Which lockdowns are the best lockdowns? Optimal interventions and the trolley problem in heterogeneous populations (preprint)

Interventions to mitigate the spread of infectious diseases, while succeeding in their goal, have economic and social costs associated with them. These limit the duration and intensity of the interventions. We study a class of interventions which reduce the reproduction number and find the optimal strength of the intervention which minimises the attack rate of an immunity inducing infection. The intervention works by eliminating the overshoot part of an epidemic, and avoids a second-wave of infections. We extend the framework by considering a heterogeneous population and find that the optimal intervention can pose an ethical dilemma for decision and policy makers. This ethical dilemma is shown to be analogous to the trolley problem and we discuss how the dilemma can be avoided.

COVID-19 vaccine coverage targets to inform reopening plans in a low incidence setting (preprint)

Since the emergence of SARS-CoV-2 in 2019 through to mid-2021, much of the Australian population lived in a COVID-19 free environment. This followed the broadly successful implementation of a strong suppression strategy, including international border closures. With the availability of COVID-19 vaccines in early 2021, the national government sought to transition from a state of minimal incidence and strong suppression activities to one of high vaccine coverage and reduced restrictions but with still-manageable transmission. This transition is articulated in the national ``re-opening" plan released in July 2021. Here we report on the dynamic modelling study that directly informed policies within the national re-opening plan including the identification of priority age groups for vaccination, target vaccine coverage thresholds and the anticipated requirements for continued public health measures --- assuming circulation of the Delta SARS-CoV-2 variant. Our findings demonstrated that adult vaccine coverage needed to be at least 70% to minimise public health and clinical impacts following the establishment of community transmission. They also supported the need for continued application of test-trace-isolate-quarantine and social measures during the vaccine roll-out phase and beyond.

The impact of network properties and mixing on control measures and disease-induced herd immunity in epidemic models: a mean-field model perspective (preprint)

The contact structure of a population plays an important role in transmission of infection. Many ``structured models'' capture aspects of the contact structure through an underlying network or a mixing matrix. An important observation in such models, is that once a fraction $1-1/\mathcal{R}_0$ has been infected, the residual susceptible population can no longer sustain an epidemic. A recent observation of some structured models is that this threshold can be crossed with a smaller fraction of infected individuals, because the disease acts like a targeted vaccine, preferentially immunizing higher-risk individuals who play a greater role in transmission. Therefore, a limited ``first wave'' may leave behind a residual population that cannot support a second wave once interventions are lifted. In this paper, we systematically analyse a number of mean-field models for networks and other structured populations to address issues relevant to the Covid-19 pandemic. In particular, we consider herd-immunity under several scenarios. We confirm that, in networks with high degree heterogeneity, the first wave confers herd-immunity with significantly fewer infections than equivalent models with lower degree heterogeneity. However, if modelling the intervention as a change in the contact network, then this effect might become more subtle. Indeed, modifying the structure can shield highly connected nodes from becoming infected during the first wave and make the second wave more substantial. We confirm this finding by using an age-structured compartmental model parameterised with real data and comparing lockdown periods implemented either as a global scaling of the mixing matrix or age-specific structural changes. We find that results regarding herd immunity levels are strongly dependent on the model, the duration of lockdown and how lockdown is implemented.

Key Questions for Modelling COVID-19 Exit Strategies (preprint)

Combinations of intense non-pharmaceutical interventions ('lockdowns') were introduced in countries worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement lockdown exit strategies that allow restrictions to be relaxed while attempting to control the risk of a surge in cases. Mathematical modelling has played a central role in guiding interventions, but the challenge of designing optimal exit strategies in the face of ongoing transmission is unprecedented. Here, we report discussions from the Isaac Newton Institute 'Models for an exit strategy' workshop (11-15 May 2020). A diverse community of modellers who are providing evidence to governments worldwide were asked to identify the main questions that, if answered, will allow for more accurate predictions of the effects of different exit strategies. Based on these questions, we propose a roadmap to facilitate the development of reliable models to guide exit strategies. The roadmap requires a global collaborative effort from the scientific community and policy-makers, and is made up of three parts: i) improve estimation of key epidemiological parameters; ii) understand sources of heterogeneity in populations; iii) focus on requirements for data collection, particularly in Low-to-Middle-Income countries. This will provide important information for planning exit strategies that balance socio-economic benefits with public health.

A Data-Driven Network Model for the Emerging COVID-19 Epidemics in Wuhan, Toronto and Italy (preprint)

The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modelling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the reported data for the COVID-19 epidemic in Wuhan (China), Toronto (Canada), and the Italian Republic using a Markov Chain Monte Carlo (MCMC) optimization algorithm. Our model fits all three regions well with narrow confidence intervals and could be adapted to simulate other megacities or regions. The model projections on the role of containment strategies can help inform public health authorities to plan control measures.

Stochasticity and heterogeneity in the transmission dynamics of SARS-CoV-2 (preprint)

SARS-CoV-2 causing COVID-19 disease has moved rapidly around the globe, infecting millions and killing hundreds of thousands. The basic reproduction number, which has been widely used and misused to characterize the transmissibility of the virus, hides the fact that transmission is stochastic, is dominated by a small number of individuals, and is driven by super-spreading events (SSEs). The distinct transmission features, such as high stochasticity under low prevalence, and the central role played by SSEs on transmission dynamics, should not be overlooked. Many explosive SSEs have occurred in indoor settings stoking the pandemic and shaping its spread, such as long-term care facilities, prisons, meat-packing plants, fish factories, cruise ships, family gatherings, parties and night clubs. These SSEs demonstrate the urgent need to understand routes of transmission, while posing an opportunity that outbreak can be effectively contained with targeted interventions to eliminate SSEs. Here, we describe the potential types of SSEs, how they influence transmission, and give recommendations for control of SARS-CoV-2.

The risk of SARS-CoV-2 transmission in the healthcare setting and potential impact of cohorting strategies (preprint)

Background Since its onset, the COVID-19 pandemic has caused significant morbidity and mortality worldwide, with particularly severe outcomes in healthcare institutions and congregate settings. To mitigate spread, healthcare systems have been cohorting patients to limit contacts between uninfected patients and potentially infected patients or healthcare workers (HCWs). A major challenge in managing the pandemic is the presence of currently asymptomatic individuals capable of transmitting the virus, who could introduce COVID-19 into uninfected cohorts. The optimal combination of personal protective equipment (PPE) and testing approaches to prevent these events is unclear, especially in light of ongoing limitations in access to both. Methods Using stochastic simulations with an SEIR model we quantified and compared the impacts of PPE use, patient and HCWs testing, and cohorting. Findings In the base case without testing or PPE, the healthcare system was rapidly overwhelmed, and became a net contributor to the force of infection. We found that effective use of PPE by both HCWs and patients could prevent this scenario, while random testing of apparently asymptomatic individuals on a weekly basis was less effective. We also found that even imperfect use of PPE could provide substantial protection by decreasing the force of infection, and that creation of smaller patient/HCW subcohorts can provide additional resilience to outbreak development. Interpretation These findings reinforce the importance of ensuring adequate PPE supplies even in the absence of testing, and provide support for strict subcohorting regimens to reduce outbreak potential in healthcare institutions.