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Outbreaks of Rift Valley fever (RVF), a relatively recently emerged zoonosis endemic to large parts of sub-Saharan Africa that has the potential to spread beyond the continent, have profound health and socio-economic impacts, particularly in communities where resilience is already low. Here output from a new, dynamic disease model [the Liverpool RVF (LRVF) model], driven by downscaled, bias-corrected climate change data from an ensemble of global circulation models from the Inter-Sectoral Impact Model Intercomparison Project run according to two radiative forcing scenarios [representative concentration pathway (RCP)4.5 and RCP8.5], is combined with results of a spatial assessment of social vulnerability to the disease in eastern Africa. The combined approach allowed for analyses of spatial and temporal variations in the risk of RVF to the end of the current century. Results for both scenarios highlight the high-risk of future RVF outbreaks, including in parts of eastern Africa to date unaffected by the disease. The results also highlight the risk of spread from/to countries adjacent to the study area, and possibly farther afield, and the value of considering the geography of future projections of disease risk. Based on the results, there is a clear need to remain vigilant and to invest not only in surveillance and early warning systems, but also in addressing the socio-economic factors that underpin social vulnerability in order to mitigate, effectively, future impacts. (VLID)2147750

HIF-1 (Hypoxia Inducible Factor-1) is an oxygen-regulated transcription factor that mediates the intracellular response to hypoxia in human cells, targeting specific genes that promote cell survival by inducing processes such as angiogenesis and glycolysis. The HIF-1 signalling pathway has been of considerable interest due to its role in mammalian development and in particular several pathologies such as ischemia and cancer. Low cellular oxygen levels are found in cancer due to the rapid proliferation of tumour cells distant to blood vessels (forming a hypoxic core) and the typically irregular vasculature is unable to properly perfuse the tumour. In the Centre for Cell Imaging at the University of Liverpool, time lapsed imaging in an oxygen-controlled environment has captured the transient dynamics of the oxygen regulated subunit of HIF-1, HIF-1α, and revealed heterogeneity between individual cells. The essential characteristics of this data are modelled with a system of differential equations describing the feedback inhibition between HIF-1α and the pathway’s effective oxygen sensors. This novel model was formulated by employing a minimalist approach initially, allowing us to use the rich variety of single-cell data to determine the structure of the feedback loop between two key pathway components. Once the central regulatory motif was identified, the model was expanded to include more complexity, including experimental measurements for model parameter values and additional system components. Oxygen plays an especially important role in the early stages of tumour formation. Measurements of oxygen within cells have been recorded in cultured spheres of neuroblastoma cells at different atmospheric conditions. This data is representative of the early development stages of an avascular tumour and a spatial oxygen-diffusion model was coupled with the single-cell HIF-1α model to describe the dynamics of HIF-1α across a developing tumour. This coupled model is used to study HIF-1α dynamics in the context of various oxygen-dependent cellular functions such as cell-cycle progression and apoptosis by integrating with modifications of published mathematical models.

Mathematical modelling details for microscale transport; parameterisation of passive diffusion; and translating the multiscale model to a simple continuum model.

Mathematical modelling details for microscale transport; parameterisation of passive diffusion; and translating the multiscale model to a simple continuum model.

Nanoparticles have the potential to increase the efficacy of anticancer drugs whilst reducing off-target side effects. However, there remain uncertainties regarding the cellular uptake kinetics of nanoparticles which could have implications for nanoparticle design and delivery. Polymersomes are nanoparticle candidates for cancer therapy which encapsulate chemotherapy drugs. Here we develop a mathematical model to simulate the uptake of polymersomes via endocytosis, a process by which polymersomes bind to the cell surface before becoming internalised by the cell where they then break down, releasing their contents which could include chemotherapy drugs. We focus on two in vitro configurations relevant to the testing and development of cancer therapies: a well-mixed culture model and a tumour spheroid setup. Our mathematical model of the well-mixed culture model comprises a set of coupled ordinary differential equations for the unbound and bound polymersomes and associated binding dynamics. Using a singular perturbation analysis we identify an optimal number of ligands on the polymersome surface which maximises internalised polymersomes and thus intracellular chemotherapy drug concentration. In our mathematical model of the spheroid, a multiphase system of partial differential equations is developed to describe the spatial and temporal distribution of bound and unbound polymersomes via advection and diffusion, alongside oxygen, tumour growth, cell proliferation and viability. Consistent with experimental observations, the model predicts the evolution of oxygen gradients leading to a necrotic core. We investigate the impact of two different internalisation functions on spheroid growth, a constant and a bond dependent function. It was found that the constant function yields faster uptake and therefore chemotherapy delivery. We also show how various parameters, such as spheroid permeability, lead to travelling wave or steady-state solutions.