containment of banditry in Kaduna State. Building on the existing model, the model extends existing approaches

by incorporating additional compartments such as rehabilitation individuals, security agents and bandit sponsors

to better capture real-world dynamics of banditry and intervention mechanisms. A system of nonlinear ordinary

differential equations is formulated to describe the interactions among population groups and qualitative analyses

including existence and uniqueness of solutions, positivity, invariant region, and banditry-free equilibrium are

carried out to ensure the mathematical validity and stability of the model. The analysis reveals that the solutions

remain non-negative and bounded within a biological feasible region, confirming the consistency and stability

of the system. In addition, the findings show that integrated government policies involving effective security

enforcement, rehabilitation programs, rehabilitation programs, intelligence gathering, and disruption of sponsor

networks significantly reduce he growth and persistence of banditry. The study highlights the importance of

Banditry in Kaduna State has become a major security concern, particularly in rural and semi-urban areas where

armed groups are involved in kidnapping, cattle rustling, and violent attacks on communities. The crisis is

especially pronounced in local government areas such as Birnin Gwari, Igabi, Giwa, and Chikun, resulting in

loss of lives, displacement of residents, and disruption of farming and commercial activities. Studies attribute

the persistence of banditry in the state to underlying factors such as poverty, unemployment, weak governance,

and limited security presence, which create opportunities for criminal networks to flourish (Abdullahi, 2019;

International Crisis Group, 2020). Despite efforts by the government through military operations, dialogue, and

community-based strategies, the situation remains largely unresolved, highlighting the need for more effective

and sustainable interventions (Amao, 2020; Sale & Abubakar, 2025).

economic productivity. In response, the government has implemented measures such as military campaigns,

peace agreements, amnesty programs, and community policing initiatives, including operations like Hadarin

Daji. However, while these interventions have recorded short-term gains, they often fail to address underlying

causes, resulting in the persistence of banditry (International Crisis Group, 2020; Amao, 2020).

More recent strategies have shifted toward non-kinetic approaches, including dialogue, socio-economic reforms,

and arms control measures. Policies such as negotiations and amnesty programs have yielded mixed outcomes,

with temporary peace in some areas and renewed violence in others. This highlights the complex and dynamic

nature of banditry, necessitating more systematic and predictive approaches to policy evaluation. Mathematical

modelling has emerged as a useful tool in conflict and policy analysis, allowing researchers to simulate scenarios

and assess the potential impact of interventions (Abdullahi & Mukhtar, 2022; Accord, 2022). Despite this,

insurgent organization after the death of its leader, Mohammed Yusuf in 2009, engaging in bombings,

abductions, and attacks across states such as Borno, Yobe, and Adamawa (Tahir & Bernard, 2021; Rufa’I, 2021).

A notable incident was the 2014 Chibok schoolgirls kidnapping, which drew global attention to the region’s

insecurity (BBC News, 2014; Amnesty International, 2015). The emergence of Islamic State West Africa

Province further complicated the security landscape, intensifying violence despite a more strategic focus on

military targets (International Crisis Group, 2019; Zenn, 2020). Although government responses, including

collaboration through the Multinational Joint Task Force, have achieved some progress, persistent challenges

such as poverty, weak governance, and resource constraints continue to sustain the crisis (UNDP, 2017).

The mathematical model by Lawal et al. (2023) provides a useful framework for understanding banditry

dynamics through five key compartments and the inclusion of control strategies such as job creation and reducing

Bello & Mukhtar present a sociological analysis of kidnapping in Nigeria, linking it to terrorism, poverty, and

political instability, and highlighting its connection with insurgent groups such as Boko Haram and Niger Delta

militancy (Bello & Mukhtar, 2017). Similarly, Lawal et al. (2023) develop a mathematical framework that

conceptualizes banditry as a socio-economic problem driven by poverty, unemployment, weak governance, and

illegal mining, aligning with earlier findings (Abdullahi, 2019; Ogbonnaya, 2020). Complementing these

perspectives, Gabriel & Nwala provide a qualitative assessment of the broader implications of banditry on

national interest, particularly in Northwestern Nigeria (Gabriel & Nwala, 2024).

In this section, we outline the methodological development of the model were employed. The model developed

by Lawal et al. (2023) presented a modeling and optimal control analysis on armed banditry and internal security

the variable

signifies the Informant Population, the Bandit population indicates

and Removed

population refers to

The model was modified due to Lawal et al. (2023) by incorporate additional mitigation measures, including

individual who undergoing Rehabilitation, Security Agent and Bandit Sponsor.

Table 2.2: Parameters of the Model

The model diagram of the modified model is presented in figure 3.2

In this section, the mathematical model analysis of the model (2.1) were analyzed by using relevant theorems

and lemmas. This analysis involves various techniques and approaches used to examine and interpret the

behavior, characteristics and implications of mathematical or computational models of banditry dynamics. In

particular, the discussion focuses on establishing the existence and uniqueness of the solution of the model,

positivity of the solution of the model, the banditry-free equilibrium point, feasible region (invariant region) of

the model and banditry reproduction number of the model.

The existence and uniqueness of solutions of the model equation (3.2) are mathematical proved following the

theorem according to Abah et al. (2024).

Suppose that the function

Lipchitz condition in the region

a natural constant number

by equation (3.1) exists in the interval

are continuous and bounded in the region

.

(3.3)

Using the partial derivatives of the second equation of (3.2)

From the sixth equation of (3.2), take the partial derivatives

by the theorem 3.1. The functions given in by equation (2.1)

satisfy Lipchitz condition and hence, there exists a unique solution of model equation (2.1) in the region

The positivity of the solution of the model (2.1) ensure banditry dynamics realism. We are to show that every

path starting from the non-negative region

Consider that the initial conditions of (2.1) are nonnegative, then the solutions for the different groups

Then the solution set

Since we are considering only the negative terms of susceptible population

, then

Using separation of variable on (3.11), we have

Integrate both side of equation (3.12) to obtained

(3.13)

In a similar way, we can text the positivity of the remaining compartments of equation (2.1).

In Banditry modeling, steady states refer to situations where the number of people in each group remains constant

over time. This happens when the rates at which people move between groups are balanced. It means the number

of System (2.1), each equation on the right-hand

side of system (2.1) is set to zero. That is

The banditry free equilibrium of the model exists at the point