Optimal Resource Allocation to Reduce an Epidemic Spread and Its Complication

Mathematical modeling represents a useful instrument to describe epidemic spread and to propose useful control actions, such as vaccination scheduling, quarantine, informative campaign, and therapy, especially in the realistic hypothesis of resources limitations. Moreover, the same representation could efficiently describe different epidemic scenarios, involving, for example, computer viruses spreading in the network. In this paper, a new model describing an infectious disease and a possible complication is proposed; after deep-model analysis discussing the role of the reproduction number, an optimal control problem is formulated and solved to reduce the number of dead patients, minimizing the control effort. The results show the reasonability of the proposed model and the effectiveness of the control action, aiming at an efficient resource allocation; the model also describes the different reactions of a population with respect to an epidemic disease depending on the economic and social original conditions. The optimal control theory applied to the proposed new epidemic model provides a sensible reduction in the number of dead patients, also suggesting the suitable scheduling of the vaccination control. Future work will be devoted to the identification of the model parameters referring to specific epidemic disease and complications, also taking into account the geographic and social scenario

Risk Minimization for Spreading Processes over Networks via Surveillance Scheduling and Sparse Control

Spreading processes, such as epidemics and wildfires, have an initial localized outbreak that spreads rapidly throughout a network. The real-world risks associated with such events have stressed the importance and current limitations of methods to quickly map and monitor outbreaks and to reduce their impact by planning appropriate intervention strategies. This thesis is, therefore, concerned with risk minimization of spreading processes over networks via surveillance scheduling and sparse control. This is achieved by providing a flexible optimization framework that combines surveillance and intervention to minimize the risk. Here, risk is defined as the product of the probability of an outbreak occurring and the future impact of that outbreak. The aim is now to bound or minimize the risk by allocation of resources and use of persistent monitoring schedules. When setting up an optimization framework, four other aspects have been found to be of importance. First of all, being able to provide targeted risk estimation and minimization for more vulnerable or high cost areas. Second and third, scalability of algorithms and sparsity of resource allocation are essential due to the large network structures. Finally, for wildfires specifically, there is a gap between the information embedded in fire propagation models and utilizing it for path planning algorithms for efficient remote sensing. The presented framework utilizes the properties of positive systems and convex optimization, in particular exponential cone programming, to provide flexible and scalable algorithms for both surveillance and intervention purposes. We demonstrate with different spreading process examples and scenarios, focusing on epidemics and wildfires, that the presented framework gives convincing and scalable results. In particular, we demonstrate how our method can include persistent monitoring scenarios and provide more targeted and sparse resource allocation compared to previous approaches