Application of Differential Equations to Population Growth Modelling in Sokoto State

Population growth dynamics in Sokoto State, North West Nigeria, one of the most densely populated states relative to arable land in the country, have profound implications for resource planning, food security, and social service delivery. This study applies the Malthusian exponential growth model, the logistic growth model, and the modified logistic model with harvesting to analyse and project the population trajectory of Sokoto State using census data from 2006 and 2023 supplemented by National Population Commission demographic estimates. Differential equation parameters are estimated using the method of exact solutions combined with least squares calibration against available data points. The exponential model predicts a state population of 8.7 million by 2035, while the logistic model, incorporating an estimated carrying capacity derived from agricultural land and water resource constraints, projects 7.9 million with decelerating growth after 2030. Sensitivity analysis examines how a 10 percent reduction in fertility rate, consistent with the National Population Policy target, alters the 2035 projection. The harvesting model explores the demographic impact of emigration flows to Abuja and Kano, estimated at 45,000 persons annually from available migration surveys. The study recommends integrating population projection outputs into the Sokoto State 10-year Development Plan for infrastructure sizing decisions. Keywords: differential equations, population modelling, Sokoto State, logistic growth, demographic projection.