## Mathematical Modeling of Intra-Communal Violence and Risk-Level Analysis. Case Study: Obiaruku Community in Delta State, Nigeria

Published: 2024-03-15

Page: 44-66

Ossaiugbo Ifeanyi Marcus *

Department of Mathematics, Delta State University, Abraka, Nigeria.

Okposo Newton Ighomaro

Department of Mathematics, Delta State University, Abraka, Nigeria.

Apanapudor Joshua Sarduana

Department of Mathematics, Delta State University, Abraka, Nigeria.

*Author to whom correspondence should be addressed.

### Abstract

This paper aims to capture the dynamics of intra-communal violence in a deterministic model of ordinary differential equations, accordingly, the Authors found some interesting results. Lack of quality education, insecurity, bad roads, drugs and alcoholism, unequal representation in government and religious decay have been identified as key factors supporting intra-communal violence over the years. In this research work we built all these factors into a deterministic model describing intra-communal violence and performed some basic mathematical analysis such as positivity of solutions, existence of invariant region, violence-free equilibrium, violence-persistent equilibrium, basic reproduction number, sensitivity analysis, stability analysis and bifurcation analysis. It was revealed that the violence-free equilibrium is globally asymptotically stable. The model exhibits a forward bifurcation. The sensitivity analysis revealed that injustice and insecurity are highly sensitive parameters of the basic reproduction number. We also designed a questionnaire to ascertain the violence risk level of Obiaruku community in Delta State, Nigeria and the analysis revealed that the community is at the medium high risk level and thus violence may occur in most cases in the community. The results of the stability analysis and the sensitivity analysis showed that under certain conditions, a community can be brought to the maximum low risk level and the maximum high peace level.

Keywords: Modeling, violence, risk-level, stability, and sensitivity

#### How to Cite

Marcus, O. I., Ighomaro , O. N., & Sarduana, A. J. (2024). Mathematical Modeling of Intra-Communal Violence and Risk-Level Analysis. Case Study: Obiaruku Community in Delta State, Nigeria. Asian Journal of Probability and Statistics, 26(3), 44–66. https://doi.org/10.9734/ajpas/2024/v26i3599

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