Applications to Epidemic Science

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 into 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 [1–3]. In [2] 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 [1], 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 [3], we outlined an approach to support the COVID-19 response with examples that are rooted in network science and data-driven modeling

Last year, we presented a preliminary report on a decision-support tool that utilizes large-scale data and epidemiological modeling to quantify the impact of changes in mobility on infection rates. Mobility restrictions have been initially a primary intervention for controlling the spread of COVID-19, but they also place a significant economic burden on individuals and businesses. To balance these competing demands, policymakers need analytical tools to assess the costs and benefits of different mobility reduction measures. We developed a model that captures the spread of COVID- 19 by using a fine-grained, dynamic mobility network that encodes the hourly movements of people from neighborhoods to individual places, with over 3 billion hourly edges. By perturbing the mobility network, we can simulate a wide variety of reopening plans and forecast their impact in terms of new infections and the loss in visits per sector. To deploy this model in practice, we built a robust computational infrastructure to support running millions of model realizations, and we worked with policymakers to develop an interactive dashboard that communicates our model’s predictions for thousands of potential policies. The publication received the Best Paper award in the Application Track at the KDD 2021 conference [4].

We partnered with the Virginia Department of Health to develop a model for recommending the placement of mobile vaccination sites for COVID-19. The deployment of vaccines across the US provides a significant defense against serious illness and death from COVID-19. Over 70% of vaccine-eligible Americans are at least partially vaccinated, but there are pockets of the population that are under-vaccinated, such as in rural areas and some demographic groups (e.g. age, race, ethnicity). These unvaccinated pockets are extremely susceptible to the Delta variant, exacerbating the healthcare crisis and increasing the risk of new variants. Our data-driven model provides real-time support to Virginia public health officials by recommending mobile vaccination site placement in order to target under-vaccinated populations. Our strategy uses fine-grained mobility data, along with US Census and vaccination uptake data, to identify locations that are most likely to be visited by unvaccinated individuals. Furthermore, the model is able to choose locations that maximize vaccine uptake among hesitant groups. We showed that the top recommended sites vary substantially across some demographics, demonstrating the value of developing customized recommendation models that integrate fine-grained, heterogeneous data sources. We also used a statistically equivalent Synthetic Population to study the effect of combined demographics (e.g. people of a particular race and age), which is not possible using US Census data alone. We validated our recommendations by analyzing the success rates of deployed vaccine sites and showed that sites placed closer to our recommended areas administered higher numbers of doses. Our model is the first of its kind to consider evolving mobility patterns in real-time for suggesting placement strategies customized for different targeted demographic groups. These results have been presented at IAAI-22 [5].

Spectral Characterization and Applications: Healthcare-associated infections (HAIs) are a major problem in hospital infection control. In contrast to diseases like influenza which usually spread with human-human contact, HAIs have multiple pathways of transmission such that additional locations can also accumulate “load” and spread the disease. Standard propagation models like Independent Cascade (IC)/Susceptible-Infected-Susceptible (SIS) do not capture such mechanisms; hence recently so-called “2-mode” models on people/location networks have been proposed where the people and location nodes behave differently in the underlying contact networks and the diseases spread via both people and location nodes. While standard models have received significant attention in prior work in data mining and epidemiology, these 2-mode models on heterogeneous networks have not. In recent work, we have developed a novel spectral characterization of such models to capture their dynamics on time-varying heterogeneous networks using non-linear system theory. We show that it explains previously observed counter-intuitive behaviors like the “dilution effect”, and can be used for decision-making via important clinical problems. We also show how to develop effective and efficient algorithms for these applications using our characterization. Our experiments show that our methods outperform several natural structural and clinical approaches on real-world hospital testbeds and pick meaningful solutions.

