Numerical Optimal Control of HIV Transmission in Octave/MATLAB
Numerical Optimal Control of HIV Transmission in Octave/MATLAB
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DOI：
10.3390/mca25010001
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发表时间：
2020-03-01
影响因子：
1.9
通讯作者：
Torres, Delfim F. M.
中科院分区：
文献类型：
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作者：
Campos, Carlos;Silva, Cristiana J.;Torres, Delfim F. M.
我们提供了易于阅读的GNU Octave/MATLAB代码，用于模拟常微分方程描述的数学模型，并通过庞特里亚金极大值原理求解最优控制问题。为此，我们考虑了一种标准化的艾滋病毒/艾滋病传播动力学模型，该模型基于我们最近的贡献（Silva， C.J.; Torres， D.F.M.）中提出的一种SICA流行病学分区模型，并应用于佛得角的艾滋病毒/艾滋病。生态。复数。2017,30,70-75)，由四个常微分方程组成的方程组给出。利用ode45 GNU Octave函数和我们在Octave/MATLAB中实现的三种标准方法：欧拉法、二阶和四阶龙格-库塔法，对一个HIV初值问题进行了数值求解。然后，在归一化的HIV模型中引入控制函数，构造最优控制问题，其目标是找到最优的HIV预防策略，使未感染HIV的个体中HIV新发感染的比例和控制措施相关的成本最大化。利用庞特里亚金极大值原理对最优控制问题进行了解析表征，并采用正向-反向四阶龙格-库塔方法对极值进行了数值计算。本文提供了在免费的GNU Octave软件下开发并与MATLAB兼容的完整算法，用于非受控初值和最优控制问题。
We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin's maximum principle. For that, we consider a normalized HIV/AIDS transmission dynamics model based on the one proposed in our recent contribution (Silva, C.J.; Torres, D.F.M. A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde. Ecol. Complex. 2017, 30, 70-75), given by a system of four ordinary differential equations. An HIV initial value problem is solved numerically using the ode45 GNU Octave function and three standard methods implemented by us in Octave/MATLAB: Euler method and second-order and fourth-order Runge-Kutta methods. Afterwards, a control function is introduced into the normalized HIV model and an optimal control problem is formulated, where the goal is to find the optimal HIV prevention strategy that maximizes the fraction of uninfected HIV individuals with the least HIV new infections and cost associated with the control measures. The optimal control problem is characterized analytically using the Pontryagin Maximum Principle, and the extremals are computed numerically by implementing a forward-backward fourth-order Runge-Kutta method. Complete algorithms, for both uncontrolled initial value and optimal control problems, developed under the free GNU Octave software and compatible with MATLAB are provided along the article.