We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Computational and Mathematical Methods in Medicine


 Coronavirus disease 2019 (COVID-19) is exacerbating inequalities in the US. We build an agent-based model to elucidate the differential causal effects of nonpharmaceutical interventions on different communities and validate the results with US data. We simulate viral transmission and the consequent deterioration of economic conditions on socioeconomically disadvantaged and privileged populations. As found in data, our model shows that the trade-off between COVID-19 deaths and deaths of despair, dependent on the lockdown level, only exists in the socioeconomically disadvantaged population. Moreover, household overcrowding is a strong predictor of the infection rate. The model also yields new insights that fill in the gaps of our data analysis. While subsidisation narrows the socioeconomic gap in deaths of despair, the combination of testing and contact tracing alone is effective at reducing disparities in both types of death. Our results contribute to policy modelling and evaluation for reducing inequality during a pandemic.

/pdf/impacts-of-covid-19-interventions-health-economics-and-3bkq7fiinw.pdf

Impacts of COVID-19 interventions: Health, economics, and inequality

Domestic and global economic effects of COVID-19 containment measures : How does Russia compare internationally?

Abstract Successful epidemic modeling requires understanding the implicit feedback control strategies used by populations to modulate the spread of contagion. While such strategies can be replicated with intricate modeling assumptions, here we propose a simple model where infection dynamics are described by a three parameter feedback policy. Rather than model individuals as directly controlling the contact rate which governs the spread of disease, we model them as controlling the contact rate’s derivative, resulting in a dynamic rather than kinematic model. The feedback policy used by populations across the United States which best fits observations is proportional-derivative control, where learned parameters strongly correlate with observed interventions (e.g., vaccination rates and mobility restrictions). However, this results in a non-zero “steady-state” of case counts, implying current mitigation strategies cannot eradicate COVID-19. Hence, we suggest making implicit policies a function of cumulative cases, resulting in proportional-integral-derivative control with higher potential to eliminate COVID-19. 

/pdf/implicit-feedback-policies-for-covid-19-why-zero-covid-1xivcpf7.pdf

Implicit feedback policies for COVID-19: why “zero-COVID” policies remain elusive

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 community's resilience to disease outbreaks is independent of its underlying network structure.

Fay Sc

Papers

Simple control for complex pandemics: the impact of testing and contact tracing on heterogeneous networks