Modelling the viral dynamics of the SARS-CoV-2 Delta and Omicron variants in different cell types.

We use viral kinetic models fitted to viral load data from in vitro studies to explain why the SARS-CoV-2 Omicron variant replicates faster than the Delta variant in nasal cells, but slower than Delta in lung cells, which could explain Omicron's higher transmission potential and lower severity. We find that in both nasal and lung cells, viral infectivity is higher for Omicron but the virus production rate is higher for Delta, with an estimated approximately 200-fold increase in infectivity and 100-fold decrease in virus production when comparing Omicron with Delta in nasal cells. However, the differences are unequal between cell types, and ultimately lead to the basic reproduction number and growth rate being higher for Omicron in nasal cells, and higher for Delta in lung cells. In nasal cells, Omicron alone can enter via a TMPRSS2-independent pathway, but it is primarily increased efficiency of TMPRSS2-dependent entry which accounts for Omicron's increased activity. This work paves the way for using within-host mathematical models to understand the transmission potential and severity of future variants.

Modelling upper respiratory viral load dynamics of SARS-CoV-2.

Relationships between viral load, severity of illness, and transmissibility of virus are fundamental to understanding pathogenesis and devising better therapeutic and prevention strategies for COVID-19. Here we present within-host modelling of viral load dynamics observed in the upper respiratory tract (URT), drawing upon 2172 serial measurements from 605 subjects, collected from 17 different studies. We developed a mechanistic model to describe viral load dynamics and host response and contrast this with simpler mixed-effects regression analysis of peak viral load and its subsequent decline. We observed wide variation in URT viral load between individuals, over 5 orders of magnitude, at any given point in time since symptom onset. This variation was not explained by age, sex, or severity of illness, and these variables were not associated with the modelled early or late phases of immune-mediated control of viral load. We explored the application of the mechanistic model to identify measured immune responses associated with the control of the viral load. Neutralising antibodies correlated strongly with modelled immune-mediated control of viral load amongst subjects who produced neutralising antibodies. Our models can be used to identify host and viral factors which control URT viral load dynamics, informing future treatment and transmission blocking interventions.

Estimating ventilation rates in rooms with varying occupancy levels: Relevance for reducing transmission risk of airborne pathogens.

BACKGROUND: In light of the role that airborne transmission plays in the spread of SARS-CoV-2, as well as the ongoing high global mortality from well-known airborne diseases such as tuberculosis and measles, there is an urgent need for practical ways of identifying congregate spaces where low ventilation levels contribute to high transmission risk. Poorly ventilated clinic spaces in particular may be high risk, due to the presence of both infectious and susceptible people. While relatively simple approaches to estimating ventilation rates exist, the approaches most frequently used in epidemiology cannot be used where occupancy varies, and so cannot be reliably applied in many of the types of spaces where they are most needed. METHODS: The aim of this study was to demonstrate the use of a non-steady state method to estimate the absolute ventilation rate, which can be applied in rooms where occupancy levels vary. We used data from a room in a primary healthcare clinic in a high TB and HIV prevalence setting, comprising indoor and outdoor carbon dioxide measurements and head counts (by age), taken over time. Two approaches were compared: approach 1 using a simple linear regression model and approach 2 using an ordinary differential equation model. RESULTS: The absolute ventilation rate, Q, using approach 1 was 2407 l/s [95% CI: 1632-3181] and Q from approach 2 was 2743 l/s [95% CI: 2139-4429]. CONCLUSIONS: We demonstrate two methods that can be used to estimate ventilation rate in busy congregate settings, such as clinic waiting rooms. Both approaches produced comparable results, however the simple linear regression method has the advantage of not requiring room volume measurements. These methods can be used to identify poorly-ventilated spaces, allowing measures to be taken to reduce the airborne transmission of pathogens such as Mycobacterium tuberculosis, measles, and SARS-CoV-2.

Estimating internationally imported cases during the early COVID-19 pandemic.

