![8
A stock is a key element of any system, which can be measured at any given time. It accumulates
the materials and information over time and represents the state of the system (Sterman, 2000).
1.2.2 Flow
Stock changes over time through the action of flow. Flow variables regulate the state of stock
variables. Flow is labelled as either inflow or outflow. Accumulating differences between all
inflows and outflows indicates whether the stock is held in dynamic equilibrium or not. In the
SD models, a flow is represented by a pipe with arrow and valve.
There are two basic components of the structure of a system. They are rates and levels. Levels
are state variables that represent the accumulation of resources in the system. They denote the
state of the system at specific points in time. For example, population and level of liquid in a
tank are state or level variables. Rate variables represent the change of a variable per unit time.
For example, births, deaths and fluid flow rate are rate variables. Rate variables effect changes in
the level variables (Azar 2012).
Azar (2012) developed a Mathematically equations for the stock element as follows:
Stock(t )=∫ Inflow(s ) - Outflow(s )]ds + Stock ( ) ……… (1)
Thus, the value of stock at time t is the sum of the value of stock at time to and the integral of
difference between inflow and outflow rates from t0 to t. In other words, it can be stated that the
rate of change in stock at any point in time is equal to the difference between inflow and outflow
at that point. Or according to Sterman (2000) where Inflow(s) represents the value of the inflow
at any time s between the initial time to and the current time t. equivalently, the net rate of
change of any stock, its derivative, is the inflow less the outflow, defining the differential
equation
= Inflow (t) – Outflow (t) = Net change in stock (t) ……… (2)
In general, the flows will be functions of the stock and other state variables and parameters.](https://image.slidesharecdn.com/analyzinginsecurityproblemsinnortheastnigeriaasystemdynamicsmodelapproach-241111124355-f2ac7d73/85/ANALYZING-INSECURITY-PROBLEMS-IN-NORTHEAST-NIGERIA-A-SYSTEM-DYNAMICS-MODEL-APPROACH-pdf-8-320.jpg)
![16
Fig 5 Developed COIN operations loop
State actors (COIN) operations place more emphasis on military operations, intelligence
gathering and protection of the population, which is achieved through; aerial surveillance, cordon
and search operation, patrol and mounting of check points, and other source of INTEL. This
determines the rate of detection and elimination of the Non state actors. As shown in figure 5.
Formulation
System dynamics model can be express as a system of differential equations. Based on the
mathematical definition of the integral, we can conclude that an amount of quantity inside of
stock is the integration of total flows on the stock. Basic stock and flow diagram can be
mathematically represented as:
S = INTEGRAL(Net inflow, S(0)) …… (3)
Stock(t) = ∫ Inflow(s) – outflow(s)]ds + stock(to) …… (4)
where, to is the initial time and t is the current time
Civilian
population
Active non
state actors Recruitment
rate
Non state actors
eliminated
Non state actors
elimination rate
-
Radicalization
rate
+
Effective fire
power
+
+
State actors
operation intensity
Attacked rate
NSA attacked
State actors
attrition rate
Total number of
state actors
+
+
+
+ Collateral
damage
-
-
LEVEL
OF INTEL
State actors
unaimed fire
+
-
INTEL gathering
operations
+
-
Hit intensity
+
-
+
-
INTEL LOOP
NSA OPERATION LOOP
Recruitment loop
+
Insider thread
Risk
Vulnerability
+
-
+](https://image.slidesharecdn.com/analyzinginsecurityproblemsinnortheastnigeriaasystemdynamicsmodelapproach-241111124355-f2ac7d73/85/ANALYZING-INSECURITY-PROBLEMS-IN-NORTHEAST-NIGERIA-A-SYSTEM-DYNAMICS-MODEL-APPROACH-pdf-16-320.jpg)
![17
Net change in stock (t) = = Inflow (t) – Outflow (t)
Using equation (2) we can estimate number of NSA at time t as
NSA(t) = ∫ Radicalization(t) – NSA eliminated (t)]dt + NSA(to)
Where, NSA eliminated = NSA eliminated rate
Net inflow = f(S)
Often the inflow is proportional to the size of the stock. The stock grows at a fractional increase
rate g, which may be constant or variable:
Net inflow = gS
The introduction of reinforcing feedback change the relationship to = gS
To solve the equation = gS, first we separate variables to obtain
= g integrating both side
∫ = ∫ we obtain
Ln(S) = gt + c where c is a constant.
Taking the exponentials of both side give S = exp(gt). where c*is exp(c). The value of S at the
initial time, when exp(gt) = 1,is by definition S(O), so c*must equal S(0). S(0) is the initial value
of S at time t=0.
Therefore, the state of the system is
S(t) = S(0)exp(gt) ………….. (5)
Model on Counterinsurgency operations](https://image.slidesharecdn.com/analyzinginsecurityproblemsinnortheastnigeriaasystemdynamicsmodelapproach-241111124355-f2ac7d73/85/ANALYZING-INSECURITY-PROBLEMS-IN-NORTHEAST-NIGERIA-A-SYSTEM-DYNAMICS-MODEL-APPROACH-pdf-17-320.jpg)
![18
We adopted and modernized Kress & Szechtman (2009), and Kaplan, Kress & Szechtman
(2009) model.
= -αI
= - {µ(t)+[1-µ(t)][ ]} ….. (6)
where I(t) is the number of NSA at time t, G(t) is the number of state actors troops, is the state
actors attrition coefficient, µ(t) is the level of intelligence (which increases with time), and P is
the population size, α(t) is the Non state actors attrition coefficient.
State actors operating intensity = ƔG. ……. (7)
Where a fraction ƔG(µ+(1-µ)I/P of this intensity hit the non- state actors and a fraction ƔG(1-
µ)(1-I/P) hit the civilian population causing collateral damage. The collateral damage generate
recruits at a rate ΠƔG(1-µ)(1-I/P).
