Abstract-A network epidemics model based on the classical Polya urn scheme is investigated. Temporal contagion processes are generated on the network nodes using a modified Polya sampling scheme that accounts for spatial infection among neighbouring nodes. The stochastic properties and the asymptotic behaviour of the resulting network contagion process are analyzed. Unlike the classical Polya process, the network process is noted to be non-stationary in general, although it is shown to be time-invariant in its first and some of its second-order statistics and to satisfy martingale convergence properties under certain conditions. Three classical Polya processes, one computational and two analytical, are proposed to statistically approximate the contagion process of each node, showing a good fit for a range of system parameters. Finally, empirical results compare and contrast our model with the well-known discrete time SIS model.

No abstract

We study the curing of epidemics of a network contagion, which is modelled using a variation of the classical Polya urn process that takes into account spatial infection among neighbouring nodes. We introduce several quantities for measuring the overall infection in the network and use them to formulate an optimal control problem for minimizing the average infection rate using limited curing resources. We prove the feasibility of this problem under high curing budgets by deriving conservative lower bounds on the amount of curing per node that turns our measures of network infection into supermartingales. We also provide a provably convergent gradient descent algorithm to find the allocation of curing under limited budgets. Motivated by the fact that this strategy is computationally expensive, we design a suit of heuristic methods that are locally implementable and nearly as effective. Extensive simulations run on largescale networks demonstrate the effectiveness of our proposed strategies.

We propose a multitask learning approach to learn the parameters of a compartmental discrete-time epidemic model from various data sources and use it to design optimal control strategies of human-mobility restrictions that both curb the epidemic and minimize the economic costs associated with implementing non-pharmaceutical interventions. We develop an extension of the SEIR epidemic model that captures the effects of changes in human mobility on the spread of the disease. The parameters of the model are learned using a multitask learning approach that leverages both data on the number of deaths across a set of regions, and cellphone data on individuals’ mobility patterns specific to each region. Using this model, we propose a nonlinear optimal control problem aiming to find the optimal mobility-based intervention strategy that curbs the spread of the epidemic while obeying a budget on the economic cost incurred. We also show that the solution to this nonlinear optimal control problem can be efficiently found, in polynomial time, using tools from geometric programming. Furthermore, in the absence of a straightforward mapping from human mobility data to economic costs, we propose a practical method by which a budget on economic losses incurred may be chosen to eliminate excess deaths due to over-utilization of hospital resources. Our results are demonstrated with numerical simulations using real data from the COVID-19 pandemic in the Philadelphia metropolitan area.

No abstract