**We will build cohesive teams to actively engage on problems of societal importance.**

**Key objectives:**

- Understand the impact of climate change, zoonosis, urbanization and increased global connectivity, anti-microbial-resistance, and individual and collective behavior on epidemic dynamics.
- Develop multi-scale multi-layer (MSML) network models of co-evolving epidemic dynamics that incorporate new emerging components.
- Establish fundamental limits on forecasting epidemic dynamics.
- Understand when and how statistical, causal, and crowdsourced methods can be used and combined for improved forecasts.
- Develop new methods to compare forecasting algorithms.
- Understand how to communicate forecasts to policymakers and the public.
- Design adaptive intervention strategies that optimize multiple cost/benefit objectives and satisfy real-world constraints.
- Assess whether interventions are likely to have unintended consequences.
- Deploy CERTES and demonstrate its use in real-world settings for planning and response in the event of an epidemic (such as COVID-19).

### Multi-scale, multi-factor, multi-layer network modeling.

A large part of the COVID-19 response has been guided by mathematical models. Although a large number of models have been proposed and deployed for the pandemic, they can all be broadly classified in to a few well studied frameworks. Further, these models are mostly data driven and a wealth of different data sources have become available during this pandemic. We wrote three survey articles on this topic [3, 4, 10]. In [4] we provide an overview of the several modeling frameworks that exist and also discuss how the models were deployed across different countries. We also consider a few popular models and explain the model structure in detail. In [3], we provide an overview of the types of datasets, which have been used in different phases of the pandemic, and their limitations for epidemiological analyses. In [10], we outlined an approach to support the COVID-19 response with examples that are rooted in network science and data-driven modeling.

Co-PI Laxminarayan led the largest COVID-19 contact tracing study in the world covering over 650,000 tested individuals in India. The study [28], which was published in Science, found that the risk of transmission from an index case to a close contact ranges from 2.6% in the community to 9.0% in the household and does not differ significantly with respect to the age of the index case. Infection probabilities ranged from 4.7-10.7% for low-risk and high-risk contact types, respectively. Same-age contacts were associated with the greatest infection risk. The study found high prevalence of infection among children who were contacts of cases around their own age; this finding of enhanced infection risk among individuals exposed to similar-age cases was also apparent among adults. Not all infected individuals transmit COVID-19. Prospective follow-up testing of exposed contacts revealed that 70% of infected individuals did not infect any of their contacts, while 8% of infected individuals accounted for 60% of observed new infections. This study presents the largest empirical demonstration of superspreading to date. Laxminarayan covered progress on tackling COVID-19 in India, a country with the second highest number of reported infections and fourth highest number of reported deaths in the world [27].

A central thrust of this group’s work has been on understanding the dynamics of influenza A, and potential for development of a universal flu vaccine (where we have been interacting with Peter Palese’s group at Mt. Sinai). A particular focus has been flu evolution, and the linking to localized charge [55]. We feel that this molecular-level analysis holds great potential for understanding flu evolution.

In [29], the Princeton group demonstrated the “bomb-like” behavior of exponential growth in COVID-19 cases can be explained by transmission of asymptomatic and mild cases that are typically unreported at the beginning of pandemic events due to lower prevalence of testing [29] In [20], we examined the potential impact on hospitalization and mortality assuming different rates of vaccine efficacy.

Even before we knew anything about COVID, the Princeton group began trying to understand virus strategies from the viewpoint of life history strategies in evolutionary ecology. It made sense that it would be advantageous to the pathogen to “lay low”, hiding from the host by being asymptomatic, at least for a portion of the life cycle. The first publication [56] was published in Royal Society Open Science earlier this year.

Our work on COVID-19 in the past year has been headlined by our influential paper in Science [59], which has already been cited 42 times in less than a year, and a second paper [58] on dosing regimes that has just been accepted in Science. This paper studies the interplay between vaccine dosing, logistics, and deployment. In the face of vaccine dose shortages and logistical challenges, various deployment strategies are being proposed to increase population immunity levels to SARS-CoV-2. Two critical issues arise: how the timing of delivery of the second dose will affect infection dynamics, and prospects for the evolution of viral immune escape via a build-up of partially immune individuals. Both hinge on the robustness of the immune response elicited by a single dose, compared to natural and two-dose immunity. Building on an existing immuno-epidemiological model, we find that in the short-term, focusing on one dose generally decreases infections, but longer-term outcomes depend on this relative immune robustness. We then explore three scenarios of selection and find that a one-dose policy may increase the potential for antigenic evolution under certain conditions of partial population immunity. We highlight the critical need to test viral loads and quantify immune responses after one vaccine dose, and to ramp up vaccination efforts throughout the world.

