A Mathematical Modeling Framework for Protest Dynamics, State Coercion, and Public Trust: Evidence from the 2024 #EndBadGovernance Protests in Nigeria

The 2024 #EndBadGovernance protests in Nigeria emerged amid severe economic hardship, rising food prices, currency depreciation, unemployment, and declining confidence in public institutions. This paper develops a nonlinear mathematical framework that links economic hardship, digital mobilization, protest intensity, state coercion, public trust, and political efficacy. A five-dimensional autonomous system of ordinary differential equations is formulated and calibrated using quantitative relationships reported in a cross-sectional survey of 2,540 respondents, state-level digital engagement indicators, a Difference-in-Differences analysis, and a Structural Equation Model. The model is shown to be mathematically well posed: solutions remain nonnegative and enter a bounded positively invariant region. A protest activation threshold, denoted by $R_p$, is derived. The protest-free equilibrium is locally asymptotically stable when $R_p < 1$ and unstable when $R_p > 1$, whereas a unique persistent-protest equilibrium exists for $R_p > 1$ and is locally asymptotically stable under the stated parameter conditions. Sensitivity indices show that economic hardship, digital amplification, and recruitment responsiveness increase protest persistence, while grievance resolution and effective non-coercive de-escalation reduce it. Model-based numerical scenarios reproduce the observed pattern in which digital engagement increases protest intensity, coercion accelerates the erosion of public trust, and excessive coercion weakens citizens' institutional political efficacy without removing the underlying economic grievance.