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Viral reproduction of SARS-CoV-2 provides opportunities for the acquisition of advantageous mutations, altering viral transmissibility, disease severity, and/or allowing escape from natural or vaccine-derived immunity. We use three mathematical models: a parsimonious deterministic model with homogeneous mixing; an age-structured model; and a stochastic importation model to investigate the effect of potential variants of concern (VOCs). Calibrating to the situation in England in May 2021, we find epidemiological trajectories for putative VOCs are wide-ranging and dependent on their transmissibility, immune escape capability, and the introduction timing of a postulated VOC-targeted vaccine. We demonstrate that a VOC with a substantial transmission advantage over resident variants, or with immune escape properties, can generate a wave of infections and hospitalisations comparable to the winter 2020-2021 wave. Moreover, a variant that is less transmissible, but shows partial immune-escape could provoke a wave of infection that would not be revealed until control measures are further relaxed. Understanding the potential impacts of new variants of SARS-CoV-2 is important for pandemic planning. Here, the authors develop a model incorporating hypothetical new variants with varying transmissibility and immune evasion properties, and use it to project possible future epidemic waves in the UK.

Early assessments of the growth rate of COVID-19 were subject to significant uncertainty, as expected with limited data and difficulties in case ascertainment, but as cases were recorded in multiple countries, more robust inferences could be made. Using multiple countries, data streams and methods, we estimated that, when unconstrained, European COVID-19 confirmed cases doubled on average every 3 days (range 2.2–4.3 days) and Italian hospital and intensive care unit admissions every 2–3 days; values that are significantly lower than the 5–7 days dominating the early published literature. Furthermore, we showed that the impact of physical distancing interventions was typically not seen until at least 9 days after implementation, during which time confirmed cases could grow eightfold. We argue that such temporal patterns are more critical than precise estimates of the time-insensitive basic reproduction number 𝑅₀ for initiating interventions, and that the combination of fast growth and long detection delays explains the struggle in countries' outbreak response better than large values of 𝑅₀ alone. One year on from first reporting these results, reproduction numbers continue to dominate the media and public discourse, but robust estimates of unconstrained growth remain essential for planning worst-case scenarios, and detection delays are still key in informing the relaxation and re-implementation of interventions. This article is part of the theme issue 'Modelling that shaped the early COVID-19 pandemic response in the UK'.

HIV-1 is a well-studied example of a pathogen that has evolved an intermediate level of virulence that maximises transmission. For a trait to evolve it must be heritable, and although viral load-a proxy for disease severity-has been shown to be a heritable trait, it is surprising that specific heritable viral factors remain mostly elusive. Rapid within-host evolution is also expected to diminish heritability. We hypothesised that rather than a small number of mutations of large effect determining viral load, the number of slightly deleterious mutations could be key. As a proof of principle, we explored how viral load is expected to evolve within and between hosts using a nested modelling approach that links within-host evolution with epidemiological outcomes. For mutations of sufficiently small effect, a mutation-selection balance is gradually reached during infection, resulting in slow changes in viral load despite rapid rates of genomic evolution. In simulated epidemics, we generated realistic population distributions of viral loads and estimates of heritability. The existence of many slightly deleterious mutations provides a mechanism that can help to explain why viral loads change slowly during infection, broad distributions of viral loads among individuals, and why searches for viral factors that determine viral load have had limited success.

The first year of the COVID-19 pandemic put considerable strain on healthcare systems worldwide. In order to predict the effect of the local epidemic on hospital capacity in England, we used a variety of data streams to inform the construction and parameterisation of a hospital progression model, EpiBeds, which was coupled to a model of the generalised epidemic. In this model, individuals progress through different pathways (e.g. may recover, die, or progress to intensive care and recover or die) and data from a partially complete patient-pathway line-list was used to provide initial estimates of the mean duration that individuals spend in the different hospital compartments. We then fitted EpiBeds using complete data on hospital occupancy and hospital deaths, enabling estimation of the proportion of individuals that follow the different clinical pathways, the reproduction number of the generalised epidemic, and to make short-term predictions of hospital bed demand. The construction of EpiBeds makes it straightforward to adapt to different patient pathways and settings beyond England. As part of the UK response to the pandemic, EpiBeds provided weekly forecasts to the NHS for hospital bed occupancy and admissions in England, Wales, Scotland, and Northern Ireland at national and regional scales.

