Mathematical modelling of the dynamical system of military population, focusing on the impact of welfare

In this work, we explored the concept of an improved welfare package for military personnel in Nigeria. This proposed package aims to address traditional needs while also meeting modern demands, such as mental health support. We recognise the critical importance of security jobs and the prompt payment of special operation allowances, as these factors provide military personnel with a sense of reassurance and stability. Key elements of the welfare package include upgrading qualified lower ranks to officer status, ensuring timely payment of death benefits to the families of military personnel who have died in active service, procuring standard and adequate weapons, and promoting equal treatment of all military personnel without bias. Poor welfare packages contribute significantly to dissatisfaction among Nigerian military personnel, which can hinder productivity and lead to unethical behaviour. Conversely, enhancing the welfare package can substantially boost productivity and reduce dissatisfaction. We formulated a deterministic military model to assess the impact of improved welfare on the productivity of Nigerian military personnel and to prevent dissatisfaction and misconduct. The model computes the disgruntlement reproduction number, Rm , which is used to demonstrate the local and global stability of both disgruntled and non-disgruntled equilibrium states. To further analyze the model, we conducted a global sensitivity analysis using Latin Hypercube Sampling (LHS) and the Partial Rank Correlation coefficient on Rm and military populations to identify the most sensitive parameters affecting military dynamics. Based on the results of this analysis, we extended the model by introducing a standard improved welfare package to control the most sensitive parameter. Numerical simulations showed that if an improved welfare package is intentionally implemented and maintained, dissatisfaction and misconduct among military personnel will drastically decrease, while productivity will significantly increase.