Seidu Baba, Makinde Oluwole D, Seini Ibrahim Y
Applied Mathematics Department, Faculty of Mathematical Sciences, University for Development, Navrongo, Ghana,
Acta Biotheor. 2015 Jun;63(2):151-82. doi: 10.1007/s10441-015-9255-y. Epub 2015 May 16.
In this paper, a nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics and effects of HIV-malaria co-infection in the workplace. Basic reproduction numbers of sub-models are derived and are shown to have LAS disease-free equilibria when their respective basic reproduction numbers are less than unity. Conditions for existence of endemic equilibria of sub-models are also derived. Unlike the HIV-only model, the malaria-only model is shown to exhibit a backward bifurcation under certain conditions. Conditions for optimal control of the co-infection are derived using the Pontryagin's maximum principle. Numerical experimentation on the resulting optimality system is performed. Using the incremental cost-effectiveness ratio, it is observed that combining preventative measures for both diseases is the best strategy for optimal control of HIV-malaria co-infection at the workplace.
本文提出了一个非线性动力系统并对其进行定性分析，以研究工作场所中艾滋病毒 - 疟疾合并感染的动态变化和影响。推导了子模型的基本再生数，并表明当各自的基本再生数小于1时，它们具有局部渐近稳定的无病平衡点。还推导了子模型地方病平衡点的存在条件。与仅考虑艾滋病毒的模型不同，仅考虑疟疾的模型在某些条件下表现出向后分岔。利用庞特里亚金极大值原理推导了合并感染的最优控制条件，并对所得最优性系统进行了数值实验。通过增量成本效益比观察到，结合两种疾病的预防措施是工作场所艾滋病毒 - 疟疾合并感染最优控制的最佳策略。
