Ethical frameworks should be applied to computational modelling of infectious disease interventions.

This perspective is part of an international effort to improve epidemiological models with the goal of reducing the unintended consequences of infectious disease interventions. The scenarios in which models are applied often involve difficult trade-offs that are well recognised in public health ethics. Unless these trade-offs are explicitly accounted for, models risk overlooking contested ethical choices and values, leading to an increased risk of unintended consequences. We argue that such risks could be reduced if modellers were more aware of ethical frameworks and had the capacity to explicitly account for the relevant values in their models. We propose that public health ethics can provide a conceptual foundation for developing this capacity. After reviewing relevant concepts in public health and clinical ethics, we discuss examples from the COVID-19 pandemic to illustrate the current separation between public health ethics and infectious disease modelling. We conclude by describing practical steps to build the capacity for ethically aware modelling. Developing this capacity constitutes a critical step towards ethical practice in computational modelling of public health interventions, which will require collaboration with experts on public health ethics, decision support, behavioural interventions, and social determinants of health, as well as direct consultation with communities and policy makers.

Large age shifts in HIV-1 incidence patterns in KwaZulu-Natal, South Africa.

Recent declines in adult HIV-1 incidence have followed the large-scale expansion of antiretroviral therapy and primary HIV prevention across high-burden communities of sub-Saharan Africa. Mathematical modeling suggests that HIV risk will decline disproportionately in younger adult age-groups as interventions scale, concentrating new HIV infections in those >age 25 over time. Yet, no empirical data exist to support these projections. We conducted a population-based cohort study over a 16-y period (2004 to 2019), spanning the early scale-up of antiretroviral therapy and voluntary medical male circumcision, to estimate changes in the age distribution of HIV incidence in a hyperepidemic region of KwaZulu-Natal, South Africa, where adult HIV incidence has recently declined. Median age of HIV seroconversion increased by 5.5 y in men and 3.0 y in women, and the age of peak HIV incidence increased by 5.0 y in men and 2.0 y in women. Incidence declined disproportionately among young men (64% in men 15 to 19, 68% in men 20 to 24, and 46% in men 25 to 29) and young women (44% in women 15 to 19, 24% in women 20 to 24) comparing periods pre- versus post-universal test and treat. Incidence was stable (<20% change) in women aged 30 to 39 and men aged 30 to 34. Age shifts in incidence occurred after 2012 and were observed earlier in men than in women. These results provide direct epidemiological evidence of the changing demographics of HIV risk in sub-Saharan Africa in the era of large-scale treatment and prevention. More attention is needed to address lagging incidence decline among older individuals.

COVID-19 vaccine coverage targets to inform reopening plans in a low incidence setting.

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 60% to minimize 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.

Superspreading events in the transmission dynamics of SARS-CoV-2: Opportunities for interventions and control.

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), the etiological agent of the Coronavirus Disease 2019 (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-appropriately and less appropriately-to characterize the transmissibility of the virus, hides the fact that transmission is stochastic, often dominated by a small number of individuals, and heavily influenced by superspreading events (SSEs). The distinct transmission features of SARS-CoV-2, e.g., high stochasticity under low prevalence (as compared to other pathogens, such as influenza), and the central role played by SSEs on transmission dynamics cannot 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, produce processing facilities, fish factories, cruise ships, family gatherings, parties, and nightclubs. These SSEs demonstrate the urgent need to understand routes of transmission, while posing an opportunity to effectively contain outbreaks with targeted interventions to eliminate SSEs. Here, we describe the different types of SSEs, how they influence transmission, empirical evidence for their role in the COVID-19 pandemic, and give recommendations for control of SARS-CoV-2.

Optimal timing of one-shot interventions for epidemic control.

The interventions and outcomes in the ongoing COVID-19 pandemic are highly varied. The disease and the interventions both impose costs and harm on society. Some interventions with particularly high costs may only be implemented briefly. The design of optimal policy requires consideration of many intervention scenarios. In this paper we investigate the optimal timing of interventions that are not sustainable for a long period. Specifically, we look at at the impact of a single short-term non-repeated intervention (a "one-shot intervention") on an epidemic and consider the impact of the intervention's timing. To minimize the total number infected, the intervention should start close to the peak so that there is minimal rebound once the intervention is stopped. To minimise the peak prevalence, it should start earlier, leading to initial reduction and then having a rebound to the same prevalence as the pre-intervention peak rather than one very large peak. To delay infections as much as possible (as might be appropriate if we expect improved interventions or treatments to be developed), earlier interventions have clear benefit. In populations with distinct subgroups, synchronized interventions are less effective than targeting the interventions in each subcommunity separately.