Early in the COVID-19 pandemic, predictions of international outbreaks were largely based on imported cases from Wuhan, China, potentially missing imports from other cities. We provide a method, combining daily COVID-19 prevalence and flight passenger volume, to estimate importations from 18 Chinese cities to 43 international destinations, including 26 in Africa. Global case importations from China in early January came primarily from Wuhan, but the inferred source shifted to other cities in mid-February, especially for importations to African destinations. We estimate that 10.4 (6.2 - 27.1) COVID-19 cases were imported to these African destinations, which exhibited marked variation in their magnitude and main sources of importation. We estimate that 90% of imported cases arrived between 17 January and 7 February, prior to the first case detections. Our results highlight the dynamic role of source locations, which can help focus surveillance and response efforts.

Quantifying mechanistic traits of influenza viral dynamics using in vitro data.

When analysing in vitro data, growth kinetics of influenza virus strains are often compared by computing their growth rates, which are sometimes used as proxies for fitness. However, analogous to mathematical models for epidemics, the growth rate can be defined as a function of mechanistic traits: the basic reproduction number (the average number of cells each infected cell infects) and the mean generation time (the average length of a replication cycle). Fitting a model to previously published and newly generated data from experiments in human lung cells, we compared estimates of growth rate, reproduction number and generation time for six influenza A strains. Of four strains in previously published data, A/Canada/RV733/2003 (seasonal H1N1) had the lowest basic reproduction number, followed by A/Mexico/INDRE4487/2009 (pandemic H1N1), then A/Indonesia/05/2005 (spill-over H5N1) and A/Anhui/1/2013 (spill-over H7N9). This ordering of strains was preserved for both generation time and growth rate, suggesting a positive biological correlation between these quantities which have not been previously observed. We further investigated these potential correlations using data from reassortant viruses with different internal proteins (from A/England/195/2009 (pandemic H1N1) and A/Turkey/05/2005 (H5N1)), and the same surface proteins (from A/Puerto Rico/8/34 (lab-adapted H1N1)). Similar correlations between traits were observed for these viruses, confirming our initial findings and suggesting that these patterns were related to the degree of human adaptation of internal genes. Also, the model predicted that strains with a smaller basic reproduction number, shorter generation time and slower growth rate underwent more replication cycles by the time of peak viral load, potentially accumulating mutations more quickly. These results illustrate the utility of mathematical models in inferring traits driving observed differences in in vitro growth of influenza strains.

Influencing public health policy with data-informed mathematical models of infectious diseases: Recent developments and new challenges.

Modern data and computational resources, coupled with algorithmic and theoretical advances to exploit these, allow disease dynamic models to be parameterised with increasing detail and accuracy. While this enhances models' usefulness in prediction and policy, major challenges remain. In particular, lack of identifiability of a model's parameters may limit the usefulness of the model. While lack of parameter identifiability may be resolved through incorporation into an inference procedure of prior knowledge, formulating such knowledge is often difficult. Furthermore, there are practical challenges associated with acquiring data of sufficient quantity and quality. Here, we discuss recent progress on these issues.

Estimating internationally imported cases during the early COVID-19 pandemic.

Early in the COVID-19 pandemic, when cases were predominantly reported in the city of Wuhan, China, local outbreaks in Europe, North America, and Asia were largely predicted from imported cases on flights from Wuhan, potentially missing imports from other key source cities. Here, we account for importations from Wuhan and from other cities in China, combining COVID-19 prevalence estimates in 18 Chinese cities with estimates of flight passenger volume to predict for each day between early December 2019 to late February 2020 the number of cases exported from China. We predict that the main source of global case importation in early January was Wuhan, but due to the Wuhan lockdown and the rapid spread of the virus, the main source of case importation from mid February became Chinese cities outside of Wuhan. For destinations in Africa in particular, non-Wuhan cities were an important source of case imports (1 case from those cities for each case from Wuhan, range of model scenarios: 0.1-9.8). Our model predicts that 18.4 (8.5 - 100) COVID-19 cases were imported to 26 destination countries in Africa, with most of them (90%) predicted to have arrived between 7th January (±10 days) and 5th February (±3 days), and all of them predicted prior to the first case detections. We finally observed marked heterogeneities in expected imported cases across those locations. Our estimates shed light on shifting sources and local risks of case importation which can help focus surveillance efforts and guide public health policy during the final stages of the pandemic. We further provide a time window for the seeding of local epidemics in African locations, a key parameter for estimating expected outbreak size and burden on local health care systems and societies, that has yet to be defined in these locations.

Sequential infection experiments for quantifying innate and adaptive immunity during influenza infection.