Our research was focused on understanding various epidemiological and population-level factors in the context of the evolution of the COVID-19 pandemic, its variants as well as vaccination campaigns [6–16]. We conducted a systematic review and meta-analysis study to inform the proportion of SARS-CoV-2 infections that do not exhibit symptoms. We found that more than one-third of infections are truly asymptomatic and asymptomaticity was even higher at younger ages, suggesting the need for heightened vigilance among younger groups to prevent spillover into the broader community. We also estimated the population immunity against COVID-19 in the United States by the end of July 2021 and found it to be 62%, indicating that population-level immunity may still have been insufficient to contain potential outbreaks. Our evaluation of the interplay between vaccine campaigns and the continuation of non-pharmaceutical interventions in mitigating the population-level spread of COVID-19 and its variants suggested that policy decisions on non-pharmaceutical interventions should be based on the local COVID-19 situation in each individual country, taking into consideration population-level immunity, vaccine efficacy and relating prevalence and transmissibility of circulating variants. In another study, we found that accelerated vaccination could prevent COVID-19 waves that would otherwise be fueled by waning adherence to non-pharmaceutical interventions. Moreover, accelerated vaccination can also avert a substantial number of cases and hospitalizations attributed to widespread dissemination of emerging more transmissible variants, and thus mitigating the public health challenges associated with highly transmissible COVID-19 variants.

A central thrust of this group’s work has been on understanding the dynamics of influenza A, and the 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 [17]. We feel that this molecular-level analysis holds great potential for understanding flu evolution.

In [18], 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 the lower prevalence of testing [18]. In [19], 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 [20] was published in the 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 [21], which has already been cited 42 times in less than a year, and a second paper [22] 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 ramp up vaccination efforts throughout the world.

Other papers, including one published in the Journal of the Royal Society Interface [23] as well as others in various stages of review [24, 25], have focused on viral evolution and on control strategies. The paper [24] 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 point 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 [26], and broader computational science challenges in epidemic modeling [3, 27].

Our work in [28] addressed what was perhaps the greatest unknown of the COVID-19 pandemic—how long immunity lasts after natural infection. It received tremendous media attention and still does. In this work, we provide an answer to what has often been called the greatest unknown factor regarding COVID-19: the durability of immunity upon natural infection. Nature Publishing Group’s Nature video on July 21 listed it as the biggest of four major questions regarding COVID-19. STAT news listed it as the first, most pressing question regarding COVID-19. The most highly touted research on this topic has reported longitudinal studies showing that the levels of neutralizing antibodies drop significantly in two to three months; however, this drop—although relevant to the immunology of the disease—is not regarded as indicative of the duration of immunity. Some have speculated that one cannot or only very rarely can get infected again, whereas others have argued on the basis of very few cases that immunity may already have waned. Many have deemed the question impossible to address because the epidemic is so recent that there have been few if any reinfections with which one might compose an informative cohort. “Only the future can tell us,” immunologist Reinhold Förster is quoted as saying in a recent Nature news feature. This paper reported our discovery that addresses these seemingly conflicting findings in a probabilistic context, demonstrating that the average natural reinfection time of endemic SARS-CoV-2 is likely to be about one and a half years. Within a few months, a non-negligible risk of reinfection begins to accrue. We have arrived at this conclusion by gathering data from longitudinal studies of antibody waning following infection by SARS-CoV-2, SARS-CoV-1, MERS, and 3 of the 4 seasonal coronaviruses (HCoV-229E, HCoV-OC43, HCoV-NL63). What previous studies have missed is that SARS- CoV-2 is genetically quite similar to other closely related coronaviruses, enabling the use of extensive viral genome sequence data to reconstruct the phylogenetic relatedness of these viruses and application of ancestral and descendent states analysis—a well-established phylogenetic approach by which we can weight the impact of each known durability inversely by its evolutionary distance and the speed at which the trait evolves. Modeling the rate of antibody decline in each viral lineage and applying ancestral and descendent state analysis to “fill in the gaps” of our understanding provides a probability density of reinfection risk through time. The resulting density results in a 5% risk of reinfection by 3 months under endemic conditions with no interventions and a 50% risk by 1.5 years. This finding reconciles the seemingly contradictory reports of rare, short-term reinfection with a steady train of immunology results demonstrating longer-term waning of antibody levels.