Effective fire power = ….. (8)
Collateral damage = ……. (9)
Where effectiveness ratio, = 0.5 the attrition rate of the non -state actors is twice the attrition
rate of the state actors (Kaplan & kress, 2009).
Rate = ( ) - 1 ……. (10)
Considering 2009 to 2022. N = 14
3.0 Result and Discussion
3.1 Data Analysis
In this study, the data was analyzed using VENSIM system dynamic model software. The
discussions were mainly to evaluate the results obtain from the secondary data and interprets the
simulated COIN intelligence operations casual loop.](https://image.slidesharecdn.com/analyzinginsecurityproblemsinnortheastnigeriaasystemdynamicsmodelapproach-241111124355-f2ac7d73/85/ANALYZING-INSECURITY-PROBLEMS-IN-NORTHEAST-NIGERIA-A-SYSTEM-DYNAMICS-MODEL-APPROACH-pdf-18-320.jpg)
![29
TIME STEP
Units: Year [0,?]
The frequency with which output is stored.
(19) State actors attrition rate=
0.03
Units: fraction
(20) State actors operation intensity=
State actors attrition rate*Total number of state actors
Units: Dmnl
(21) State actors unaimed fire=
1-LEVEL OF INTEL
Units: **undefined**
(22) TIME STEP = 1
Units: Year [0,?]
The time step for the simulation.
(23) Total number of state actors=
13500
Units: People
(24) Vulnerability=
0.15
Units: Dmnl
We adopted 15% vulnerability rate, from the raking. i.e 50% very
high, 25% high, 15% medium, and 10% low.](https://image.slidesharecdn.com/analyzinginsecurityproblemsinnortheastnigeriaasystemdynamicsmodelapproach-241111124355-f2ac7d73/85/ANALYZING-INSECURITY-PROBLEMS-IN-NORTHEAST-NIGERIA-A-SYSTEM-DYNAMICS-MODEL-APPROACH-pdf-29-320.jpg)
ANALYZING INSECURITY PROBLEMS IN NORTHEAST NIGERIA A SYSTEM DYNAMICS MODEL APPROACH.pdf
- 1. 1 ANALYZING INSECURITY PROBLEMS IN NORTHEAST NIGERIA: A SYSTEM DYNAMICS MODEL APPROACH 1 Moses Inuwa, 2 Hammandikko Gaya Muazu, 3 Madu Barma, and 4 Hayatudeen Abubakar 1234 Department of Operations Research Modibbo Adama University Yola Correspondent mail MOSESINUWA1@GMAIL.COM Keywords: System dynamics, state actors, non- state actors, intelligence, insurgency, counterinsurgency, Stock and flow. Abstract The security situation and challenges in Nigeria today has become what everyone cannot ignore as it has put both government and the populace on their toes. These activities hindered business activities, discourage local and foreign investor and effect economic growth and development. This research focused on assessing the performance level of intelligence relative to insurgency attack. A system dynamics model was used to analyze insecurity problems in Northeast Nigeria via VENSIM system dynamics software. Secondary data were collected and used for the study. The simulation was run and the result showed how system dynamics handles complex insecurity problems. The result also showed the level of intelligence increases from zero to one. This implies increase in effective aimed fire power and hit intensity, which in turn minimize active non state actors‘ activities, reduces collateral damage and gain more support from the civilian population. The results further demonstrated operational intelligence as a vital factor in counterinsurgency and counterterrorism operations. Introduction The security situation and challenges in Nigeria today has become what everyone cannot ignore as it has put both government and the populace on their toes. World over, countries are facing different dimensions of insecurity and combating these has forged major global alliance from erstwhile unfriendly neighbors. Nigeria is not left out as she is also faced with different dimensions of insecurity, ranging from the activities of the Boko Haram, banditry, kidnapping, Farmers-Herders clash. Obi (2015) stated that some of these insurgency activities include bombing, suicide bomb attacks, sporadic shooting of unarmed and innocent citizens, burning of police stations, churches, mosque, kidnapping, armed robbery, rape, murder, ritual killings, assassinations, destruction of oil facilities by Niger Delta militants, etc. In all the regions, the conflicts involved fighting between states and non-state actors seeking to overthrow the government or to take territorial control of a region within the country (Anderson and Fuemmeler, 2012). Many lives and properties have been lost and a large number of citizens
- 2. 2 rendered homeless. Government had made frantic efforts to tackle these challenges posed by insecurity in the country with a view to ending it, but the situation is still persisting (Obi, 2015). These activities hindered business activities, discouraged local and foreign investors and affects economics growth and development. According to Ramsey (2021), security starts with results; the country will feel safe if its armed forces manage to defeat the enemy. But what we see now is that the enemy is in the same place as always, striking any time it wants. State and local law enforcement agencies are important partners in preventing insurgency and terrorism, with responsibilities that include identifying and investigating local terrorist threats and protecting potential targets from attack. To meet these responsibilities, law enforcement must develop better ways to find and analyze pieces of information that could spotlight potential terrorist activity. The Federal Government has so far provided limited guidance to law enforcement agencies on how to collect, analyze, and disseminate data that could be used for counterterrorism and counterinsurgency purposes (Strom, Hollywood, Pope, Weintraub, Daye, & Gemeinhardt, 2011). In Nigeria today, the ability to identify, report, and analyze information that is potentially terrorist-related is a big challenge to the security forces. Proper data collection and analysis can help to determine suspected criminal behaviors and led to (or could have led to) their discovery and prevention (Strom et al., 2011). In U. S, information has been used to prevent terrorist plots. More than 80% of foiled terrorist plots were discovered via initial clues provided from law enforcement or the general public (Strom et al., 2011). In most parts of the world, organized crime destabilizes government activities, undermines institutions and greatly affects how the regional powers interact on trade, and economic matters. Yet, we seem to have few answers to it and repeat mistakes learned in battles past (Dudley & Mcdermott, 2020). By ―control‖ we understand the prevention of human rights violations, such as systematic attacks, killings, rape, and torture. The second indicator, i.e. the implementation of measures for the protection of civilians, assesses whether the mission‘s activities, such as patrols, cordon-and-search operations etc. have been successful in significantly reducing attacks on the civilian population (Lamp & Trif, 2009). However, the security forces have not been able to effectively stop these attacks, which may be as a result of getting appropriate information that can aid their control strategies. Lamp and Trif
