K-State Epicenter, Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS 66506-5204, United States.
Math Biosci Eng. 2013 Aug;10(4):1227-51. doi: 10.3934/mbe.2013.10.1227.
This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights.
本文提出了一种最优控制问题的公式化方法，以最小化易感染-感染-恢复 SIR 传染病在接触网络中传播过程中的总感染病例数。在新方法中，节点之间的接触权重被降低，并且网络中保持了全局最小接触水平。此外，感染成本和与接触减少相关的成本在单个目标函数中线性组合。因此，最优控制公式解决了总感染病例数最小化和接触权重减少最小化之间的权衡问题。使用庞特里亚金定理，得到的解是表示动态加权接触网络的唯一候选解。为了以分散的方式找到近似最优解，我们分别基于 Bang-Bang 控制函数和分段非线性控制函数提出了两种启发式方法。我们在不同的网络上进行了广泛的模拟，以评估这两种启发式方法。我们的结果表明，分段非线性控制函数在最小化总感染病例数和接触权重减少方面优于著名的 Bang-Bang 控制函数。最后，我们的结果表明，人们意识到感染水平，从而有效地将缓解策略应用于接触权重。