This estimated immunological resistance to SARS-CoV-2 reinfection is less than that of other seasonal coronaviruses, and most similar to MERS. Until a long-term cohort study comprehensively quantifying the durability of immunity gained from SARS-CoV-2 infections becomes feasible, our analysis of the timeframe for reinfection is the most rigorous science revealing knowledge that is vital for informing public health decision-making in diverse areas, including travel restrictions, decisions regarding how students obtain their education, prospective revaccination protocols and all long-term public-health modeling projections for COVID-19. Importantly, our analysis warns that reinfections are likely to happen on a 1–2 year timescale. The accumulation of herd immunity in the absence of a well-developed, widespread, repeated vaccination strategy will be ineffective at forestalling infection, morbidity, or deaths due to COVID-19.

The paper was published before Omicron, before reinfection was widespread and before any substantial reinfection study could be conducted. Since then, it has been validated by two subsequent papers examining empirical frequencies of reinfection in monitored cohorts. Our comparative evolutionary analysis predicted an 18% probability of reinfection at 270 days, which matched subsequent empirical findings.

Co-PI Laxminarayan led the largest COVID-19 contact tracing study in the world covering over 650,000 tested individuals in India. The study [29], 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 a 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 super-spreading to date. Laxminarayan covered progress in 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 [30].

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 [31] 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 the 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. Symptom-based surveillance must be supplemented by rapid contact-based surveillance.

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[8]  T. N. Vilches, P. Sah, E. Abdollahi, S. M. Moghadas, and A. P. Galvani, “Importance of non- pharmaceutical interventions in the covid-19 vaccination era: A case study of the seychelles,” Journal of Global Health, vol. 11, 2021.

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[10]  S. M. Moghadas, T. N. Vilches, K. Zhang, C. R. Wells, A. Shoukat, B. H. Singer, L. A. Meyers, K. M. Neuzil, J. M. Langley, M. C. Fitzpatrick, et al., “The impact of vaccination on covid-19 outbreaks in the united states,” Clinical Infectious Diseases, pp. 2257–2264, 2021.

[11]  C. Wells and A. P. Galvani, “The interplay between covid-19 restrictions and vaccination,” Lancet Infect Dis., pp. 1053–1054, 2021.

[12]  S. M. Moghadas, P. Sah, T. N. Vilches, and A. P. Galvani, “Can the usa return to pre-covid-19 normal by july 4?,” The Lancet Infectious Diseases, vol. 21, no. 8, pp. 1073–1074, 2021.

[13]  A. Pandey, P. Sah, S. M. Moghadas, S. Mandal, S. Banerjee, P. J. Hotez, and A. P. Galvani, “Challenges facing covid-19 vaccination in india: Lessons from the initial vaccine rollout,” Journal of Global Health, vol. 11, 2021.

[14]  S. M. Moghadas, T. N. Vilches, K. Zhang, S. Nourbakhsh, P. Sah, M. C. Fitzpatrick, and A. P. Galvani, “Evaluation of covid-19 vaccination strategies with a delayed second dose,” PLoS biology, vol. 19, no. 4, p. e3001211, 2021.

[15]  S. M. Moghadas, M. C. Fitzpatrick, A. Shoukat, K. Zhang, and A. P. Galvani, “Simulated identification of silent covid-19 infections among children and estimated future infection rates with vaccination,” JAMA network open, vol. 4, no. 4, pp. e217097–e217097, 2021.

[16]  P. Sah, T. N. Vilches, S. M. Moghadas, M. C. Fitzpatrick, B. H. Singer, P. J. Hotez, and A. P. Galvani, “Accelerated vaccine rollout is imperative to mitigate highly transmissible covid-19 variants,” EClinicalMedicine, vol. 35, p. 100865, 2021.