Other papers, including one published in the Journal of the Royal Society Interface [57] as well as others in various stages of review [38, 73], have focused on viral evolution and on control strategies. The paper [38] explores optimal control methods for COVID-19 in the face of uncertainty. Simple theories can lead to optimal timing regimes for social distancing and quarantine regimes, but the papers points out that application of such measures would be extremely dangerous given the uncertainty associated with surveillance and other matters. Slight errors in timing can lead to catastrophic consequences. A more distributed and sustained effort is much safer, so that the optimal regime in the face of uncertainty, flattening the curve, is quite different than trying to time measures precisely and for shorter periods of time.

Other publications have dealt with the social science dimensions of viral hesitancy and antibiotic overuse [63], and broader computational science challenges in epidemic modeling [10, 31].

A significant proportion of individuals who are infected with COVID-19 develop no symptoms while continuing to spread infections. Therefore, understanding their contribution to transmission is critical. The Yale group translated clinical study data to population level to evaluate the contribution of asymptomatic and pre-symptomatic individuals on overall transmission.

As shown in [35] the pre-symptomatic stage of infection accounted for 48% of transmission and asymptomatic infections accounted for 3.4% of transmission if 17.9% of infections are asymptomatic. For a higher asymptomatic proportion of infections (30.8%), the pre-symptomatic phase and asymptomatic infections accounted for 47% and 6.6% of transmission respectively. More importantly, the study found that even immediate isolation of all symptomatic cases is insufficient to achieve control. Specifically, mean attack rates remained 25% of the population, despite immediate isolation of all symptomatic cases.

Results from this study suggest that silent disease transmission is responsible for more than 50% of the overall attack rate and is capable of sustaining outbreak alone, making the control of COVID-19 even more challenging. Therefore, symptom-based interventions alone would not be sufficient to curtail the transmission, and it is important to identify exposed individuals prior to their infectious period. A symptom- based surveillance must be supplemented by rapid contact-based surveillance.

The VT group focused on the different kinds of superspreading phenomena for COVID-19 in social contact networks. Besides keeping current with the relevant COVID-19 literature, we implemented network-based simulation algorithms. While continuing this line of investigation, we have more recently expanded to study the effects of vaccination and testing. We plan to investigate vaccine allocation fairness and effectiveness in networks. We also plan to model the network spread of the SARS-CoV-2 virus as its genome mutates to improve on the fidelity of current models.

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### Planning and response for real-time epidemic science: The overall goals of this RO are to design public health intervention strategies for planning and response to epidemic outbreaks that satisfy multiple cost/benefit criteria, and take into account real-world constraints, impact of human behaviors, as well as the environmental and ecological setting. We have made progress on different aspects of these problems, including evaluating the impacts of social distancing, vaccinations, and contact tracing with respect to epidemic outcomes as well as economic outcomes.

In [43], we assess the impact of social distancing on the daily growth rate of COVID-19 infections in US counties during the initial phase of the pandemic. This research further performs a comparative analysis of the impact on urban versus rural counties, as well as counties with low versus high social vulnerability index. To account for spatial correlations among neighboring counties we use a spatial Durbin model, and find a substantial reduction in the growth rate of confirmed cases resulting from social distancing. Results show significant and sizable spillover effects induced by neighboring counties’ social distancing compliance levels even in the absence of significant within-county effects. Comparative analyses reveal that social distancing compliance exhibits larger impact in slowing down infection growth rates in urban areas and counties with high social vulnerability index as compared to rural areas and counties with low social vulnerability index. Furthermore, we find a high compliance level of social distancing is needed in urban counties and in socially vulnerable areas to achieve the largest impact at slowing down growth in infection rate, whereas moderate-compliance is enough in reaching the peak marginal impact in rural regions and counties with low social vulnerability.

Several countries around the world have begun vaccinating people. In the US, vaccines are being deployed to priority groups. Understanding the population-level impact of vaccination can guide the desired vaccination coverage necessary to halt the ongoing epidemic in the US. Therefore, we evaluated the impact of vaccination on the COVID-19 outbreaks. We used an agent-based model of SARS-CoV-2 transmission and parameterized it with US demographics and age-specific COVID-19 outcomes. We simulated a vaccine campaign, such that healthcare workers and high-risk individuals were prioritized for vaccination, while children under 19 years of age were not vaccinated. As shown in [36], the Yale team found that if a vaccine with an efficacy of 90% is administered to 40% of the overall population of the US, it can reduce the overall attack rate to less than 2% from more than 7% across the same period without vaccination. The highest relative reduction would be observed among the elderly population above 65. Vaccination would also reduce the adverse outcomes substantially with non-ICU, ICU hospitalizations, and death all decreasing by more than 80%.