Laboratory models are often used to understand the interaction of related pathogens via host immunity. For example, recent experiments where ferrets were exposed to two influenza strains within a short period of time have shown how the effects of cross-immunity vary with the time between exposures and the specific strains used. On the other hand, studies of the workings of different arms of the immune response, and their relative importance, typically use experiments involving a single infection. However, inferring the relative importance of different immune components from this type of data is challenging. Using simulations and mathematical modelling, here we investigate whether the sequential infection experiment design can be used not only to determine immune components contributing to cross-protection, but also to gain insight into the immune response during a single infection. We show that virological data from sequential infection experiments can be used to accurately extract the timing and extent of cross-protection. Moreover, the broad immune components responsible for such cross-protection can be determined. Such data can also be used to infer the timing and strength of some immune components in controlling a primary infection, even in the absence of serological data. By contrast, single infection data cannot be used to reliably recover this information. Hence, sequential infection data enhances our understanding of the mechanisms underlying the control and resolution of infection, and generates new insight into how previous exposure influences the time course of a subsequent infection.

The distribution of the time taken for an epidemic to spread between two communities.

Assessing the risk of disease spread between communities is important in our highly connected modern world. However, the impact of disease- and population-specific factors on the time taken for an epidemic to spread between communities, as well as the impact of stochastic disease dynamics on this spreading time, are not well understood. In this study, we model the spread of an acute infection between two communities ('patches') using a susceptible-infectious-removed (SIR) metapopulation model. We develop approximations to efficiently evaluate the probability of a major outbreak in a second patch given disease introduction in a source patch, and the distribution of the time taken for this to occur. We use these approximations to assess how interventions, which either control disease spread within a patch or decrease the travel rate between patches, change the spreading probability and median spreading time. We find that decreasing the basic reproduction number in the source patch is the most effective way of both decreasing the spreading probability, and delaying epidemic spread to the second patch should this occur. Moreover, we show that the qualitative effects of interventions are the same regardless of the approximations used to evaluate the spreading time distribution, but for some regions in parameter space, quantitative findings depend upon the approximations used. Importantly, if we neglect the possibility that an intervention prevents a large outbreak in the source patch altogether, then intervention effectiveness is not estimated accurately.

Modelling cross-reactivity and memory in the cellular adaptive immune response to influenza infection in the host.

The cellular adaptive immune response plays a key role in resolving influenza infection. Experiments where individuals are successively infected with different strains within a short timeframe provide insight into the underlying viral dynamics and the role of a cross-reactive immune response in resolving an acute infection. We construct a mathematical model of within-host influenza viral dynamics including three possible factors which determine the strength of the cross-reactive cellular adaptive immune response: the initial naive T cell number, the avidity of the interaction between T cells and the epitopes presented by infected cells, and the epitope abundance per infected cell. Our model explains the experimentally observed shortening of a second infection when cross-reactivity is present, and shows that memory in the cellular adaptive immune response is necessary to protect against a second infection.

On the extinction probability in models of within-host infection: the role of latency and immunity.

Not every exposure to virus establishes infection in the host; instead, the small amount of initial virus could become extinct due to stochastic events. Different diseases and routes of transmission have a different average number of exposures required to establish an infection. Furthermore, the host immune response and antiviral treatment affect not only the time course of the viral load provided infection occurs, but can prevent infection altogether by increasing the extinction probability. We show that the extinction probability when there is a time-dependent immune response depends on the chosen form of the model-specifically, on the presence or absence of a delay between infection of a cell and production of virus, and the distribution of latent and infectious periods of an infected cell. We hypothesise that experimentally measuring the extinction probability when the virus is introduced at different stages of the immune response, alongside the viral load which is usually measured, will improve parameter estimates and determine the most suitable mathematical form of the model.

On the Role of CD8+ T Cells in Determining Recovery Time from Influenza Virus Infection.

