Abstract
Mesquite (Prosopis juliflora) invasion has become a major ecological and socio-economic challenge in arid and semi-arid ecosystems due to its rapid spread through interconnected land, water, and animal-mediated dispersal pathways. Unlike previous studies that primarily considered isolated invasion mechanisms or single control interventions, this study develops an integrated mathematical model combining ecological transmission dynamics, sensitivity analysis, optimal control, and cost-effectiveness evaluation. Model parameterization was based on field observations conducted in Kahe Ward and published ecological studies. Parameters lacking direct empirical measurements, namely: and were estimated by calibrating the model to observed field data in MATLAB using the adaptive Runge–Kutta (RK45) numerical solver, whereas the remaining parameters were adopted from previous studies. The model was analyzed through positivity, boundedness, equilibrium analysis, and invasion threshold derivation using the Next Generation Matrix approach. Sensitivity analysis identified the ecological parameters with the greatest influence on invasion persistence. Optimal control strategies were derived using Pontryagin's Maximum Principle and solved numerically using the fourth-order Runge–Kutta method. Simulation results showed that mesquite invasion increased steadily without intervention, whereas integrated adaptive control substantially reduced invasion across all transmission pathways. Cost-effectiveness analysis further demonstrated that although the combined control strategy incurred the highest implementation cost of USD 347.54 hectares per year, it achieved the lowest ecological burden of 2.1048 hectares per year, confirming integrated adaptive management as the most sustainable long-term strategy for mesquite invasion control.