Sufficient reproduction numbers to prevent recurrent epidemics (preprint)

Current practice in the design and evaluation of epidemic control measures, including vaccination, is largely based on reproduction numbers (RNs), which represent prognostic indexes of long-term disease transmission, both in naive populations (basic RN) and in the presence of prior exposure or interventions (effective RN). A standard control objective is to establish herd immunity, e.g., by immunizing enough susceptible individuals to achieve RN<1. However, attaining this goal is not sufficient to avoid transient outbreaks that, in the short term, might revamp epidemics by coalescence of subthreshold flare-ups. Using reactivity analysis applied to a discrete SIR model with age-of-infection structure, we determine sufficient conditions to prevent transient epidemic dynamics and recurrent, non-periodic outbreaks due to imported cases. These conditions are based on fundamental infection characteristics, namely the average infectiousness clearance rate, the generation time distribution, and the RN. We show that preventing subthreshold epidemicity requires stricter RN thresholds than simply maintaining RN<1. Taking into account a wide spectrum of respiratory viral infections, epidemicity-curbing RN thresholds vary between 0.10 (rubella) and 0.51 (MERS), with a median of 0.26 close to the estimate of 0.24 for the ancestral SARS-CoV-2 virus. The portion of the population that needs to be included in containment efforts to avoid short-term outbreaks is considerably higher than herd immunity thresholds (HITs) based solely on the basic RN (e.g., 93% vs. 72% for ancestral SARS-CoV-2). We also find that subthreshold epidemicity is harder to prevent for pathogens with a longer mean generation time, smaller standard deviation of the generation time distribution, longer duration of infection, and higher RN. Determining sufficient RN thresholds to prevent transient outbreaks is a key challenge in disease ecology, with practical consequences for the design of control measures, as the weaker RN reductions and HITs associated with customary control targets may prove ineffective in preventing potentially recurrent flare-ups. Due to its modest data requirements, our modeling framework may also have important implications for human and non-human diseases caused by emerging pathogens.

Optimizing the spatio-temporal allocation of COVID-19 vaccines: Italy as a case study (preprint)

While SARS-CoV-2 vaccine distribution campaigns are underway across the world, communities face the challenge of a fair and effective distribution of limited supplies. We wonder whether suitable spatial allocation strategies might significantly improve a campaigns efficacy in averting damaging outcomes. To that end, we address the problem of optimal control of COVID-19 vaccinations in a country-wide geographic and epidemiological context characterized by strong spatial heterogeneities in transmission rate and disease history. We seek the vaccine allocation strategies in space and time that minimize the number of infections in a prescribed time horizon. We examine scenarios of unfolding disease transmission across the 107 provinces of Italy, from January to April 2021, generated by a spatially explicit compartmental COVID-19 model tailored to the Italian geographic and epidemiological context. We propose a novel optimal control framework to derive optimal vaccination strategies given the epidemiological projections and constraints on vaccine supply and distribution logistic. Optimal schemes significantly outperform the explored alternative allocation strategies based on incidence, population distribution, or prevalence of susceptibles in each province. Our results suggest that the complex interplay between the mobility network and the spatial heterogeneities imply highly non-trivial prioritization of local vaccination campaigns. The extent of the overall improvements in the objectives grants further inquiry aimed at refining other possibly relevant factors so far neglected. Our work thus provides a proof-of-concept of the potential of optimal control for complex and heterogeneous epidemiological contexts at country, and possibly global, scales. Author summaryThe development of vaccines has sparked high hopes towards the control of SARS-CoV-2 transmission without resorting to extensive community-wide restrictions. A fundamental unanswered question concerns the best possible allocation of a limited vaccine stock in space and time given a specific goal. We address this through an optimal control framework based on a reliable spatially explicit COVID-19 epidemiological model, where vaccine distribution is optimized under supply and deployment capacity constraints. This tool provides strategies for optimal allocations in different scenarios, yielding important improvements over considered alternatives. By accounting for spatial heterogeneities and human mobility networks, the presented approach complements currently used allocation methods based on criteria such as age or risk.

Assessing the impact of non-pharmaceutical interventions on SARS-CoV-2 transmission in Switzerland (preprint)

Following the rapid dissemination of COVID-19 cases in Switzerland, large-scale non-pharmaceutical interventions (NPIs) were implemented by the cantons and the federal government between February 28 and March 20. Estimates of the impact of these interventions on SARS-CoV-2 transmission are critical for decision making in this and future outbreaks. We here aim to assess the impact of these NPIs on disease transmission by estimating changes in the basic reproduction number (R0) at national and cantonal levels in relation to the timing of these NPIs. We estimate the time-varying R0 nationally and in twelve cantons by fitting a stochastic transmission model explicitly simulating within hospital dynamics. We use individual-level data of >1,000 hospitalized patients in Switzerland and public daily reports of hospitalizations and deaths. We estimate the national R0 was 3.15 (95% CI: 2.13-3.76) at the start of the epidemic. Starting from around March 6, we find a strong reduction in R0 with a 85% median decrease (95% quantile range, QR: 83%-90%) to a value of 0.44 (95% QR: 0.27-0.65) in the period of March 29-April 5. At the cantonal-level R0 decreased over the course of the epidemic between 71% and 94%. We found that reductions in R0 were synchronous with changes in mobility patterns as estimated through smartphone activity, which started before the official implementation of NPIs. We found that most of the reduction of transmission is due to behavioural changes as opposed to natural immunity, the latter accounting for only about 3% of the total reduction in effective transmission. As Switzerland considers relaxing some of the restrictions of social mixing, current estimates of R0 well below one are promising. However most of inferred transmission reduction was due to behaviour change (<3% due to natural immunity buildup), with an estimated 97% (95% QR: 96.6%-97.2%) of the Swiss population still susceptible to SARS-CoV-2 as of April 24. These results warrant a cautious relaxation of social distance practices and close monitoring of changes in both the basic and effective reproduction numbers.

The geography of COVID-19 spread in Italy and implications for the relaxation of confinement measures (preprint)

We examine the spread of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) in Italy, to address the appropriate methodological choices for the design of selective relaxations of the current containment measures. Pressing relevance stems from the need to restart the economy dramatically affected by the lockdown. We employ a spatially explicit, data-intensive model of the patterns of disease spread in Italy, which devotes proper attention to the paramount role of inapparent infections. We aim at providing tools to: estimate the baseline trajectory, i.e. the expected unfolding of the outbreak if the current containment measures were kept in place indefinitely; assess possible deviations from the baseline, should relaxations of the current lockdown result in increased disease transmission; and estimate the isolation effort required to prevent a resurgence of the outbreak. A 40% increase in effective transmission as a result of the loosening of confinement measures would yield an epidemic curve that shows a major rebound, larger than the previous peaks in most regions. A control effort capable of isolating a daily percentage of approximately 5.5 % of the exposed and highly infectious individuals proves necessary to counterbalance such an increase and maintain the epidemic curve onto the decreasing baseline trajectory. We explore several scenarios, provide the basic data to design the related control strategies, and discuss their feasibility. Should suitable control via tracing and testing prove unfeasible, stop-and-go enforcement or delay of the lockdown relaxations would be necessary to reduce the isolation effort required to maintain the epidemic trajectory under control.