[17] C. M. Saad-Roy, N. Arinaminpathy, N. S. Wingreen, S. A. Levin, J. M. Akey, and B. T. Grenfell, “Implications of localized charge for human influenza a h1n1 hemagglutinin evolution: Insights from deep mutational scans,” PLoS computational biology, vol. 16, no. 6, p. e1007892, 2020.

[18] G. Lin, A. T. Strauss, M. Pinz, D. A. Martinez, K. K. Tseng, E. Schueller, O. Gatalo, Y. Yang, S. A. Levin, E. Y. Klein, et al., “Explaining the “bomb-like” dynamics of covid-19 with modeling and the implications for policy,” medRxiv, 2020.

[19] F. Haghpanah, G. Lin, S. Levin, and E. Y. Klein, “Analysis of the potential efficacy and timing of covid-19 vaccine on morbidity and mortality,” eClinicalMedicine, 2021

[20] C. M. Saad-Roy, B. T. Grenfell, S. A. Levin, L. Pellis, H. B. Stage, P. van den Driessche, and N. S. Wingreen, “Superinfection and the evolution of an initial asymptomatic stage,” Royal Society open science, vol. 8, no. 1, p. 202212, 2021.

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[26] C. E. Wagner, J. A. Prentice, C. M. Saad-Roy, L. Yang, B. T. Grenfell, S. A. Levin, and R. Laxminarayan, “Economic and behavioral influencers of vaccination and antimicrobial use,” Frontiers in public health, vol. 8, p. 975, 2020.

[27] M. Marathe, A. Vullikanti, D. Rosenkratz, S. Ravi, R. Stearns, and S. Levin, “Computational challenges and opportunities for forecasting epidemic dynamics using network models,” 2020.

[28]  J. P. Townsend, H. B. Hassler, Z. Wang, S. Miura, J. Singh, S. Kumar, N. H. Ruddle, A. P. Galvani, and A. Dornburg, “The durability of immunity against reinfection by sars-cov-2: a comparative evolutionary study,” The Lancet Microbe, vol. 2, no. 12, pp. e666–e675, 2021.

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[30] R. Laxminarayan, S. Jameel, and S. Sarkar, “India’s battle against covid-19: Progress and challenges,” The American Journal of Tropical Medicine and Hygiene, vol. 103, no. 4, p. 1343, 2020.

[31] S. M. Moghadas, M. C. Fitzpatrick, P. Sah, A. Pandey, A. Shoukat, B. H. Singer, and A. P. Galvani, “The implications of silent transmission for the control of covid-19 outbreaks,” Proceedings of the National Academy of Sciences, vol. 117, no. 30, pp. 17513–17515, 2020.

The risk factors and disease burden associated with COVID-19 remain poorly understood. In order to assess predictors of infection and mortality within an active surveillance study, case-fatality and infection-fatality ratios on the basis of age-specific seroprevalence were estimated in [1]. Data collected under expanded programmatic surveillance testing for SARS-CoV-2 in the district of Madurai, Tamil Nadu, India was used to assess the completeness of case and mortality surveillance. Equal risk of asymptomatic infection among children, teenagers, and working-age adults, and increased risk of infection and death associated with older age and co-morbidities were identified. Among RT-PCR-confirmed cases, older age, male sex, and history of cancer, diabetes, other endocrine dis- orders, hypertension, other chronic circulatory disorders, respiratory disorders, and chronic kidney disease were each associated with an elevated risk of mortality. These results helped establish whether surveillance practices or differences in infection severity account for gaps between observed and expected mortality is of crucial importance to establishing the burden of COVID-19 in India.

