A non-linear mechanistic model for the transmission dynamics of HIV/AIDS is developed and analyzed. The model classified the infected individuals based on their CD4 count level. Furthermore, education campaign, voluntary testing and counseling and treatment are considered as intervention strategies for controlling the disease. The analysis of the model reveals that imperfect public enlightenment campaign can induce backward bifurcation. It has been shown that when public enlightenment campaign is \(100\%\) effective, the disease free equilibrium is globally asymptotically stable for \(R_{eff} \le 1\), whereas for \(R_{eff} > 1\) the global stability of the endemic equilibrium is proved only in a special case. Time dependent controls of the intervention strategies mentioned above are incorporated into the model and the optimal control strategies with minimal implementation cost are identified. In addition, cost effectiveness analysis in the form of incremental cost effectiveness ratio is carried-out to identify the most cost effective strategies. The results suggest that out of the three non dominated strategies, the strategy of educating the newly entrants only or combination of newly entrants and susceptible individuals is very cost effective using per capita GDP of Nigeria as at 2018. However, the choice of which strategy to implement depends on budgetary allocation and resource availability.

建立并分析了HIV / AIDS传播动力学的非线性机理模型。该模型根据受感染者的CD4计数水平对其进行分类。此外，教育运动，自愿检测以及咨询和治疗被认为是控制该疾病的干预策略。对模型的分析表明，不完善的公众启蒙运动会导致向后的分歧。研究表明，当公众启蒙运动达到\（100 \％\）有效时，\（R_ {eff} \ le 1 \）的无病平衡在全局渐近稳定，而对于\（R_ {eff}> 1 \）仅在特殊情况下证明了地方均衡的全局稳定性。将上述干预策略的时间相关控制纳入模型，并确定实现成本最低的最佳控制策略。此外，还以增量成本效率比率的形式进行了成本效益分析，以找出最具成本效益的策略。结果表明，在三种非主导战略中，仅使用新进入者或新进入者与易受感染者的组合进行教育的策略，使用尼日利亚截至2018年的人均GDP，是非常划算的。但是，选择哪种策略实施取决于预算分配和资源可用性。