- 3. 3 (2009) further assess that, any armed elements deliberately targeting civilians is term a terrorist group. According to Unal (2016) violence is the term of trade for insurgent groups seeking a negotiated settlement in a conflict. Thus, analyzing the character and form of violence and understanding its purpose are crucial matters both for understanding the conflict and for developing effective Counter measures. If noncombatant civilians are deliberately threatened or targeted as part of an indirect challenge to convey the perpetrators‘ message, then it is considered terrorism. Obi (2015) also define terrorism as a premeditated use of threat or violence by subnational groups to obtain a political or self-interest objectives through intimidation of people, attacking of states, territories either by bombing, hijackings, and suicide attacks, among others. It implies a premeditated, political motivated violence perpetrated against non-combatant targets by subnational groups or clandestine agents. If military and security personnel are the only targets of political violence, then it can be considered as an insurgency (Unal, 2016; Lamp and Trif 2009). Effective counterinsurgency operations require good intelligence. Absent of intelligence, not only might made the insurgents escape unharmed and continue their violent actions, but collateral damage caused to the general population from poor targeting may generate adverse response against the government and create popular support for the insurgents, which may result in higher recruitment to the insurgency. Counter-terrorism consists of actions or strategies aimed at preventing terrorism from escalating, controlling the damage from terrorist attacks that do occur, and ultimately seeking to eradicate terrorism in a given context. Counter-terrorism can be classified according to four theoretical models: Defensive, Reconciliatory, Criminal- Justice, and War (Unal, 2016). The UN Global Counter-Terrorism Strategy in the form of a resolution and an annexed Plan of Action (A/RES/60/288) is composed of 4 pillars, namely: Addressing the conditions conducive to the spread of terrorism; Measures to prevent and combat terrorism; Measures to build states‘ capacity to prevent and combat terrorism and to strengthen the role of the United Nations system in that regard; Measures to ensure respect for human rights for all and the rule of law as the fundamental basis for the fight against terrorism. The strategy does not only send a clear message that terrorism is unacceptable in all its forms and manifestations but it also resolves to take practical steps, individually and collectively, to prevent and combat terrorism. Those practical steps include a wide array of measures ranging from
- 4. 4 strengthening state capacity to counter terrorist threats to better coordinating UN System‘s counter- terrorism activities (United Nation, 2022). In today‘s technological world, the used of drone and other technological devices have improved and make it easier for collection, processing, assessing surveillance and intelligence tips. A drone is an unmanned aircraft. Drones have continued to be a mainstay in the military as part of the military Internet of things (IoT), playing the following roles: intelligence, aerial surveillance, force protection, search and rescue, artillery spotting, target following and acquisition, battle damage assessment, reconnaissance, weaponry, etc (Lutkevich and Earls, 2021). In Cambodia today, Rats are used as new explosive-detection techniques, for example, Magawa was a Tanzanian-born African giant pouched rat. With careful training, he and his rat colleagues learned to identify land mines and alert their human handlers, so the mines can be safely removed. In four years he helped to clear more than 2.4 million square feet of land. In the process, he found 71 land mines and 38 items of unexploded ordnance. (Kennedy and Wamsley, 2022). Anyone following the news surely realizes that there remain lives to save and battles to win, and improving intelligence is a crucial part of that picture (Kaplan, 2012). Thus, while intelligence is a key component in any conflict situation, it is critical in counterinsurgency (COIN) operations. The problem of the state is how to divide limited COIN resources between gathering information about the insurgents and accumulating firepower that can effectively engage them (Kress and Mackay, 2013). As Calvin (2009) noted, counterinsurgency is an intelligence war. Intelligence in counterinsurgency is about people. Modeling warfare is not trivial; it is complex in terms of its variety of factors such as landscape (Kim, Moon, Park and Shin, 2017), composition of troops, weapons, logistics, communication systems, and sensors, as well as soft factors such as training, tactics, leadership, situational awareness, and coordination (Kress, 2012). However, as the problem becomes more complex, it becomes intractable to solve analytically; thus, it requires heavy numerical computations (Kim et al, 2017). System Dynamics (SD) is arguably the most popular technique of insurgency modeling (Kott and Skarin, 2016). According to Kress (2012) SD models are used for analyzing threat situations, military operations, and force structures.
