State-controlled epidemic in a game against a novel pathogen

The pandemic reminded us that the pathogen evolution still has a serious effect on human societies. States, however, can prepare themselves for the emergence of a novel pathogen with unknown characteristics by analysing potential scenarios. Game theory offers such an appropriate tool. In our game-theoretical framework, the state is playing against a pathogen by introducing non-pharmaceutical interventions to fulfil its socio-political goals, such as guaranteeing hospital care to all needed patients, keeping the country functioning, while the applied social restrictions should be as soft as possible. With the inclusion of activity and economic sector dependent transmission rate, optimal control of lockdowns and health care capacity management is calculated. We identify the presence and length of a pre-symptomatic infectious stage of the disease to have the greatest effect on the probability to cause a pandemic. Here we show that contrary to intuition, the state should not strive for the great expansion of its health care capacities even if its goal is to provide care for all requiring it and minimize the cost of lockdowns

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