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Register a new userOn the Effectiveness of Tracking and Testing in SEIR Models
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We study the effectiveness of tracking and testing in mitigating or suppressing epidemic outbreaks, in combination with or as an alternative to quarantines and global lockdowns. We study these intervention methods on a network-based SEIR model, augmented with an additional probability to model symptomatic, asymptomatic and pre-symptomatic cases. Our focus is on the basic trade-offs between economic costs and human lives lost, and how these trade-offs change under different lockdown, quarantine, tracking and testing policies. Our main findings are as follows: (i) Tests combined with patient quarantines reduce both economic costs and mortality, but require a large-scale testing capacity to achieve a significant improvement; (ii) Tracking significantly reduces both economic costs and mortality; (iii) Tracking combined with a limited number of tests can achieve containment without lockdowns; (iv) If there is a small flow of new incoming infections, dynamic On-Off lockdowns are more efficient than fixed lockdowns. Our simulation results underline the extreme effectiveness of tracking and testing policies in reducing both economic costs and mortality and their potential to contain epidemic outbreaks without imposing social distancing restrictions. This highlights the difficult social question of trading-off these gains with the privacy loss that tracking necessarily entails.
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Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then explores where these models agree and disagree under relaxed specifications. For the population models, the requirement of homogeneous mixing prevents prediction of extinctions due to local resource depletion. These models also suggest equilibrium based on attainment of constant population levels though underlying population characteristics may be nowhere close to equilibrium. The discrete stochastic gene frequency models assume well mixed populations at constant levels. The models predictions for non-constant populations in strongly oscillating and chaotic regimes are surprisingly good, only diverging from the ABM at the most chaotic levels.
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 been performed widely, the mathematical understanding of contact tracing has not been fully established and it has not been clearly understood what determines the efficacy of contact tracing. Here, we reveal that, compared with forward tracing---tracing to whom disease spreads, backward tracing---tracing from whom disease spreads---is profoundly more effective. The effectiveness of backward tracing is due to simple but overlooked biases arising from the heterogeneity in contacts. Using simulations on both synthetic and high-resolution empirical contact datasets, we show that even at a small probability of detecting infected individuals, strategically executed contact tracing can prevent a significant fraction of further transmissions. We also show that---in terms of the number of prevented transmissions per isolation---case isolation combined with a small amount of contact tracing is more efficient than case isolation alone. By demonstrating that backward contact tracing is highly effective at discovering super-spreading events, we argue that the potential effectiveness of contact tracing has been underestimated. Therefore, there is a critical need for revisiting current contact tracing strategies so that they leverage all forms of biases. Our results also have important consequences for digital contact tracing because it will be crucial to incorporate the capability for backward and deep tracing while adhering to the privacy-preserving requirements of these new platforms.
We consider the emergent behavior of viral spread when agents in a large population interact with each other over a contact network. When the number of agents is large and the contact network is a complete graph, it is well known that the population behavior -- that is, the fraction of susceptible, infected and recovered agents -- converges to the solution of an ordinary differential equation (ODE) known as the classical SIR model as the population size approaches infinity. In contrast, we study interactions over contact networks with generic topologies and derive conditions under which the population behavior concentrates around either the classic SIR model or other deterministic models. Specifically, we show that when most vertex degrees in the contact network are sufficiently large, the population behavior concentrates around an ODE known as the network SIR model. We then study the short and intermediate-term evolution of the network SIR model and show that if the contact network has an expander-type property or the initial set of infections is well-mixed in the population, the network SIR model reduces to the classical SIR model. To complement these results, we illustrate through simulations that the two models can yield drastically different predictions, hence use of the classical SIR model can be misleading in certain cases.
COVID-19 has forced quarantine measures in several countries across the world. These measures have proven to be effective in significantly reducing the prevalence of the virus. To date, no effective treatment or vaccine is available. In the effort of preserving both public health as well as the economical and social textures, France and Italy governments have partially released lockdown measures. Here we extrapolate the long-term behavior of the epidemics in both countries using a Susceptible-Exposed-Infected-Recovered (SEIR) model where parameters are stochastically perturbed to handle the uncertainty in the estimates of COVID-19 prevalence. Our results suggest that uncertainties in both parameters and initial conditions rapidly propagate in the model and can result in different outcomes of the epidemics leading or not to a second wave of infections. Using actual knowledge, asymptotic estimates of COVID-19 prevalence can fluctuate of order of ten millions units in both countries.
There is a continuing debate on relative benefits of various mitigation and suppression strategies aimed to control the spread of COVID-19. Here we report the results of agent-based modelling using a fine-grained computational simulation of the ongoing COVID-19 pandemic in Australia. This model is calibrated to match key characteristics of COVID-19 transmission. An important calibration outcome is the age-dependent fraction of symptomatic cases, with this fraction for children found to be one-fifth of such fraction for adults. We apply the model to compare several intervention strategies, including restrictions on international air travel, case isolation, home quarantine, social distancing with varying levels of compliance, and school closures. School closures are not found to bring decisive benefits, unless coupled with high level of social distancing compliance. We report several trade-offs, and an important transition across the levels of social distancing compliance, in the range between 70% and 80% levels, with compliance at the 90% level found to control the disease within 13--14 weeks, when coupled with effective case isolation and international travel restrictions.
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