A nonlinear differential equation model is proposed to study the dynamics of HIV/AIDS and its effects on workforce productivity. The disease-free equilibrium point of the model is shown to be locally asymptotically stable when the associated basic reproduction number \(\mathcal{{R}}_{0}\) is less than unity. The model is also shown to exhibit multiple endemic states for some parameter values when \(\mathcal{{R}}_{0}<1\) and \(\mathcal{{R}}_{0}>1\). Global asymptotic stability of the disease-free equilibrium is guaranteed only when the fractions of the Susceptible subclass populations are within some bounds. Optimal control analysis of the model revealed that the most cost effective strategy that should be adopted in the fight against HIV/AIDS spread within the workforce is one that seeks to prevent infections and the treatment of infected individuals.

提出了一个非线性微分方程模型来研究 HIV/AIDS 的动态及其对劳动力生产力的影响。当相关的基本再生数\(\mathcal{{R}}_{0}\)小于 1时，模型的无病平衡点被证明是局部渐近稳定的。当\(\mathcal{{R}}_{0}<1\)和\(\mathcal{{R}}_{0}>1\). 只有当易感子类种群的分数在某个范围内时，才能保证无病平衡的全局渐近稳定性。该模型的最佳控制分析表明，在与劳动力中的 HIV/AIDS 传播作斗争中应采用的最具成本效益的策略是寻求预防感染和治疗受感染个体的策略。