Model-informed health and socio-economic benefits of enhancing global equity and access to Covid-19 vaccines.

We take a model-informed approach to the view that a global equitable access (GEA) to Covid-19 vaccines is the key to bring this pandemic to an end. We show that the equitable redistribution (proportional to population size) of the currently available vaccines is not sufficient to stop the pandemic, whereas a 60% increase in vaccine access (the global share of vaccinated people) would have allowed the current distribution to stop the pandemic in about a year of vaccination, saving millions of people in poor countries. We then investigate the interplay between access to vaccines and their distribution among rich and poor countries, showing that the access increase to stop the pandemic gets minimized at + 32% by the equitable distribution (- 36% in rich countries and + 60% in poor ones). To estimate the socio-economic benefits of a vaccination campaign with enhanced global equity and access (eGEA), we compare calibrated simulations of the current scenario with a hypothetical, vaccination-intensive scenario that assumes high rollouts (shown however by many rich and poor countries during the 2021-2022 vaccination campaign) and an improved equity from the current 2.5:1 to a 2:1 rich/poor-ratio of the population fractions vaccinated per day. Assuming that the corresponding + 130% of vaccine production is made possible by an Intellectual Property waiver, we show that the money saved on vaccines globally by the selected eGEA scenario overcomes the 5-year profit of the rights holders in the current situation. This justifies compensation mechanisms in exchange for the necessary licensing agreements. The good news is that the benefits of this eGEA scenario are still relevant, were we ready to implement it now.

Mathematical Model of Clonal Evolution Proposes a Personalised Multi-Modal Therapy for High-Risk Neuroblastoma.

Neuroblastoma is the most common extra-cranial solid tumour in children. Despite multi-modal therapy, over half of the high-risk patients will succumb. One contributing factor is the one-size-fits-all nature of multi-modal therapy. For example, during the first step (induction chemotherapy), the standard regimen (rapid COJEC) administers fixed doses of chemotherapeutic agents in eight two-week cycles. Perhaps because of differences in resistance, this standard regimen results in highly heterogeneous outcomes in different tumours. In this study, we formulated a mathematical model comprising ordinary differential equations. The equations describe the clonal evolution within a neuroblastoma tumour being treated with vincristine and cyclophosphamide, which are used in the rapid COJEC regimen, including genetically conferred and phenotypic drug resistance. The equations also describe the agents' pharmacokinetics. We devised an optimisation algorithm to find the best chemotherapy schedules for tumours with different pre-treatment clonal compositions. The optimised chemotherapy schedules exploit the cytotoxic difference between the two drugs and intra-tumoural clonal competition to shrink the tumours as much as possible during induction chemotherapy and before surgical removal. They indicate that induction chemotherapy can be improved by finding and using personalised schedules. More broadly, we propose that the overall multi-modal therapy can be enhanced by employing targeted therapies against the mutations and oncogenic pathways enriched and activated by the chemotherapeutic agents. To translate the proposed personalised multi-modal therapy into clinical use, patient-specific model calibration and treatment optimisation are necessary. This entails a decision support system informed by emerging medical technologies such as multi-region sequencing and liquid biopsies. The results and tools presented in this paper could be the foundation of this decision support system.

A calibrated model with a single-generator simulating polysomnographically recorded periodic leg movements.

The aim of this study was to assess, with numerical simulations, if the complex mechanism of two (or more) interacting spinal/supraspinal structures generating periodic leg movements can be modelled with a single-generator approach. For this, we have developed the first phenomenological model to generate periodic leg movements in-silico. We defined the onset of a movement in one leg as the firing of a neuron integrating excitatory and inhibitory inputs from the central nervous system, while the duration of the movement was defined in accordance to statistical evidence. For this study, polysomnographic leg movement data from 32 subjects without periodic leg movements and 65 subjects with periodic leg movements were used. The proportion of single-leg and double-leg inputs, as well as their strength and frequency, were calibrated on the without periodic leg movements dataset. For periodic leg movements subjects, we added a periodic excitatory input common to both legs, and the distributions of the generator period and intensity were fitted to their dataset. Besides the many simplifying assumptions - the strongest being the stationarity of the generator processes during sleep - the model-simulated data did not differ significantly, to a large extent, from the real polysomnographic data. This represents convincing preliminary support for the validity of our single-generator model for periodic leg movements. Future model extensions will pursue the ambitious project of a supportive diagnostic and therapeutic tool, helping the specialist with realistic forecasting, and with cross-correlations and clustering with other patient meta-data.

Optimal chemotherapy counteracts cancer adaptive resistance in a cell-based, spatially-extended, evolutionary model.

Most aggressive cancers are incurable due to their fast evolution of drug resistance. We model cancer growth and adaptive response in a simplified cell-based (CB) setting, assuming a genetic resistance to two chemotherapeutic drugs. We show that optimal administration protocols can steer cells resistance and turned it into a weakness for the disease. Our work extends the population-based model proposed by Orlandoet al(2012Phys. Biol.), in which a homogeneous population of cancer cells evolves according to a fitness landscape. The landscape models three types of trade-offs, differing on whether the cells are more, less, or equal effective when generalizing resistance to two drugs as opposed to specializing to a single one. The CB framework allows us to include genetic heterogeneity, spatial competition, and drugs diffusion, as well as realistic administration protocols. By calibrating our model on Orlandoet al's assumptions, we show that dynamical protocols that alternate the two drugs minimize the cancer size at the end of (or at mid-points during) treatment. These results significantly differ from those obtained with the homogeneous model-suggesting static protocols under the pro-generalizing and neutral allocation trade-offs-highlighting the important role of spatial and genetic heterogeneities. Our work is the first attempt to search for optimal treatments in a CB setting, a step forward toward realistic clinical applications.

Inclined layer convection in a colloidal suspension with negative Soret coefficient at large solutal Rayleigh numbers.

Convection in an inclined layer of fluid is affected by the presence of a component of the acceleration of gravity perpendicular to the density gradient that drives the convective motion. In this work we investigate the solutal convection of a colloidal suspension characterized by a negative Soret coefficient. Convection is induced by heating the suspension from above, and at large solutal Rayleigh numbers (of the order of 10(7)-10(8)) convective spoke patterns form. We show that in the presence of a marginal inclination of the cell as small as 19 mrad the isotropy of the spoke pattern is broken and the convective patterns tend to align in the direction of the inclination. At intermediate inclinations of the order of 33 mrad ordered square patterns are obtained, while at inclination of the order of 67 mrad the strong shear flow determined by the inclination gives rise to ascending and descending sheets of fluid aligned parallel to the direction of inclination.