Within-host models have been used to successfully describe the dynamics of multiple viral infections, however, the dynamics of SARS-CoV-2 virus infection remain poorly understood. A greater understanding of how the virus interacts with the host can contribute to more realistic epidemiological models and help evaluate the effect of antiviral therapies and vaccines. Here, we present a within-host model to describe SARS-CoV-2 viral dynamics in the upper respiratory tract of individuals enrolled in the UK COVID-19 Human Challenge Study. Using this model, we investigate the viral dynamics and provide timescales of infection that independently verify key epidemiological parameters important in the management of an epidemic. In particular, we estimate that an infected individual is first capable of transmitting the virus after approximately 2.1 days, remains infectious for a further 8.3 days, but can continue to test positive using a PCR test for up to 27 days.

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Understanding the mechanistic dynamics of transmission is key to designing more targeted and effective interventions to limit the spread of infectious diseases. A well-described within-host model allows explicit simulation of how infectiousness changes over time at an individual level. This can then be coupled with dose-response models to investigate the impact of timing on transmission. We collected and compared a range of within-host models used in previous studies and identified a minimally-complex model that provides suitable within-host dynamics while keeping a reduced number of parameters to allow inference and limit unidentifiability issues. Furthermore, non-dimensionalised models were developed to further overcome the uncertainty in estimates of the size of the susceptible cell population, a common problem in many of these approaches. We will discuss these models, and their fit to data from the human challenge study for SARS-CoV-2 and the model selection results, which has been performed using ABC-SMC. The parameter posteriors have then used to simulate viral-load based infectiousness profiles via a range of dose-response models, which illustrate the large variability of the periods of infection window observed for COVID-19.

In this paper, the objective is to study the continuous mean–variance portfolio selection with a no-short-selling constraint and obtain a time-consistent solution. We assume that there is a self-financing portfolio with wealth process [Formula: see text], in which [Formula: see text] represents the fraction of wealth invested in the risk asset under the short selling prohibition. We investigate the mean–variance optimal constrained problem defined by obtaining the supremum over all admissible controls of the difference between the expectation of the value process at some designated terminal time [Formula: see text] and a positive constant times the variance of [Formula: see text]. To envisage the quadratic nonlinearity introduced by the variance, the method of Lagrangian multipliers reduces the nonlinear problem into a set of linear problems which can be solved by applying the Hamilton–Jacobi–Bellman equation and change of variables formula with local time on curves. Solving the HJB system provides the time-inconsistent solution and from there, we derive the time-consistent optimal control.