Protective impacts of household-based tuberculosis contact tracing are robust across endemic incidence levels and community contact patterns.

There is an emerging consensus that achieving global tuberculosis control targets will require more proactive case finding approaches than are currently used in high-incidence settings. Household contact tracing (HHCT), for which households of newly diagnosed cases are actively screened for additional infected individuals is a potentially efficient approach to finding new cases of tuberculosis, however randomized trials assessing the population-level effects of such interventions in settings with sustained community transmission have shown mixed results. One potential explanation for this is that household transmission is responsible for a variable proportion of population-level tuberculosis burden between settings. For example, transmission is more likely to occur in households in settings with a lower tuberculosis burden and where individuals mix preferentially in local areas, compared with settings with higher disease burden and more dispersed mixing. To better understand the relationship between endemic incidence levels, social mixing, and the impact of HHCT, we developed a spatially explicit model of coupled household and community transmission. We found that the impact of HHCT was robust across settings of varied incidence and community contact patterns. In contrast, we found that the effects of community contact tracing interventions were sensitive to community contact patterns. Our results suggest that the protective benefits of HHCT are robust and the benefits of this intervention are likely to be maintained across epidemiological settings.

The Impact of Contact Structure and Mixing on Control Measures and Disease-Induced Herd Immunity in Epidemic Models: A Mean-Field Model Perspective.

The contact structure of a population plays an important role in transmission of infection. Many 'structured models' capture aspects of the contact pattern through an underlying network or a mixing matrix. An important observation in unstructured models of a disease that confers immunity is that once a fraction [Formula: see text] 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 immunising 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 set out to investigate this more systematically. While networks offer a flexible framework to model contact patterns explicitly, they suffer from several shortcomings: (i) high-fidelity network models require a large amount of data which can be difficult to harvest, and (ii) very few, if any, theoretical contact network models offer the flexibility to tune different contact network properties within the same framework. Therefore, we opt to systematically analyse a number of well-known mean-field models. These are computationally efficient and provide good flexibility in varying contact network properties such as heterogeneity in the number contacts, clustering and household structure or differentiating between local and global contacts. In particular, we consider the question of herd immunity under several scenarios. When modelling interventions as changes in transmission rates, we confirm that in networks with significant degree heterogeneity, the first wave of the epidemic confers herd immunity with significantly fewer infections than equivalent models with less or no degree heterogeneity. However, if modelling the intervention as a change in the contact network, then this effect may become much more subtle. Indeed, modifying the structure disproportionately can shield highly connected nodes from becoming infected during the first wave and therefore make the second wave more substantial. We strengthen 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. Overall, we find that results regarding (disease-induced) herd immunity levels are strongly dependent on the model, the duration of the lockdown and how the lockdown is implemented in the model.

Approximating Quasi-Stationary Behaviour in Network-Based SIS Dynamics.

Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relate to the underlying stochastic dynamics, which has no endemic steady-state but can exhibit approximately stable behaviour. Here, we relate the approximate models to the stochastic dynamics via the definition of the quasi-stationary distribution (QSD), which captures this approximately stable behaviour. We develop a system of ordinary differential equations that approximate the number of infected individuals in the QSD for arbitrary contact networks and parameter values. When the epidemic level is high, these QSD approximations coincide with the existing approximation methods. However, as we approach the epidemic threshold, the models deviate, with these models following the QSD and the existing methods approaching the all susceptible state. Through consistently approximating the QSD, the proposed methods provide a more robust link to the stochastic models.

Key questions for modelling COVID-19 exit strategies.

Combinations of intense non-pharmaceutical interventions (lockdowns) were introduced worldwide to reduce SARS-CoV-2 transmission. Many governments have begun to implement exit strategies that relax restrictions 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, would 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. This roadmap requires a global collaborative effort from the scientific community and policymakers, and has three parts: (i) improve estimation of key epidemiological parameters; (ii) understand sources of heterogeneity in populations; and (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.

Seasonality in risk of pandemic influenza emergence.