In this other study [2], changes in mortality during the pandemic in Chennai, Tamil Nadu, using data on all-cause mortality within the district were assessed. The study found that reported COVID-19 deaths greatly underestimated pandemic-associated mortality, with the greatest burden concentrated in disadvantaged communities. Neighborhoods with lower socioeconomic status had increases in pandemic-associated mortality with increases in each measure of community disadvantage, due largely to a disproportionate increase in mortality within these neighborhoods during the second wave. Conversely, differences in excess mortality across communities were not clearly associated with socioeconomic status measures during the first wave. Where the greatest reductions in mortality during this early lockdown period were observed among men aged 20–29 years with fewer deaths than expected from pre-pandemic trends. This study shows that socioeconomically disadvantaged communities shouldered a greater burden of deaths during the pandemic in Chennai than higher-resource communities, although non-pharmaceutical interventions might have reduced deaths due to certain causes before widespread SARS-CoV-2 transmission was underway.

The work in [3] details the optimal testing frequency and coverage in the US and India to mitigate an emerging outbreak even in a vaccinated population: overall, maximizing frequency is more important, but high coverage remains necessary when there is sustained transmission. The study shows that a resource-limited vaccination strategy still requires high-frequency testing and is more effective in India than in the United States. Moreover, the relative importance of frequency versus coverage differs by setting and the type of test used. Notably, at lower coverages, increasing frequency is more beneficial than increasing coverage. Consequently, the study suggests that with limited resources, frequency should be prioritized unless coverage can be increased beyond half of the population surveilled. In other words, the trade-off between frequency and coverage should be tailored to community needs. When given a constant budget constraint, since antigen testing is not only more effective but also substantially cheaper than the use of RT-PCR assays, antigen testing can be done more frequently or at wider coverage and result in fewer cases than the use of RT-PCR assays.

Vaccination provides a powerful tool for mitigating and controlling the COVID-19 pandemic. However, a number of factors reduce these potential benefits. By extending recent models of SARS-CoV-2 dynamics, the Princeton team studied the number of cases and potential for viral evolution in two hypothetical regions, one with high access and one with low access to vaccines is studied. By exploring variations in the strength and duration of natural and vaccine-induced immunity–aspects of the virus and host response that remain uncertain, different immuno-epidemiological scenarios of SARS-CoV-2 are studied, focusing on medium- and long-term dynamics in both regions as a function of the fraction of vaccines shared. Vaccine-sharing scenarios are incorporated in two countries whose infection dynamics are either otherwise independent or coupled through the immigration of infectious individuals and evolution-driven increases in transmission rates. The models indicate that the prompt redistribution of vaccine surpluses is likely advantageous in terms of epidemiological and evolutionary outcomes in both countries and, by extension, globally [4]. The combination of infection of remaining susceptible individuals and breakthrough infections of vaccinees can have significant effects in promoting infection of invading variants, even when vaccination rates are high and onward transmission from vaccinees relatively weak. In [5] the Princeton team, show how heterogeneities in immunity and mixing between vaccinated and unvaccinated sub-populations modulate these effects. These results indicate that high vaccination coverage still leaves no room for complacency if variants are circulating that can elude immunity, even if this happens at very low rates. Where a susceptible epidemic can potentiate vaccine breakthroughs even when the reproduction ratio for vaccinees is less than unity. The simple invasion model illustrates a possible future for highly vaccinated countries in a world of vaccine nationalism: a series of new invading variants with ensuing epidemics and a scramble to revaccinate.

With an evolutionary-epidemiological model, the role of population structure on the evolutionary dynamics of latency is explored in [6]. The study found that simple population heterogeneity can lead to local evolutionarily stable strategies (ESSs) at zero and infinite latency in situations where a unique ESS exists in the corresponding homogeneous case. Furthermore, there can exist more than one interior evolutionarily singular strategy. Moreover, the diversity of outcomes is due to the (possibly slight) advantage of across-group transmission for pathogens that produce fewer symptoms in the first infectious stage. This work reveals that allowing individuals without symptoms to travel can have important unintended evolutionary effects and is thus fundamentally problematic in view of the evolutionary dynamics of latency.

In [7], 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 a larger impact on 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 to reach 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 [8], 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 [9], 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 between 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 in curtailing transmission but also in 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 [10], we use an individual-based model and national-level epidemic simulations to estimate the medical costs of keeping the US economy open during the COVID-19 pandemic under different counterfactual scenarios. We model an unmitigated scenario and 12 mitigation scenarios that 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 orders. 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 on controlling additional deaths.

