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Amidst the current COVID-19 pandemic, quantifying the effects of strategies that mitigate the spread of infectious diseases is critical. This article presents a compartmental model that addresses the role of random viral testing, follow-up contact tracing, and subsequent isolation of infectious individuals to stabilize the spread of a disease. We propose a branching model and an individual (or agent) based model, both of which capture the stochastic, heterogeneous nature of interactions within a community. The branching model is used to derive new analytical results for the trade-offs between the different mitigation strategies, with the surprising result that a communitys resilience to disease outbreaks is independent of its underlying network structure.
Discovering and isolating infected individuals is a cornerstone of epidemic control. Because many infectious diseases spread through close contacts, contact tracing is a key tool for case discovery and control. However, although contact tracing has b
Stochastic epidemic models on networks are inherently high-dimensional and the resulting exact models are intractable numerically even for modest network sizes. Mean-field models provide an alternative but can only capture average quantities, thus of
During a pandemic, there are conflicting demands arising from public health and economic cost. Lockdowns are a common way of containing infections, but they adversely affect the economy. We study the question of how to minimise the economic damage of
We first generalise ideas discussed by Kiss et al. (2015) to prove a theorem for generating exact closures (here expressing joint probabilities in terms of their constituent marginal probabilities) for susceptible-infectious-removed (SIR) dynamics on
We present a new mathematical model to explicitly capture the effects that the three restriction measures: the lockdown date and duration, social distancing and masks, and, schools and border closing, have in controlling the spread of COVID-19 infect