A vaccination model for COVID-19 in Gauteng, South Africa.

The COVID-19 pandemic provides an opportunity to explore the impact of government mandates on movement restrictions and non-pharmaceutical interventions on a novel infection, and we investigate these strategies in early-stage outbreak dynamics. The rate of disease spread in South Africa varied over time as individuals changed behavior in response to the ongoing pandemic and to changing government policies. Using a system of ordinary differential equations, we model the outbreak in the province of Gauteng, assuming that several parameters vary over time. Analyzing data from the time period before vaccination gives the approximate dates of parameter changes, and those dates are linked to government policies. Unknown parameters are then estimated from available case data and used to assess the impact of each policy. Looking forward in time, possible scenarios give projections involving the implementation of two different vaccines at varying times. Our results quantify the impact of different government policies and demonstrate how vaccinations can alter infection spread.

Skin pharmacokinetics of diclofenac and co-delivered functional excipients.

An important question in the development of a dermatological drug product is whether a target concentration has been achieved in, for example, the viable epidermis following topical administration. When attempting to address this challenge, it is essential to consider the role of excipients in the formulation that may influence drug partitioning and diffusion in the different layers of the skin. The objective, therefore, was to correlate, in human subjects, the skin pharmacokinetics of diclofenac (specifically, its uptake into and clearance from the stratum corneum (SC)) from an approved drug product (Voltaren® medicated plaster) with the in vivo co-uptake of two key excipients, namely propylene glycol and butylene glycol. SC sampling was used to assess diclofenac input into the skin during patch application, and its subsequent clearance post-removal of the delivery system. In parallel the uptake of the two glycol excipients was also measured. Drug and excipient amounts in the SC increased with time of application up to 6 h and, for diclofenac, no further increase was observed when the administration was prolonged to 12 h. When the plaster was removed after 6 h of wear, diclofenac cleared relatively slowly from the SC suggesting that drug binding with a slow off-rate had occurred. The results indicate that the optimisation of drug delivery from a topical formulation must take into account the disposition of key excipients and their impact on dermato-pharmacokinetics in general.

The Effect of Covert and Overt Infections on Disease Dynamics in Honey-Bee Colonies.

Viral diseases of honey bees are important economically and ecologically and have been widely modelled. The models reflect the fact that, in contrast to the typical case for vertebrates, invertebrates cannot acquire immunity to a viral disease, so they are of SIS or (more often) SI type. Very often, these diseases may be transmitted vertically as well as horizontally, by vectors as well as directly, and through the environment, although models do not generally reflect all these transmission mechanisms. Here, we shall consider an important additional complication the consequences of which have yet to be fully explored in a model, namely that both infected honey bees and their vectors may best be described using more than one infection class. For honey bees, we consider three infection classes. Covert infections occur when bees have the virus under control, such that they do not display symptoms of the disease, and are minimally or not at all affected by it. Acutely overtly infected bees often exhibit severe symptoms and have a greatly curtailed lifespan. Chronically overtly infected bees typically have milder symptoms and a moderately shortened lifespan. For the vector, we consider just two infection classes which are covert infected and overt infected as has been observed in deformed-wing virus (DWV) vectored by varroa mites. Using this structure, we explore the impact of spontaneous transition of both mites and bees from a covertly to an overtly infected state, which is also a novel element in modelling viral diseases of honey bees made possible by including the different infected classes. The dynamics of these diseases are unsurprisingly rather different from the dynamics of a standard SI or SIS disease. In this paper, we highlight how our compartmental structure for infection in honey bees and their vectors impact the disease dynamics observed, concentrating in particular on DWV vectored by varroa mites. If there is no spontaneous transition, then a basic reproduction number [Formula: see text] exists. We derive a condition for [Formula: see text] that reflects the complexities of the system, with components for vertical and for direct and vector-mediated horizontal transmission, using the directed graph of the next-generation matrix of the system. Such a condition has never previously been derived for a honey-bee-mite-virus system. When spontaneous transitions do occur, then [Formula: see text] no longer exists, but we introduce a modification of the analysis that allows us to determine whether (i) the disease remains largely covert or (ii) a substantial outbreak of overt disease occurs.

The role of optimal control in assessing the most cost-effective implementation of a vaccination programme: HPV as a case study.

Vaccination against the human papillomavirus (HPV) is a recent development in the UK. This paper uses an optimal control model to explore how best to target vaccination. We find that the vaccination of sexually active individuals has a greater impact on disease control than the vaccination of sexually non-active individuals. Extending the model to include male vaccination, we find that including males in a vaccination strategy is cost-effective. We compare the optimal control solution to that from a constant control model and show that the optimal control model is more efficient at forcing the system to a disease-controlled steady state.

The role of initial inoculum on epidemic dynamics.

Transient dynamics are important in many epidemics in agricultural and ecological systems that are prone to regular disturbance, cyclical and random perturbations. Here, using a simple host-pathogen model for a sessile host and a pathogen that can move by diffusion and advection, we use a range of mathematical techniques to examine the effect of initial spatial distribution of inoculum of the pathogen on the transient dynamics of the epidemic. We consider an isolated patch and a group of patches with different boundary conditions. We first determine bounds on the host population for the full model, then non-dimensionalizing the model allows us to obtain approximate solutions for the system. We identify two biologically intuitive groups of parameters to analyse transient behaviour using perturbation techniques. The first parameter group is a measure of the relative strength of initial primary to secondary infection. The second group is derived from the ratio of host removal rate (via infection) to pathogen removal rate (by decay and natural mortality) and measures the infectivity of initial inoculum on the system. By restricting the model to mimic primary infection only (in which all infections arise from initial inoculum), we obtain exact solutions and demonstrate how these depend on initial conditions, boundary conditions and model parameters. Finally, we suggest that the analyses on the balance of primary and secondary infection provide the epidemiologist with some simple rules to predict the transient behaviours.