The results highlight the substantial impact that vaccination will have on reducing disease transmission and adverse clinical outcomes. Therefore, vaccination will play a critical role in ensuring that healthcare infrastructure would not be overburdened. However, with an uptake of 40% or less in the population, vaccination is unlikely to eliminate the need for non-pharmaceutical interventions completely.

Additionally, the Yale team also succeeded in estimating the durability of immunity against infection of SARS-CoV-2. The expected reinfection time is between 3 and 65 months, with a median of 17 months. The manuscript on this research is currently in submission.

COVID-19 has killed over a million people since its emergence in late 2019. However, there has been substantial variability in the policies and intensity of diagnostic efforts between countries. In [74], the Yale team quantitatively evaluated the association between national contact tracing policies and case fatality rates of COVID-19 in 138 countries. The regression analyses indicate that countries that implement comprehensive contact tracing have significantly lower case fatality rates. This association of contact tracing policy and case fatality rates is robust in our longitudinal regression models, even after controlling for the number of tests conducted and non-pharmaceutical control measures adopted by governments. The results suggest that comprehensive contact tracing is instrumental not only to curtailing transmission but also to reducing case fatality rates. Contact tracing achieves the early detection and isolation of secondary cases which are particularly important given that the peak in infectiousness occurs during the pre-symptomatic phase.

The early detection achieved by contact tracing accelerates the rate at which infected individuals receive the medical care they need to maximize their chance of recovery. In addition, the combination of reduced transmission and more rapid recovery diminishes the burden on the healthcare system which in turn ensures that the resources remain available for individuals who do become infected.

In [11], we use an individual based model and national level epidemic simulations to estimate the medical costs of keeping the US economy open during COVID-19 pandemic under different counterfactual scenarios. We model an unmitigated scenario and 12 mitigation scenarios which differ in compliance behavior to social distancing strategies and in the duration of the stay-home order. Under each scenario we estimate the number of people who are likely to get infected and require medical attention, hospitalization, and ventilators. Given the per capita medical cost for each of these health states, we compute the total medical costs for each scenario and show the trade-offs between deaths, costs, infections, compliance, and the duration of stay-home order. We also consider the hospital bed capacity of each Hospital Referral Region (HRR) in the US to estimate the deficit in beds each HRR will likely encounter given the demand for hospital beds. We consider a case where HRRs share hospital beds among the neighboring HRRs during a surge in demand beyond the available beds and the impact it has in controlling additional deaths.

In [12], we measure the epidemiological and economic impact of COVID-19 spread in the US under different mitigation scenarios, comprising of non-pharmaceutical interventions. A detailed disease model of COVID-19 is combined with a model of the US economy to estimate the direct impact of labor supply shock to each sector arising from morbidity, mortality, and lock down, as well as the indirect impact caused by the interdependencies between sectors. During a lockdown, estimates of jobs that are workable from home in each sector are used to modify the shock to labor supply. Results show that trade-offs between economic losses and lives saved and infections averted are non-linear in compliance to social distancing and the duration of lockdown. Sectors that are worst hit are not the labor-intensive sectors such as Agriculture and Construction, but the ones with high valued jobs such as Professional Services, even after the teleworkability of jobs is accounted for. Additionally, the findings show that a low compliance to interventions can be overcome by a longer shutdown period and vice versa to arrive at similar epidemiological impact but their net effect on economic loss depends on the interplay between the marginal gains from averting infections and deaths, versus the marginal loss from having healthy workers stay at home during the shutdown.

In a paper that appeared in Nature [9], the Stanford team developed scalable computational models that predicted the spread of COVID-19 in 10 major cities this spring by analyzing three factors that drive infection risk: where people go in the course of a day, how long they linger and how many other people are visiting the same place at the same time. The team merged demographic data, epidemiological estimates, and anonymous cellphone location information, and appears to confirm that most COVID-19 transmissions occur at “superspreader” sites like full-service restaurants, fitness centers, and cafes, where people remain in close quarters for extended periods. The model shows how reopening businesses with lower occupancy caps tend to benefit disadvantaged groups the most. The study traced the movements of 98 million Americans in 10 of the nation’s largest metropolitan areas through half a million different establishments, from restaurants and fitness centers to pet stores and new car dealerships.

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