurgencies encountered in the 21st Century become the norm, military defeat and victory are irrelevant.

Analytic Modeling of Insurgencies

“…A fourth player is the international community [4], [10] who may (e.g., Libya, 2011) or may not (e.g., Syria, 2011-2014) be actively involved in the conflict. Because international forces, if they get actively involved in the insurgency, typically side with either the government (e.g., Afghanistan) or the insurgents (e.g., Libya), we will focus only on the three main players, as shown in Figure 1.…”

Analytic Modeling of Insurgencies

“…The three major players in an insurgency are the two adversaries -the government forces and the insurgents -and the civilian population, which is caught in the middle. A fourth player is the international community [4], [10] who may (e.g., Libya, 2011) or may not (e.g., Syria, 2011-2014) be actively involved in the conflict. Because international forces, if they get actively involved in the insurgency, typically side with either the government (e.g., Afghanistan) or the insurgents (e.g., Libya), we will focus only on the three main players, as shown in Figure 1.…”

Discrete Combat Models

“…where k 1 and k 2 are kill rates. Models of this form have been used to model modern guerilla warfare according to Deitchman (1962), Schaffer (1968Schaffer ( , 2007, Fowler (2006), and Giordano and McCormick (2007). In the later stages of the Vietnam War, General William Westmoreland requested an increase in the U.S. troop strength of 206,000 to obtain victory.…”

“…Schaffer (2007) states that modern, 21 st century, terrorist-inspired insurgencies are comparable to the Vietnam experience and can be modeled using Lanchester's equations. It has been pointed out by Schaffer (2007) as well as other documents that the North Vietnamese force size never exceeded approximately 250,000, yet over time they received over 660,000 casualties. This suggests a different model form that allows for growth of the insurgency as well as attrition by combat.…”