- 5. 5 Effective intelligence analysis and collection are crucial for timely detection and interception of insurgency plots. Extensive research has been conducted on insecurity over the years especially on Military personnel deployment, Military resources allocation, defense budgeting, strategic intelligence but little or no attention has been given to operational intelligence at the operational environment or battle field. Where non- state actors find it easy to overran military bases and carter away arms and ammunition, and killing military personnel (Sahara reporters, 2018) burning everything on sight. On April 25th , 2021 the insurgents‘ attacked 156 Task Force Battalion in Mainok, the insurgents entered the facility undetected and unchallenged (Premium times, 2021). Poor intelligence report which made the security forces failed effectively to stop these attacks not only because of their often insufficient presence on the ground, but also because the troops more often seem lack clear information (intelligence report) on the attack. Adequate Operational intelligence at the operational environment is key for a successful counterinsurgency. SD models can improve the efficiency of intelligence collection. Kilcullen (2010) argued that Cartesian or reductionist quantitative analysis to model insurgencies may not be the best approach, and instead complexity theory and systems theory approaches may be more practical. Although some model such as that of Anderson (2011), Lofdahl (2012), and Clancy (2016) have proven to be effective as compared to other System dynamics models; however, in assessing insecurity these models have their own draw backs. Anderson model did not consider collateral damage which sometimes leads to radicalization. Lofdahl model stated that collateral damage can be reduce through information operations (word of mouth, tv, and radio campaign), but collateral damage can only be reduced through improve/better intelligence. Clancy model did not consider the role of intelligence in COIN operations, and intelligence plays a vital role in every successful COIN operation. The security forces have lost the trust and respect of the people. This is due to unprofessionalism and brutality of the security operatives thereby alienating the people who should be eyes and ears for security intelligence (Nextier, 2021). Achieving peace in Nigeria is therefore fundamental for economic development regardless of whether governments pursue this as a policy or to solve inequality issues. Indeed, a common argument focuses on the need for greater peace. The need for more approach to assess counter terrorism and insurgency in Nigeria cannot be over emphasized. Therefore, this study use system dynamics to analyze problem such as these.
- 6. 6 1.1 What is System Dynamics System dynamics is a computer based mathematical modeling approach for strategy development and better decision making in complex systems. SD deals with dynamic, non- linear, closed boundary systems and is concerned with building quantitative and qualitative models of complex problem situations and then experimenting with and studying the behavior of these models over time (Azar, 2012). System dynamics has also a holistic and causality driven approach to describe and understand the relations between components or variables within a system which influences it internally or externally. System dynamics quantifies relations between variables to develop a view of behavior of the system over time through computer simulations. We need holistic approaches to tackle the problems we encounter in this complex and developing world. Missing the holistic view could lead us to struggle with the symptoms of a larger problem arising from the structure of the system (www.uib.no, 2022). The systems dynamics field provides a framework for modeling complex and dynamic systems (Azar, 2012). Zarghami, Gunawan, & Schultmann (2018) define System dynamics as an approach aims to capture the dynamic interactions within complex systems from a holistic perspective. Sapiri, Zulkepli, Ahmad, Abidin, and Hawari (2016) describe a system as a set of independent elements that are interconnected with each other and any changes of any element in the system will affect the set as a whole. The methodology focuses on the way one quantity can affect others through the flow of physical entities and information. Often such flows come back to the original quantity causing a feedback loop. The behaviour of the system is governed by these feedback loops. There are two important advantages of taking systems dynamics approach. The interrelationship of the different elements of the systems can be easily seen in terms of cause and effects. Thus the true cause of the behaviour can be identified. The other advantage is that it possible to investigate which parameters or structures need to be changed in order to improve behavior (Azar, 2012). SD provides a ways to develop, fit, filter, and organize metrics. Too often metrics are developed to acquire data that are unconnected to other relevant metrics. The SD methodology provides a well-developed way to create systems of causally connected metrics. Second, SD provides a working definition of complexity, a combination of nonlinear, feedback, and stock-flow (i.e., integration) causal relationships. Each of these confuses human cognition, and together they overwhelm it (Lofdahl 2012). According to Future health care network (2005) System dynamics is a way of thinking about the future which focuses on ‗stocks‘ and ‗flows‘
- 7. 7 within processes and the relationships between them. It can facilitate ideas for both specific solutions and generic ‗new world‘ rules. It is a risk-free way of refining plans before implementation, and of testing ideas using computer simulation. It is currently being used in ways of achieving win–win solutions, make assumptions more explicit, and identify inconsistencies between data, process and policy. SD naturally synthesizes information, represents complex causal connections, and calculates their behavior over time (Lofdahl, 2012). According to Onggo (2021), An SD model can be used as both a qualitative and a quantitative tool. As a qualitative tool, a SD model is used to capture the causality and feedback loops of a system that is being studied. On causality, we say that P causes Q when, other things being equal (also known as ceteris paribus), a change in P causes Q to change. The change can move in the same direction (for example, both P and Q increase) or in different directions (for example P increases and Q decreases). In a complex system, it is common to find many interacting feedback loops. In this situation, we need to use SD as a quantitative tool so that we can simulate the dynamic behaviour of the system. To do this, we need to collect data to quantify how a component affects another component in the system. To use SD as a quantitative tool, we can view a system as a collection of stocks and flow. Hidden beneath the stock-and-flow diagram is a set of differential equations that will need to be solved numerically to produce the simulation result. 1.2 Building Blocks of System Dynamics Developing an appropriate mental map of cause and effect is a fundamental step in understanding the dynamics of a system (Azar, 2012). This section presents the building blocks of SD, which provide a basis for developing SD modelling approach. 1.2.1 Stock Figure 1, Classification of system variables: stock and flow diagram. Source: www.uib.no
- 8. 8 A stock is a key element of any system, which can be measured at any given time. It accumulates the materials and information over time and represents the state of the system (Sterman, 2000). 1.2.2 Flow Stock changes over time through the action of flow. Flow variables regulate the state of stock variables. Flow is labelled as either inflow or outflow. Accumulating differences between all inflows and outflows indicates whether the stock is held in dynamic equilibrium or not. In the SD models, a flow is represented by a pipe with arrow and valve. There are two basic components of the structure of a system. They are rates and levels. Levels are state variables that represent the accumulation of resources in the system. They denote the state of the system at specific points in time. For example, population and level of liquid in a tank are state or level variables. Rate variables represent the change of a variable per unit time. For example, births, deaths and fluid flow rate are rate variables. Rate variables effect changes in the level variables (Azar 2012). Azar (2012) developed a Mathematically equations for the stock element as follows: Stock(t )=∫ Inflow(s ) - Outflow(s )]ds + Stock ( ) ……… (1) Thus, the value of stock at time t is the sum of the value of stock at time to and the integral of difference between inflow and outflow rates from t0 to t. In other words, it can be stated that the rate of change in stock at any point in time is equal to the difference between inflow and outflow at that point. Or according to Sterman (2000) where Inflow(s) represents the value of the inflow at any time s between the initial time to and the current time t. equivalently, the net rate of change of any stock, its derivative, is the inflow less the outflow, defining the differential equation = Inflow (t) – Outflow (t) = Net change in stock (t) ……… (2) In general, the flows will be functions of the stock and other state variables and parameters.