In [11], we measure the epidemiological and economic impact of COVID-19 spread in the US under different mitigation scenarios, comprising 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 on each sector arising from morbidity, mortality, and lockdown, 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 with 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 highly valued jobs such as Professional Services, even after the teleworkability of jobs is accounted for. Additionally, the findings show that low compliance to interventions can be overcome by a longer shutdown period and vice versa to arrive at a 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 [12], 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.

Team member Alexander has worked closely with the Botswana government in supporting their response efforts to COVID-19, as well as other health problems in the following ways: (i) Served on the Botswana Presidential Covid Task Force as a Scientific advisor, (ii) Led the government team in investigating a Elephant mass mortality event, (iii) Participated in mortality investigation for dwarf mongoose, (iv) participated in Diarrheal disease outbreak investigation, with the Kasane Primary Hospital, (v) Provided assistance with screening patients for salmonella and Campylobacter, (vi) Responded to a poisoning event involving white back vultures for the Department of Wildlife and National Parks, and (vii) Gave a keynote at the Botswana Biodiversity Symposium.

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[2]  J. A. Lewnard, A. Mahmud, T. Narayan, B. Wahl, T. Selvavinayagam, R. Laxminarayan, et al., “All-cause mortality during the covid-19 pandemic in chennai, india: an observational study,” The Lancet Infectious Diseases, 2021.

[3]  C. K. Kumar, R. Balasubramanian, S. Ongarello, S. Carmona, and R. Laxminarayan, “Sars-cov-2 testing strategies for outbreak mitigation in vaccinated populations,” medRxiv, 2022.

[4]  C. E. Wagner, C. M. Saad-Roy, S. E. Morris, R. E. Baker, M. J. Mina, J. Farrar, E. C. Holmes, O. G. Pybus, A. L. Graham, E. J. Emanuel, et al., “Vaccine nationalism and the dynamics and control of sars-cov-2,” Science, vol. 373, no. 6562, p. eabj7364, 2021.

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[6] C. M. Saad-Roy, B. T. Grenfell, S. A. Levin, P. Van Den Driessche, and N. S. Wingreen, “Evolution of an asymptomatic first stage of infection in a heterogeneous population,” Journal of the Royal Society Interface, vol. 18, no. 179, p. 20210175, 2021.

[7] A. Pilehvari, W. You, J. Chen, S. Venkatramanan, J. Krulick, and A. Marathe, “Differential impact of social distancing on covid-19 spread in the us: by rurality and social vulnerability,” 2021. Submitted.

[8] S. M. Moghadas, T. N. Vilches, K. Zhang, C. R. Wells, A. Shoukat, B. H. Singer, L. A. Meyers, K. M. Neuzil, J. M. Langley, M. C. Fitzpatrick, et al., “The impact of vaccination on covid-19 outbreaks in the united states,” Clinical Infectious Diseases, pp. 2257–2264, 2021.

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[10] J. Chen, A. Vullikanti, S. Hoops, H. Mortveit, B. Lewis, S. Venkatramanan, W. You, S. Eubank, M. Marathe, C. Barrett, and M. A, “Medical costs of keeping the us economy open during covid-19,” Scientific Reports, Oct 2020.

[11] J. Chen, A. Vullikanti, J. Santos, S. Venkatramanan, S. Hoops, H. Mortveit, B. Lewis, W. You, S. Eubank, M. Marathe, C. Barrett, and A. Marathe, “Epidemiological and economic impact of covid-19 in the us,” Nature News, Oct 2021

[12] S. Chang, E. Pierson, P. W. Koh, J. Gerardin, B. Redbird, D. Grusky, and J. Leskovec, “Mobility network models of covid-19 explain inequities and inform reopening,” Nature, vol. 589, no. 7840, p. 82–87, 2020.