No abstract

No abstract

We present a general framework for adaptive allocation of viral tests in social contact networks. We pose and solve several complementary problems. First, we consider the design of a social sensing system whose objective is the early detection of a novel epidemic outbreak. In particular, we propose an algorithm to select a subset of individuals to be tested in order to detect the onset of an epidemic outbreak as fast as possible. We pose this problem as a hitting time probability maximization problem and use submodularity optimization techniques to derive explicit quality guarantees for the proposed solution. Second, once an epidemic outbreak has been detected, we consider the problem of adaptively distributing viral tests over time in order to maximize the information gained about the current state of the epidemic. We formalize this problem in terms of information entropy and mutual information and propose an adaptive allocation strategy with quality guarantees. For these problems, we derive analytical solutions for any stochastic compartmental epidemic model with Markovian dynamics, as well as efficient Monte-Carlo-based algorithms for non-Markovian dynamics. Finally, we illustrate the performance of the proposed framework in numerical experiments involving a model of Covid-19 applied to a real human contact network.

A usual qualitative analogy used to explain gravitation in general relativity is comparing spacetime warping by massive objects with deformation in a rubber sheet. Motivated by this analogy, which identifies planet orbits with trajectories of rolling objects on the rubber sheet, the movement of a small ball in a trampoline bent because of the presence of a heavy mass in its center is studied. It is concluded that the similarities between how masses move under warped spacetime and under a warped trampoline are only qualitative, and later some analogy flaws are outlined, which can be useful for general relativity teaching. Since the "relativistic model" does not match the ball movement in the experimental conditions, two models based on classical mechanics are presented to describe it. The models are implemented computationally and parameters of such models are optimized to match experimental trajectories. In the case of the most complex of these two models, the high accuracy between optimized and observed trajectories implies that the model is able to explain the experiment behaviour.