- 9. 9 The number of level variables in a feedback loop determines the order of the differential equations describing the feedback loop, i.e. if there are n level variables in a feedback loop then the mathematical model for that feedback loop would be an nth order differential equation. The quantitative effects can be easily discovered using a structural diagram termed as a stock flow diagram. The stocks and flows explicitly appear in the model equations as they are the basic building blocks in a system dynamics model (Sapiri et al, 2016). 1.2.3 Feedback Feedback is the way that a system runs itself. Feedback loop is a mechanism that creates a persistent behaviour of a system over a long period of time (Zarghami et al, 2018). In complex systems nothing is stand alone, everything is connected to everything else. They interact with each other through feedbacks. Consider a system of two elements that affect each other. The change in one element will affect the other. This effect will act as a cause and will in turn affect the first element; this is a simple example of feedback. There are two basic types of feedback loops – positive (self-reinforcing) loops (Azar, 2012) which reinforce the original change (Zarghami et al, 2018), and negative (balancing) loops (Azar, 2012), which oppose the original change (Zarghami et al, 2018). As the name suggests, positive loops reinforces the effect to grow exponentially and negative loop approaches the equilibrium state by continuously reducing the gap between current state of the system and the equilibrium state (Azar, 2012). 1.2.4 Causal-loop Diagrams This is an important tool for displaying the cause-and-effect interactions among key variables when developing the model of a dynamic system. The first step when developing a causal diagram is to identify the key variables that describe the problem. Causal-loop diagrams consist of two or more causal links that connect the various elements in the model. Each link is assigned a polarity to indicate the direction of change of the affected element with respect to the causing element (Azar, 2012). The direction of the arrow indicates the direction of causation for a pair of variables. The variable at the head of the arrow is the dependent variable; the variable at the tail is the independent variable for the given pair of variables (Lofdahl 2012). According to Lofdahl (2012), the insurgencies that modern military forces seek to counter can be thought of as a complex social system. Complex social system requires developing metrics that
- 10. 10 are tracked over time to help provide that long-term perspective and measure progress against key objectives. While much experimentation has been undertaken to address military and COIN complexity with computation, successfully applying the resulting intuitions and insights in an actual operational theatre remains an open problem. System dynamics provides a set of thinking skills and a set of modeling tools, as described below (Future health care network, 2005). Thinking skills: A wide range of thinking skills and abilities are required to understand complex adaptive organizations. These include: i. dynamic thinking – conceptualizing how organizations behave over time and how we would like them to behave ii. ‗system-as-cause‘ thinking – determining plausible explanations for the behavior of the organization over time in terms of past actions iii. ‗forest‘ thinking – seeing the ‗big picture‘ and transcending organizational boundaries iv. operational thinking – analyzing the contribution which different operational factors make to overall behavior v. ‗closed-loop‘ thinking – analyzing ‗feedback loops‘, including the way that results can influence causes vi. quantitative thinking – determining the mathematical relationships needed to model cause and effect vii. scientific thinking – using models to construct and test hypotheses. 2.11.2.5 Modelling tools The key elements of system dynamics are Stocks and flows. Recognizing the difference between stocks and flows is fundamental to understanding systems and modeling it. Steps of the Modelling Process Sterman (2000) stated that Modeling is a feedback process, not a linear sequence of steps, modeling process is an iterative cycle. According to Zarghami et al, 2018 SD modeling processes include: i Problem Articulation Problem articulation shapes the entire modeling. This is the most important step in modeling process. In this phase, the problem is identified, defined and clearly stated. Base on;
- 11. 11 Theme selection: What is the problem? Why is it a problem? Key variables: What are the key variables and concepts we must consider? Time horizon: How far in the future should we consider? How far back in the past lie the roots of the problem? Dynamic problem definition (reference modes): What is the historical behavior of the key concepts and variables? What might their behavior be in the future? (Sterman, 2000) ii Dynamic Hypothesis. Preliminary sketch of the main interactions and feedback loops represents the dynamic hypothesis. The hypothesis is called dynamic because it must characterize the problem in terms of the underlying feedback and stock and flows structures of the system and it must manifest itself over time (Azar, 2012). Dynamics diagrams such as casual loop diagram and stock and flows diagram are formulated (Zarghami et al, 2018). Iii Formulation Zarghami et al (2018) stated that in the formulation step, the dynamic hypothesis is transformed into the detail diagram of feedback processes; subsequently, the algebraic equations are established for the model. A set of mathematical equations are determined. Iv Model Testing The validity of results in a system dynamics model is strongly dependent on the validity of the model. Model testing mainly (not necessarily) takes place after the initial model formulation and before the policy analysis step, In the model testing and validation phase, the model is compared with the real world and the decision to accept or reject the model is made in this step. Part of testing, of course, is comparing the simulated behavior of the model to the actual behavior of the system. v Policy Formulation and Evaluation The purpose of policy analysis is to investigate how specific change in a parameter in a system dynamics model affects the system‘s response. Policy analysis enables the system modellers to identify the policy that will have the desired impact on the model.
