Abstract We develop and analyse a four-dimensional nonlinear ordinary differential equation model for normalised soil quality S, agricultural productivity A, food security F and soil-degradation pressure D, closed by the hypothesis that low food security raises production pressure and hence degradation. We prove positivity, boundedness and global existence on an explicit invariant region. The equilibrium problem is reduced to one strictly monotone scalar equation, which gives a sharp threshold: a unique positive equilibrium E* exists if and only if the productivity number R_A=(r_a+β+ξ)/θ exceeds one, and when R_A≤1 the productivity-free equilibrium is globally asymptotically stable. At E* we derive the Jacobian and characteristic polynomial, prove that all four coefficients are positive for every admissible parameter set, and conclude that E* can lose stability only through a Hopf bifurcation, with an explicit Routh–Hurwitz criterion. A centre-manifold calculation shows that the transcritical bifurcation at R_A=1 is forward. Numerical work, with hypothetical parameter values, gives eigenvalues and eigenvectors for four management scenarios, local and global sensitivity rankings, and a verified supercritical Hopf bifurcation in a stress-test parameter set. In the illustrative baseline, combining soil restoration with reduced degradation intensity raises equilibrium soil quality by about 110%, productivity by about 60% and food security by about 27%, with sub-additive gains. Global stability of E* is not claimed, and the results are not calibrated to data.