Influenza pandemics can emerge unexpectedly and wreak global devastation. However, each of the six pandemics since 1889 emerged in the Northern Hemisphere just after the flu season, suggesting that pandemic timing may be predictable. Using a stochastic model fit to seasonal flu surveillance data from the United States, we find that seasonal flu leaves a transient wake of heterosubtypic immunity that impedes the emergence of novel flu viruses. This refractory period provides a simple explanation for not only the spring-summer timing of historical pandemics, but also early increases in pandemic severity and multiple waves of transmission. Thus, pandemic risk may be seasonal and predictable, with the accuracy of pre-pandemic and real-time risk assessments hinging on reliable seasonal influenza surveillance and precise estimates of the breadth and duration of heterosubtypic immunity.

Edge-Based Compartmental Modelling of an SIR Epidemic on a Dual-Layer Static-Dynamic Multiplex Network with Tunable Clustering.

The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a dual-layer static-dynamic multiplex network. The static network layer affords tunable clustering and describes an individual's permanent community structure. The dynamic network layer describes the transient connections an individual makes with members of the wider population by imposing constant edge rewiring. We follow the edge-based compartmental modelling approach to derive equations describing the evolution of a susceptible-infected-recovered epidemic spreading through this multiplex network of individuals. We derive the basic reproduction number, measuring the expected number of new infectious cases caused by a single infectious individual in an otherwise susceptible population. We validate model equations by showing convergence to pre-existing edge-based compartmental model equations in limiting cases and by comparison with stochastically simulated epidemics. We explore the effects of altering model parameters and multiplex network attributes on resultant epidemic dynamics. We validate the basic reproduction number by plotting its value against associated final epidemic sizes measured from simulation and predicted by model equations for a number of set-ups. Further, we explore the effect of varying individual model parameters on the basic reproduction number. We conclude with a discussion of the significance and interpretation of the model and its relation to existing research literature. We highlight intrinsic limitations and potential extensions of the present model and outline future research considerations, both experimental and theoretical.

Mean-field models for non-Markovian epidemics on networks.

This paper introduces a novel extension of the edge-based compartmental model to epidemics where the transmission and recovery processes are driven by general independent probability distributions. Edge-based compartmental modelling is just one of many different approaches used to model the spread of an infectious disease on a network; the major result of this paper is the rigorous proof that the edge-based compartmental model and the message passing models are equivalent for general independent transmission and recovery processes. This implies that the new model is exact on the ensemble of configuration model networks of infinite size. For the case of Markovian transmission the message passing model is re-parametrised into a pairwise-like model which is then used to derive many well-known pairwise models for regular networks, or when the infectious period is exponentially distributed or is of a fixed length.

Ethical dilemma arises from optimizing interventions for epidemics in heterogeneous populations.

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 minimizes the final epidemic size for 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 policymakers. This ethical dilemma is shown to be analogous to the trolley problem. We apply this optimization strategy to real-world contact data and case fatality rates from three pandemics to underline the importance of this ethical dilemma in real-world scenarios.

High connectivity and human movement limits the impact of travel time on infectious disease transmission.

The speed of spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) during the coronavirus disease 2019 (COVID-19) pandemic highlights the importance of understanding how infections are transmitted in a highly connected world. Prior to vaccination, changes in human mobility patterns were used as non-pharmaceutical interventions to eliminate or suppress viral transmission. The rapid spread of respiratory viruses, various intervention approaches, and the global dissemination of SARS-CoV-2 underscore the necessity for epidemiological models that incorporate mobility to comprehend the spread of the virus. Here, we introduce a metapopulation susceptible-exposed-infectious-recovered model parametrized with human movement data from 340 cities in China. Our model replicates the early-case trajectory in the COVID-19 pandemic. We then use machine learning algorithms to determine which network properties best predict spread between cities and find travel time to be most important, followed by the human movement-weighted personalized PageRank. However, we show that travel time is most influential locally, after which the high connectivity between cities reduces the impact of travel time between individual cities on transmission speed. Additionally, we demonstrate that only significantly reduced movement substantially impacts infection spread times throughout the network.

Model hierarchies in edge-based compartmental modeling for infectious disease spread.

We consider the family of edge-based compartmental models for epidemic spread developed in Miller et al. (J R Soc Interface 9(70):890-906, 2012). These models allow for a range of complex behaviors, and in particular allow us to explicitly incorporate duration of a contact into our mathematical models. Our focus here is to identify conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide conditions under which it is appropriate to use the standard mass action SIR model, and we show what happens when these conditions fail. Using our hierarchy, we provide a procedure leading to the choice of the appropriate model for a given population. Our result about the convergence of models to the mass action model gives clear, rigorous conditions under which the mass action model is accurate.

Heterogeneity in network structure switches the dominant transmission mode of infectious diseases.

