Mathematical and Scenario Analysis of an Improved Six-Compartment Japa Model Incorporating Anticipated Rewards and Talent Retention Using LADM and NBS 2023 Population Data

In this work, we develop and analyze a six-compartmental mathematical model on brain drain dynamics within a source country. The compartments of interest include the source population, employment opportunities, frustrated population due to corruption, unemployment population, immigrants, and emigrants. In addition, the work explores the impacts of anticipated rewards, talent retention, and media awareness on changes in the above compartmental populations. We explore non-negativity and boundedness of the system, determine brain-drain-free and persistent equilibria, compute the basic reproduction number, and investigate parameter sensitivity. For the initial population, we use statistical data of Nigeria's National Bureau of Statistics while others are from the literature or are assumed. With the updated baseline parameter set, the value of R₀ is 0.0126874 which is less than one and meets the threshold condition for the local asymptotic stability of the brain-drain-free equilibrium under the assumed conditions. Numerical solution of the model is obtained using the restarted two-correction scheme of Laplace-Adomian decomposition method (LADM) algorithm and analyzed using Radau IIA and LSODA algorithms. With reduction of the time step, the maximum scaled error is decreased from 8.20 × 10⁻⁶ to while the maximum scaled difference between Radau IIA and LSODA is approximately .The Scenario results provide away to compare how selected parameter values relate to the modeled corruption-frustrated and unemployment trajectories.