Myriad experiments have identified an important role for CD8+ T cell response mechanisms in determining recovery from influenza A virus infection. Animal models of influenza infection further implicate multiple elements of the immune response in defining the dynamical characteristics of viral infection. To date, influenza virus models, while capturing particular aspects of the natural infection history, have been unable to reproduce the full gamut of observed viral kinetic behavior in a single coherent framework. Here, we introduce a mathematical model of influenza viral dynamics incorporating innate, humoral, and cellular immune components and explore its properties with a particular emphasis on the role of cellular immunity. Calibrated against a range of murine data, our model is capable of recapitulating observed viral kinetics from a multitude of experiments. Importantly, the model predicts a robust exponential relationship between the level of effector CD8+ T cells and recovery time, whereby recovery time rapidly decreases to a fixed minimum recovery time with an increasing level of effector CD8+ T cells. We find support for this relationship in recent clinical data from influenza A (H7N9) hospitalized patients. The exponential relationship implies that people with a lower level of naive CD8+ T cells may receive significantly more benefit from induction of additional effector CD8+ T cells arising from immunological memory, itself established through either previous viral infection or T cell-based vaccines.

Innate Immunity and the Inter-exposure Interval Determine the Dynamics of Secondary Influenza Virus Infection and Explain Observed Viral Hierarchies.

Influenza is an infectious disease that primarily attacks the respiratory system. Innate immunity provides both a very early defense to influenza virus invasion and an effective control of viral growth. Previous modelling studies of virus-innate immune response interactions have focused on infection with a single virus and, while improving our understanding of viral and immune dynamics, have been unable to effectively evaluate the relative feasibility of different hypothesised mechanisms of antiviral immunity. In recent experiments, we have applied consecutive exposures to different virus strains in a ferret model, and demonstrated that viruses differed in their ability to induce a state of temporary immunity or viral interference capable of modifying the infection kinetics of the subsequent exposure. These results imply that virus-induced early immune responses may be responsible for the observed viral hierarchy. Here we introduce and analyse a family of within-host models of re-infection viral kinetics which allow for different viruses to stimulate the innate immune response to different degrees. The proposed models differ in their hypothesised mechanisms of action of the non-specific innate immune response. We compare these alternative models in terms of their abilities to reproduce the re-exposure data. Our results show that 1) a model with viral control mediated solely by a virus-resistant state, as commonly considered in the literature, is not able to reproduce the observed viral hierarchy; 2) the synchronised and desynchronised behaviour of consecutive virus infections is highly dependent upon the interval between primary virus and challenge virus exposures and is consistent with virus-dependent stimulation of the innate immune response. Our study provides the first mechanistic explanation for the recently observed influenza viral hierarchies and demonstrates the importance of understanding the host response to multi-strain viral infections. Re-exposure experiments provide a new paradigm in which to study the immune response to influenza and its role in viral control.

Interval Between Infections and Viral Hierarchy Are Determinants of Viral Interference Following Influenza Virus Infection in a Ferret Model.

BACKGROUND: Epidemiological studies suggest that, following infection with influenza virus, there is a short period during which a host experiences a lower susceptibility to infection with other influenza viruses. This viral interference appears to be independent of any antigenic similarities between the viruses. We used the ferret model of human influenza to systematically investigate viral interference. METHODS: Ferrets were first infected then challenged 1-14 days later with pairs of influenza A(H1N1)pdm09, influenza A(H3N2), and influenza B viruses circulating in 2009 and 2010. RESULTS: Viral interference was observed when the interval between initiation of primary infection and subsequent challenge was <1 week. This effect was virus specific and occurred between antigenically related and unrelated viruses. Coinfections occurred when 1 or 3 days separated infections. Ongoing shedding from the primary virus infection was associated with viral interference after the secondary challenge. CONCLUSIONS: The interval between infections and the sequential combination of viruses were important determinants of viral interference. The influenza viruses in this study appear to have an ordered hierarchy according to their ability to block or delay infection, which may contribute to the dominance of different viruses often seen in an influenza season.

Fast deterministic ptychographic imaging using X-rays.

We present a deterministic approach to the ptychographic retrieval of the wave at the exit surface of a specimen of condensed matter illuminated by X-rays. The method is based on the solution of an overdetermined set of linear equations, and is robust to measurement noise. The set of linear equations is efficiently solved using the conjugate gradient least-squares method implemented using fast Fourier transforms. The method is demonstrated using a data set obtained from a gold-chromium nanostructured test object. It is shown that the transmission function retrieved by this linear method is quantitatively comparable with established methods of ptychography, with a large decrease in computational time, and is thus a good candidate for real-time reconstruction.