- 12. 12 2.0 Methodology 2.1 Method of Data Collection This study used secondary data obtained from the defence headquarters Nigeria (https://defence.gov.ng), global terrorism database (http://www.start.umd.edu/gtd/), Nigeria security traker (https://www.cfr.org/nigeria/nigeria-security-tracker/p29483), statista (https://www.statista.com/topics/7396/terrorism-in-nigeria/), sahara reporters, vanguard, daily trust, and North East Development Commission. 2.2 Method of Data Analysis Data for this study was analyzed using system dynamic model adopted from Anderson (2011), Lofdahl (2012), Kress & Szechtman (2008) and Clancy (2016) modernized. The construction of a system dynamic model requires two basic ingredients, namely Stocks and Flows diagram, and Casual loop diagrams based on feedback mechanism analysis. Components of a system build feedback loops and the relationship between these feedback loops creates structures, which form the behavior in a system. Feedback loops are chains of cause and effect relations. SD uses feedback to understand complexity. Therefore, identifying the feedback loops is crucial in SD methodology. 2.3 Problem Articulation/Conceptualization In this study we have three actors: The government forces (state actors), the insurgents (non state actors) (NSA) and the general population (civilian). The time horizon for these study is 2009 to 2022. First, both the State actors and non state actors set a goals, the goals motivate their decisions. That decision change the system (operation environment), that create new information which change their next decision. All their decisions are going to manifest side effects on the system (operation environment and the general population) as shown in fig. 2
- 13. 13 Fig. 2 State actors and Non state actors cause and effect loop 2.4 Dynamic hypothesis Here we characterize the problem in terms of the underlying feedback, stock and flows structures of the system as it manifest over time. System dynamics describe systems in terms of state variables (stocks) and their rate of change with respect to time (flows). If a component increases or decreases due its causal variable, it is important to know by how much it changed and at which rate it did. Stocks and flows are the concepts that account for such quantities. Adopting Lofdahl (2012) insurgent subtraction model and modernizing we obtain: State actors Goals State Actors Decisions State of the system Side Effects Non State actors Action Non State Actors Goals Side effects of Non state actors action Radicalization rate Civilian population Death rate State Actors action Collateral damage COIN INTEL Active non state actors Non state actors eliminated/loosed Elimination rate Radicalization Death Non state actors induced death rate
- 14. 14 Fig. 3, Non State Actors Recruitment Stock and flow diagram Figure 3 shows the non- state actors model which consists of eight variables. Starting at the beginning, state actors action, which results in elimination ―neutralization‖ or ―arrest‖ of ―Insurgents‖ Non state actors. This reduces the number of non- state actors. However there is a secondary consequence to state-actors action, ―collateral damage.‖ The application of military force can result in civilian population getting hurt. When state actors action events occur, collateral damage- whether real or imagined -can be exploited through INTEL. But they can achieve ―radicalization‖ of a certain percentage of the ―civilian Population resentment,‖ who in turn becomes non state actors. Non state actors attack and state actors action are directly propositional. Active Non State actors is the stock, inflow is the new recruits and/or due to civilian population resentment. Outflow is the decrease in the number of active non state actors either arrested or neutralized (Elimination). Each of these variables has values that can be measured and displayed. Finally, the variables are causally connected, which allows for the system‘s direct, indirect, and cascading consequences to be analyzed. A causal loop diagram consists of variables connected by arrows denoting the causal influences among the variables. Therefore, identifying the feedback loops is crucial in system dynamics methodology. Non state actors: increase in the number of non state actors leads to the increase in non state actors attacks. The growing number of attacks inturn leads to an increase in civilian population weariness. Which also prompt more state actors actions, and decrease the number of non state actors as showed in figure 4. Figure 4 shows a negative link pointing from state actors action to Non state actors which means that the dependent variable NSA is negatively changing
- 15. 15 corresponding to the independent variable state actors action. Fig. 4 Non state actors captured territory loop At this stage, the non- state actors use clandestine terrorism to target the population or the government. This increases a perception of instability within the targeted civilian- population that weakens the legitimacy of government perceived as being unable to control the violence. Simultaneously, the state actor desire to credibly govern the targeted non state actors often declines in response to the violence and other military actions. The non- state actors actions performed within the general uprising and resistance begin to focus on recruiting into organized formal groups. These groups begin to exert a shadow-influence on the civilian population gaining support from some and intimidating others. Criminal/looting activities gain finances which fund further military actions. The non -state actors actions in this model not only terrify or intimidate civilian populations, but also seizes territory. Non-state actor uses methods of irregular warfare to capture territory to influence populations (―coercive power‖), which it then attempts to govern in furtherance of its objective to become a functioning state (―legitimate power‖). State actors are designed to seize territory. The loops complete into a positive feedback loop of exponential growth. More combatants mean more military actions, which means more territory and access to controlled populations, which can begin to be governed, fueling finances, which fund more combatants and more attacks. State Actors action Territory Cattle roostling/Looting Finances External donor Non State Actors Action Aerial Surveillance COIN Cordon & Search Operations COIN INTEL gathering Fear of Retribution Security of Populance + + + + + + + + + - - - INTEL LOOP LAW & ORDER LOOP FINANCE LOOP - - Population Control by coercive power + + security loop