Climate change and anthropogenic activity are currently driving large changes in nutritional availability across ecosystems, with consequences for infectious disease. An increase in host nutrition could lead to more resources for hosts to expend on the immune system or for pathogens to exploit. In this paper, we report a meta-analysis of studies on host–pathogen systems across the tree of life, to examine the impact of host nutritional quality and quantity on pathogen virulence. We did not find broad support across studies for a one-way effect of nutrient availability on pathogen virulence. We thus discuss a hypothesis that there is a balance between the effect of host nutrition on the immune system and on pathogen resources, with the pivot point of the balance differing for vertebrate and invertebrate hosts. Our results suggest that variation in nutrition, caused by natural or anthropogenic factors, can have diverse effects on infectious disease outcomes across species.

The existence of long-lived reservoirs of latently infected CD4+ T cells is the major barrier to curing HIV, and has been extensively studied in this light. However, the effect of these reservoirs on the evolutionary dynamics of the virus has received little attention. Here, we present a within-host quasispecies model that incorporates a long-lived reservoir, which we then nest into an epidemiological model of HIV dynamics. For biologically plausible parameter values, we find that the presence of a latent reservoir can severely delay evolutionary dynamics within a single host, with longer delays associated with larger relative reservoir sizes and/or homeostatic proliferation of cells within the reservoir. These delays can fundamentally change the dynamics of the virus at the epidemiological scale. In particular, the delay in within-host evolutionary dynamics can be sufficient for the virus to evolve intermediate viral loads consistent with maximising transmission, as is observed, and not the very high viral loads that previous models have predicted, an effect that can be further enhanced if viruses similar to those that initiate infection are preferentially transmitted. These results depend strongly on within-host characteristics such as the relative reservoir size, with the evolution of intermediate viral loads observed only when the within-host dynamics are sufficiently delayed. In conclusion, we argue that the latent reservoir has important, and hitherto under-appreciated, roles in both within- and between-host viral evolution.

SARS-CoV-2 has spread across the world, causing high mortality and unprecedented restrictions on social and economic activity. Policymakers are assessing how best to navigate through the ongoing epidemic, with computational models being used to predict the spread of infection and assess the impact of public health measures. Here, we present OpenABM-Covid19: an agent-based simulation of the epidemic including detailed age-stratification and realistic social networks. By default the model is parameterised to UK demographics and calibrated to the UK epidemic, however, it can easily be re-parameterised for other countries. OpenABM-Covid19 can evaluate non-pharmaceutical interventions, including both manual and digital contact tracing, and vaccination programmes. It can simulate a population of 1 million people in seconds per day, allowing parameter sweeps and formal statistical model-based inference. The code is open-source and has been developed by teams both inside and outside academia, with an emphasis on formal testing, documentation, modularity and transparency. A key feature of OpenABM-Covid19 are its Python and R interfaces, which has allowed scientists and policymakers to simulate dynamic packages of interventions and help compare options to suppress the COVID-19 epidemic.

Over calendar time, HIV-1 evolves considerably faster within individuals than it does at the epidemic level. This is a surprising observation since, from basic population genetic theory, we would expect the genetic substitution rate to be similar across different levels of biological organization. Three different mechanisms could potentially cause the observed mismatch in phylogenetic rates of divergence: temporal changes in selection pressure during the course of infection; frequent reversion of adaptive mutations after transmission; and the storage of the virus in the body followed by the preferential transmission of stored ancestral virus. We evaluate each of these mechanisms to determine whether they are likely to make a major contribution to the mismatch in phylogenetic rates. We conclude that the cycling of the virus through very long-lived memory CD4+ T cells, a process that we call ‘store and retrieve’, is probably the major contributing factor to the rate mismatch. The preferential transmission of ancestral virus needs to be integrated into evolutionary models if we are to accurately predict the evolution of immune escape, drug resistance and virulence in HIV-1 at the population level. Moreover, early infection viruses should be the major target for vaccine design, because these are the viral strains primarily involved in transmission.

An important component of pathogen evolution at the population level is evolution within hosts. Unless evolution within hosts is very slow compared to the duration of infection, the composition of pathogen genotypes within a host is likely to change during the course of an infection, thus altering the composition of genotypes available for transmission as infection progresses. We develop a nested modeling approach that allows us to follow the evolution of pathogens at the epidemiological level by explicitly considering within-host evolutionary dynamics of multiple competing strains and the timing of transmission. We use the framework to investigate the impact of short-sighted within-host evolution on the evolution of virulence of human immunodeficiency virus (HIV), and find that the topology of the within-host adaptive landscape determines how virulence evolves at the epidemiological level. If viral reproduction rates increase significantly during the course of infection, the viral population will evolve a high level of virulence even though this will reduce the transmission potential of the virus. However, if reproduction rates increase more modestly, as data suggest, our model predicts that HIV virulence will be only marginally higher than the level that maximizes the transmission potential of the virus.