Several recent emerging diseases have exhibited both sexual and nonsexual transmission modes (Ebola, Zika, and mpox). In the recent mpox outbreaks, transmission through sexual contacts appears to be the dominant mode of transmission. Motivated by this, we use an SIR-like model to argue that an initially dominant sexual transmission mode can be overtaken by casual transmission at later stages, even if the basic casual reproduction number is less than one. Our results highlight the risk of intervention designs which are informed only by the early dynamics of the disease.

If Long-Term Suppression is not Possible, how do we Minimize Mortality for Infectious Disease Outbreaks?

OBJECTIVE: For any emerging pathogen, the preferred approach is to drive it to extinction with non-pharmaceutical interventions (NPI) or suppress its spread until effective drugs or vaccines are available. However, this might not always be possible. If containment is infeasible, the best people can hope for is pathogen transmission until population level immunity is achieved, with as little morbidity and mortality as possible. METHODS: A simple computational model was used to explore how people should choose NPI in a non-containment scenario to minimize mortality if mortality risk differs by age. RESULTS: Results show that strong NPI might be worse overall if they cannot be sustained compared to weaker NPI of the same duration. It was also shown that targeting NPI at different age groups can lead to similar reductions in the total number of infected, but can have strong differences regarding the reduction in mortality. CONCLUSIONS: Strong NPI that can be sustained until drugs or vaccines become available are always preferred for preventing infection and mortality. However, if people encounter a worst-case scenario where interventions cannot be sustained, allowing some infections to occur in lower-risk groups might lead to an overall greater reduction in mortality than trying to protect everyone equally.

Quantifying the impact of individual and collective compliance with infection control measures for ethical public health policy.

Infectious disease control measures often require collective compliance of large numbers of individuals to benefit public health. This raises ethical questions regarding the value of the public health benefit created by individual and collective compliance. Answering these requires estimating the extent to which individual actions prevent infection of others. We develop mathematical techniques enabling quantification of the impacts of individuals or groups complying with three public health measures: border quarantine, isolation of infected individuals, and prevention via vaccination/prophylaxis. The results suggest that (i) these interventions exhibit synergy: They become more effective on a per-individual basis as compliance increases, and (ii) there is often substantial "overdetermination" of transmission. If a susceptible person contacts multiple infectious individuals, an intervention preventing one transmission may not change the ultimate outcome (thus, risk imposed by some individuals may erode the benefits of others' compliance). These results have implications for public health policy during epidemics.

Cholera modeling: challenges to quantitative analysis and predicting the impact of interventions.

Several mathematical models of epidemic cholera have recently been proposed in response to outbreaks in Zimbabwe and Haiti. These models aim to estimate the dynamics of cholera transmission and the impact of possible interventions, with a goal of providing guidance to policy makers in deciding among alternative courses of action, including vaccination, provision of clean water, and antibiotics. Here, we discuss concerns about model misspecification, parameter uncertainty, and spatial heterogeneity intrinsic to models for cholera. We argue for caution in interpreting quantitative predictions, particularly predictions of the effectiveness of interventions. We specify sensitivity analyses that would be necessary to improve confidence in model-based quantitative prediction, and suggest types of monitoring in future epidemic settings that would improve analysis and prediction.

Effects of heterogeneous and clustered contact patterns on infectious disease dynamics.

The spread of infectious diseases fundamentally depends on the pattern of contacts between individuals. Although studies of contact networks have shown that heterogeneity in the number of contacts and the duration of contacts can have far-reaching epidemiological consequences, models often assume that contacts are chosen at random and thereby ignore the sociological, temporal and/or spatial clustering of contacts. Here we investigate the simultaneous effects of heterogeneous and clustered contact patterns on epidemic dynamics. To model population structure, we generalize the configuration model which has a tunable degree distribution (number of contacts per node) and level of clustering (number of three cliques). To model epidemic dynamics for this class of random graph, we derive a tractable, low-dimensional system of ordinary differential equations that accounts for the effects of network structure on the course of the epidemic. We find that the interaction between clustering and the degree distribution is complex. Clustering always slows an epidemic, but simultaneously increasing clustering and the variance of the degree distribution can increase final epidemic size. We also show that bond percolation-based approximations can be highly biased if one incorrectly assumes that infectious periods are homogeneous, and the magnitude of this bias increases with the amount of clustering in the network. We apply this approach to model the high clustering of contacts within households, using contact parameters estimated from survey data of social interactions, and we identify conditions under which network models that do not account for household structure will be biased.