论文标题
数学分析，对HIV/AIDS时空传播的预测和最佳控制，具有反应扩散SICA模型
Mathematical Analysis, Forecasting and Optimal Control of HIV/AIDS Spatiotemporal Transmission with a Reaction Diffusion SICA Model
论文作者
论文摘要
我们提出了具有控制策略的数学时空流行病模型。空间行为是通过使用拉普拉斯操作员添加扩散项来建模的，拉普拉斯操作员在数学上和物理上都是合理的和解释的。通过对普通微分方程进行半群理论，我们证明了我们所提出的系统及其某些重要特征的全球积极时空解决方案的存在和独特性。进行了一些说明性的数值模拟，激励我们考虑最佳控制理论。然后提出和研究合适的最佳控制问题。使用基于弱拓扑内某些特性的有效方法，我们证明存在最佳控制，并开发出适当的必要最佳条件，以找到最大程度地减少感染个体密度和治疗计划的成本的最佳控制对。
We propose a mathematical spatiotemporal epidemic SICA model with a control strategy. The spatial behavior is modeled by adding a diffusion term with the Laplace operator, which is justified and interpreted both mathematically and physically. By applying semigroup theory on the ordinary differential equations, we prove existence and uniqueness of the global positive spatiotemporal solution for our proposed system and some of its important characteristics. Some illustrative numerical simulations are carried out that motivate us to consider optimal control theory. A suitable optimal control problem is then posed and investigated. Using an effective method based on some properties within the weak topology, we prove existence of an optimal control and develop an appropriate set of necessary optimality conditions to find the optimal control pair that minimizes the density of infected individuals and the cost of the treatment program.
