A target-cell limited model can reproduce influenza infection dynamics in hosts with differing immune responses.

We consider a hierarchy of ordinary differential equation models that describe the within-host viral kinetics of influenza infections: the IR model explicitly accounts for an immune response to the virus, while the simpler, target-cell limited TEIV and TV models do not. We show that when the IR model is fitted to pooled experimental murine data of the viral load, fraction of dead cells, and immune response levels, its parameters values can be determined. However, if, as is common, only viral load data are available, we can estimate parameters of the TEIV and TV models but not the IR model. These results are substantiated by a structural and practical identifiability analysis. We then use the IR model to generate synthetic data representing infections in hosts whose immune responses differ. We fit the TV model to these synthetic datasets and show that it can reproduce the characteristic exponential increase and decay of viral load generated by the IR model. Furthermore, the values of the fitted parameters of the TV model can be mapped from the immune response parameters in the IR model. We conclude that, if only viral load data are available, a simple target-cell limited model can reproduce influenza infection dynamics and distinguish between hosts with differing immune responses.

The risk of SARS-CoV-2 outbreaks in low prevalence settings following the removal of travel restrictions.

Background: Countries around the world have introduced travel restrictions to reduce SARS-CoV-2 transmission. As vaccines are gradually rolled out, attention has turned to when travel restrictions and other non-pharmaceutical interventions (NPIs) can be relaxed. Methods: Using SARS-CoV-2 as a case study, we develop a mathematical branching process model to assess the risk that, following the removal of NPIs, cases arriving in low prevalence settings initiate a local outbreak. Our model accounts for changes in background population immunity due to vaccination. We consider two locations with low prevalence in which the vaccine rollout has progressed quickly - specifically, the Isle of Man (a British crown dependency in the Irish Sea) and the country of Israel. Results: We show that the outbreak risk is unlikely to be eliminated completely when travel restrictions and other NPIs are removed. This general result is the most important finding of this study, rather than exact quantitative outbreak risk estimates in different locations. It holds even once vaccine programmes are completed. Key factors underlying this result are the potential for transmission even following vaccination, incomplete vaccine uptake, and the recent emergence of SARS-CoV-2 variants with increased transmissibility. Conclusions: Combined, the factors described above suggest that, when travel restrictions are relaxed, it may still be necessary to implement surveillance of incoming passengers to identify infected individuals quickly. This measure, as well as tracing and testing (and/or isolating) contacts of detected infected passengers, remains useful to suppress potential outbreaks while global case numbers are high.

Accounting for cross-immunity can improve forecast accuracy during influenza epidemics.

Previous exposure to influenza viruses confers cross-immunity against future infections with related strains. However, this is not always accounted for explicitly in mathematical models used for forecasting during influenza outbreaks. We show that, if an influenza outbreak is due to a strain that is similar to one that has emerged previously, then accounting for cross-immunity explicitly can improve the accuracy of real-time forecasts. To do this, we consider two infectious disease outbreak forecasting models. In the first (the "1-group model"), all individuals are assumed to be identical and cross-immunity is not accounted for. In the second (the "2-group model"), individuals who have previously been infected by a related strain are assumed to be less likely to experience severe disease, and therefore recover more quickly, than immunologically naive individuals. We fit both models to estimated case notification data (including symptomatic individuals as well as laboratory-confirmed cases) from Japan from the 2009 H1N1 influenza pandemic, and then generate synthetic data for a future outbreak by assuming that the 2-group model represents the epidemiology of influenza infections more accurately. We use the 1-group model (as well as the 2-group model for comparison) to generate forecasts that would be obtained in real-time as the future outbreak is ongoing, using parameter values estimated from the 2009 epidemic as informative priors, motivated by the fact that without using prior information from 2009, the forecasts are highly uncertain. In the scenario that we consider, the 1-group model only produces accurate outbreak forecasts once the peak of the epidemic has passed, even when the values of important epidemiological parameters such as the lengths of the mean incubation and infectious periods are known exactly. As a result, it is necessary to use the more epidemiologically realistic 2-group model to generate accurate forecasts. Accounting for cross-immunity driven by exposures in previous outbreaks explicitly is expected to improve the accuracy of epidemiological modelling forecasts during influenza outbreaks.

Infection, inflammation and intervention: mechanistic modelling of epithelial cells in COVID-19.

While the pathological mechanisms in COVID-19 illness are still poorly understood, it is increasingly clear that high levels of pro-inflammatory mediators play a major role in clinical deterioration in patients with severe disease. Current evidence points to a hyperinflammatory state as the driver of respiratory compromise in severe COVID-19 disease, with a clinical trajectory resembling acute respiratory distress syndrome, but how this 'runaway train' inflammatory response emerges and is maintained is not known. Here, we present the first mathematical model of lung hyperinflammation due to SARS-CoV-2 infection. This model is based on a network of purported mechanistic and physiological pathways linking together five distinct biochemical species involved in the inflammatory response. Simulations of our model give rise to distinct qualitative classes of COVID-19 patients: (i) individuals who naturally clear the virus, (ii) asymptomatic carriers and (iii-v) individuals who develop a case of mild, moderate, or severe illness. These findings, supported by a comprehensive sensitivity analysis, point to potential therapeutic interventions to prevent the emergence of hyperinflammation. Specifically, we suggest that early intervention with a locally acting anti-inflammatory agent (such as inhaled corticosteroids) may effectively blockade the pathological hyperinflammatory reaction as it emerges.