- 16. 16 Fig 5 Developed COIN operations loop State actors (COIN) operations place more emphasis on military operations, intelligence gathering and protection of the population, which is achieved through; aerial surveillance, cordon and search operation, patrol and mounting of check points, and other source of INTEL. This determines the rate of detection and elimination of the Non state actors. As shown in figure 5. Formulation System dynamics model can be express as a system of differential equations. Based on the mathematical definition of the integral, we can conclude that an amount of quantity inside of stock is the integration of total flows on the stock. Basic stock and flow diagram can be mathematically represented as: S = INTEGRAL(Net inflow, S(0)) …… (3) Stock(t) = ∫ Inflow(s) – outflow(s)]ds + stock(to) …… (4) where, to is the initial time and t is the current time Civilian population Active non state actors Recruitment rate Non state actors eliminated Non state actors elimination rate - Radicalization rate + Effective fire power + + State actors operation intensity Attacked rate NSA attacked State actors attrition rate Total number of state actors + + + + Collateral damage - - LEVEL OF INTEL State actors unaimed fire + - INTEL gathering operations + - Hit intensity + - + - INTEL LOOP NSA OPERATION LOOP Recruitment loop + Insider thread Risk Vulnerability + - +
- 17. 17 Net change in stock (t) = = Inflow (t) – Outflow (t) Using equation (2) we can estimate number of NSA at time t as NSA(t) = ∫ Radicalization(t) – NSA eliminated (t)]dt + NSA(to) Where, NSA eliminated = NSA eliminated rate Net inflow = f(S) Often the inflow is proportional to the size of the stock. The stock grows at a fractional increase rate g, which may be constant or variable: Net inflow = gS The introduction of reinforcing feedback change the relationship to = gS To solve the equation = gS, first we separate variables to obtain = g integrating both side ∫ = ∫ we obtain Ln(S) = gt + c where c is a constant. Taking the exponentials of both side give S = exp(gt). where c*is exp(c). The value of S at the initial time, when exp(gt) = 1,is by definition S(O), so c*must equal S(0). S(0) is the initial value of S at time t=0. Therefore, the state of the system is S(t) = S(0)exp(gt) ………….. (5) Model on Counterinsurgency operations
- 18. 18 We adopted and modernized Kress & Szechtman (2009), and Kaplan, Kress & Szechtman (2009) model. = -αI = - {µ(t)+[1-µ(t)][ ]} ….. (6) where I(t) is the number of NSA at time t, G(t) is the number of state actors troops, is the state actors attrition coefficient, µ(t) is the level of intelligence (which increases with time), and P is the population size, α(t) is the Non state actors attrition coefficient. State actors operating intensity = ƔG. ……. (7) Where a fraction ƔG(µ+(1-µ)I/P of this intensity hit the non- state actors and a fraction ƔG(1- µ)(1-I/P) hit the civilian population causing collateral damage. The collateral damage generate recruits at a rate ΠƔG(1-µ)(1-I/P). Effective fire power = ….. (8) Collateral damage = ……. (9) Where effectiveness ratio, = 0.5 the attrition rate of the non -state actors is twice the attrition rate of the state actors (Kaplan & kress, 2009). Rate = ( ) - 1 ……. (10) Considering 2009 to 2022. N = 14 3.0 Result and Discussion 3.1 Data Analysis In this study, the data was analyzed using VENSIM system dynamic model software. The discussions were mainly to evaluate the results obtain from the secondary data and interprets the simulated COIN intelligence operations casual loop.
- 19. 19 Figure 6 showed the number of non-state actors attacked. The figure also showed the attacks carried out by the non-state actors from 2009 to 2022. The figure showed 2015 recorded the highest number of attacked and 2009 the lowest. The figure showed clearly the nonlinear dynamic behavior of non -state actors. Figure 6 Actual number of non- state actors attacked Considering 2009 as the base year. Using equation 10 and value in figure 6 we compute non state actors attacked rate as Rate of attacked = ( ) - 1 = ( ) - 1 = 0.19721 Figure 7 showed the non-state actors eliminated (arrested and neutralized). The figure 7 showed 2014 was the year they suffered the worst loosed and 2011 where the suffered they least (477). Using fig 7 and equation 10 we compute non state actors elimination rate as: 0 50 100 150 200 250 300 350 400 NUMBER OF NON STATE ACTORS ATTACKED YEAR ACTUAL NUMBER OF NON STATE ACTORS ATTACKED NON STATE ACTORS ATTACKED
- 20. 20 Rate of elimination = ( ) - 1 = ( ) - 1 = 0.01265 Figure 7 Actual numbers of non- state actors eliminated. 3.2 Model Testing At this stage we simulate the model and test the dynamic hypothesis. In figure 8, Active Non State actors is the stock, inflow is the new recruits and/or due to civilian population radicalization and intimidation. Outflow is the decrease in the number of active non state actors either arrested or neutralized (NSA eliminated). When simulated we obtained the graph in figure 4. The model shows that civilian combatants whether local or foreign join the non-state actors either through intimidation or radicalization. Figure 8 showed that State actors operate with intensity ƔG, where a fraction of this intensity hit the non- state actors (causing elimination) and a fraction hit the civilian population causing collateral damage. The collateral damage generates recruits into the non- state actors (radicalization). INTEL gathering operations (is not 0 1000 2000 3000 4000 5000 6000 7000 8000 NUMBER OF NON STATE ACTORS ELIMINATED YEAR REAL NUMBER OF NON STATE ACTORS ELIMINATED ELIMINATED
