Optimal control model of tumor treatment in the context of cancer stem cell.

We consider cancer cytotoxic drugs as an optimal control problem to stabilize a heterogeneous tumor by attacking not the most abundant cancer cells, but those that are crucial in the tumor ecosystem. We propose a mathematical cancer stem cell model that translates the hierarchy and heterogeneity of cancer cell types by including highly structured tumorigenic cancer stem cells that yield low differentiated cancer cells. With respect to the optimal control problem, under a certain admissibility hypothesis, the optimal controls of our problem are bang-bang controls. These control treatments can retain the entire tumor in the neighborhood of an equilibrium. We simulate the bang-bang control numerically and demonstrate that the optimal drug scheduling should be administered continuously over long periods with short rest periods. Moreover, our simulations indicate that combining multidrug therapies and monotherapies is more efficient for heterogeneous tumors than using each one separately.

Non-pharmaceutical interventions and COVID-19 vaccination strategies in Senegal: a modelling study.

BACKGROUND: When vaccines against the novel COVID-19 were available in Senegal, many questions were raised. How long should non-pharmaceutical interventions (NPIs) be maintained during vaccination roll-out? What are the best vaccination strategies? METHODS: In this study, we used an age-structured dynamic mathematical model. This model uses parameters based on SARS-CoV-2 virus, information on different types of NPIs, epidemiological and demographic data, some parameters relating to hospitalisations and vaccination in Senegal. RESULTS: In all scenarios explored, the model predicts a larger third epidemic wave of COVID-19 in terms of new cases and deaths than the previous waves. In a context of limited vaccine supply, vaccination alone will not be sufficient to control the epidemic, and the continuation of NPIs is necessary to flatten the epidemic curve. Assuming 20% of the population have been vaccinated, the optimal period to relax NPIs would be a few days from the last peak. Regarding the prioritisation of age groups to be vaccinated, the model shows that it is better to vaccinate individuals aged 5-60 years and not just the elderly (over 60 years) and those in high-risk groups. This strategy could be more cost-effective for the government, as it would reduce the high costs associated with hospitalisation. In terms of vaccine distribution, the optimal strategy would be to allocate full dose to the elderly. If vaccine doses are limited, half dose followed by full dose would be sufficient for people under 40 years because whether they receive half or full dose, the reduction in hospitalisations would be similar and their death-to-case ratio is very low. CONCLUSIONS: This study could be presented as a decision support tool to help devise strategies to control the COVID-19 pandemic and help the Ministry of Health to better manage and allocate the available vaccine doses.

Individual based model for grouper populations.

Dusky groupers (Epinephelus marginatus) are characterized by a complex sex allocation strategies and overexploitation of bigger individuals. We developed an individual based model to investigate the long-term effects of density dependence on grouper population dynamics and to analyze the variabilities of extinction probabilities as a result of interacting mortalities at different life stages. We conduct several simulations with different forms of sex allocation functions and different combinations of mortality rates. The model was parametrized using data on dusky grouper populations from the literature. The most important insights produced by this simulation study are that density dependence of sex allocation is an evolutionarily stable strategy, increases the population biomass, mitigates the effect of the removal of large male and indicates a need for protection of females and flexible stages.