Differential Equation Modelling of Cholera Outbreak Dynamics in Borno State

Cholera outbreaks in Borno State, North East Nigeria, have been intensified by the protracted humanitarian crisis displacing millions of residents into overcrowded camps with inadequate water and sanitation infrastructure. This study formulates and analyses a system of ordinary differential equations using the Susceptible-Infected-Recovered-Water compartmental model to simulate cholera transmission dynamics in selected internally displaced persons camps around Maiduguri. Parameter values including transmission rate, recovery rate, and bacterial decay rate in water sources are estimated from outbreak surveillance data provided by the Borno State Ministry of Health and the World Health Organization for the 2021 to 2023 period. The basic reproduction number is derived analytically and computed as 3.17, confirming active endemic transmission. Equilibrium analysis identifies a disease-free equilibrium and an endemic equilibrium, with stability analysis demonstrating that the endemic state is locally asymptotically stable when R-naught exceeds unity. Numerical simulations using the fourth-order Runge-Kutta method explore the impact of water chlorination and oral rehydration therapy deployment on infection trajectory. Results show that simultaneous intervention on both water contamination and treatment pathways reduces peak infection load by 67 percent within 90 days. The study provides a quantitative tool for outbreak response planning in North East Nigeria. Keywords: cholera modelling, SIR model, Borno State, basic reproduction number, humanitarian crisis.