- 21. 21 cordon and search, and aerial surveillance only but includes HUMINT, COMINT, GEOINT, OSINT, etc) increases the level of INTEL or lead to improve INTEL, this implies reduction in state actors area fire (unaimed fire), reduction in collateral damage, reduction in radicalization (recruitment), reduction in attacks, and increase in hit intensity. Figure 8 Developed COIN intelligence loop Substituting attack rate, elimination rate, radicalization rate in figure 8 and simulating we obtained figure 9. Figure 9 provide a level of intelligence dynamics scenario during COIN operations that demonstrates several simulation features first, the even took place over a period of time (2009 – 2022). Graphs showed the level of INTEL (µ) over those 14 years, as it increases over time. Improving from 0 to 1 as a result of effective operational INTEL gathering operations, hence increase in effective aimed fire power and hit intensity thereby minimizing collateral damage or zero collateral damage and gaining more support from the population. Reducing collateral damage also provides a way to reduce radicalization and avert casualties. According to Kaplan, Kress & Szechtman (2009), as level of INTEL increases and operational INTEL improves, the state actors are able to engage more of the non- state actors. Once level of INTEL reaches 0.5 all non -state actors‘ strongholds are attacked as showed in figure 9. The delay on the INTEL gathering operations causal link mean the process of digesting INTEL information gathered, developing policies, and disseminating them to the troops. Civilian population Active non state actors Recruitment rate Non state actors eliminated Non state actors elimination rate - Radicalization rate + Effective fire power + + State actors operation intensity Attacked rate NSA attacked State actors attrition rate Total number of state actors + + + + Collateral damage - - LEVEL OF INTEL State actors unaimed fire + - INTEL gathering operations + - Hit intensity + - + - INTEL LOOP NSA OPERAT ION LOOP Recruitment loop + Insider thread Risk Vulnerability + - +
- 22. 22 Figure 9 Graph of intelligence level Figure 10, the simulated result shows that at zero level of intelligence (no action was taken) non state actors will keep growing exponentially. Active Non -state actors population is directly proportional to the number of attacked, simply put more active non state actors more attacked. Active non state actors activities not only terrifies or intimidate civilian population, but also seizes territory. The only way to reduce their ability to recruit local or foreign combatants is by acting on improve operational intelligence timely, and reducing collateral damage. The simulated result showed a clear effect of intelligence in counterinsurgency and counterterrorism operations. The active non state actors‘ population dives down from 2014 to 2022. Meaning that with improve intelligence at this period all their location is known, the state actors have block all their logistic route and source of funding. Either the non-state actors, realized it cannot grow, settles with the government and the insurgency situation ends, or keep fighting still they are no more, resulting in less violence.
- 23. 23 Figure 10 Graph of active non state actors as INTEL increases from 0-1 2.1 Conclusion System dynamics model has been successfully applied in analyzing insecurity problems in northeast Nigeria to demonstrate the importance of operational intelligence in counterinsurgency and counterterrorism operations, and the vital role intelligence gathering and application played in minimizing collateral damage and restricting non state actors from recruiting more members and increasing their attacked. We also conclude that the government cannot completely eradicate the insurgency by force alone; they also need soft action, program to address the humanitarian needs of the people. The government can also gather significant accurate intelligence from the non- state actors arrested or surrendered. It can reduce the insurgency to a small manageable size. The choice of system dynamics model was because of its nature in handle dynamics complex real life problems. In conclusion, with improve intelligence µ=1, collateral damage can be eliminated. Once the level of intelligence reaches 0.5 all the non- state actors stronghold is known and attacked. Countering insurgency requires a holistic approach and total collaboration within all the military and para military agencies. It also requires fighting them on all levels. They war cannot be won just on the battle field; their source of funding and all other logistics must be block. This study showed that real time monitoring is a crucial aspect of security INTEL gathering for today‘s technological world. REFERENCES
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- 27. 27 Https://www.uib.no/en/rg/dynamics/39282/what-system-dynamics Appendix (01) Active non state actors= INTEG ( Recruitment rate-Non state actors eliminated, 2000) Units: People/period (02) Attacked rate= 0.19721 Units: fraction (03) Civilian population= 3.05419e+07 Units: People/period Total population of Adamawa, Bauchi, Borno, Gombe, Taraba and Yobe as at 2009 (04) Collateral damage= State actors operation intensity*State actors unaimed fire*(1-Effective fire power ) Units: People (05) Effective fire power= Active non state actors/Civilian population Units: Dmnl (06) FINAL TIME = 2022 Units: Year The final time for the simulation. (07) Hit intensity= -State actors operation intensity*(1-Collateral damage/State actors operation intensity )*Effective fire power Units: Dmnl (08) INITIAL TIME = 2009 Units: Year The initial time for the simulation. (09) Insider threat= Risk/Vulnerability Units: Dmnl Risk= Thread*Vulnerability
- 28. 28 (10) INTEL gathering operations= NSA attacked/State actors operation intensity*Insider threat*0.1 Units: fraction These include cordon and search, aerial surveillance, HUMINT, COMINT, GEOINT, OSINT, etc. (11) LEVEL OF INTEL= INTEG ( INTEL gathering operations, 0.1) Units: fraction Once level of INTEL reaches 0.5 all non -state actors‘ strongholds are attacked. (12) Non state actors eliminated= Active non state actors*Non state actors elimination rate Units: People/period (13) Non state actors elimination rate= 0.01265 Units: fraction (14) NSA attacked= Active non state actors*Attacked rate Units: Action/ period (15) Radicalization rate= 0.0001 Units: Dmnl Clancy (2016) (16) Recruitment rate= Hit intensity+Radicalization rate Units: fraction The fraction of state actors intensity that hits the non state actors (17) Risk= 0.5*0.7*0.3 Units: Dmnl There is 50/50 chance( i.e we dont know) that the NSA have an informat and will like to attack. There is a 70% chance that the will use the information. There is a 30% chance of success (Moteff, 2005). (18) SAVEPER =
- 29. 29 TIME STEP Units: Year [0,?] The frequency with which output is stored. (19) State actors attrition rate= 0.03 Units: fraction (20) State actors operation intensity= State actors attrition rate*Total number of state actors Units: Dmnl (21) State actors unaimed fire= 1-LEVEL OF INTEL Units: **undefined** (22) TIME STEP = 1 Units: Year [0,?] The time step for the simulation. (23) Total number of state actors= 13500 Units: People (24) Vulnerability= 0.15 Units: Dmnl We adopted 15% vulnerability rate, from the raking. i.e 50% very high, 25% high, 15% medium, and 10% low.