Inactivation of alleles in tumor suppressor genes (TSG) is one of the important issues resulting in evolution of cancerous cells. In this paper, the evolution of healthy, one and two missed allele cells is modeled using the concept of evolutionary game theory and replicator dynamics. The proposed model also takes into account the interaction rates of the cells as designing parameters of the system. Different combinations of the equilibrium points of the parameterized nonlinear system is studied and categorized into some cases. In each case, the interaction rates' values are suggested in a way that the equilibrium points of the replicator dynamics are located on an appropriate region of the state space. Based on the suggested interaction rates, it is proved that the system doesn't have any undesirable interior equilibrium point as well. Therefore, the system will converge to the desirable region, where there is a scanty level of cancerous cells. In addition, the proposed conditions for interaction rates guarantee that, when a trajectory of the system reaches the boundaries, then it will stay there forever which is a desirable property since the equilibrium points have been already located on the boundaries, appropriately. The simulation results show the effectiveness of the suggestions in the elimination of the cancerous cells in different scenarios.
Blood glucose level prediction is a critical aspect of diabetes management. It enables individuals to make informed decisions about their insulin dosing, diet, and physical activity. This, in turn, improves their quality of life and reduces the risk of chronic and acute complications. One conundrum in developing time-series forecasting models for blood glucose level prediction is to determine an appropriate length for look-back windows. On the one hand, studying short histories foists the risk of information incompletion. On the other hand, analysing long histories might induce information redundancy due to the data shift phenomenon. Additionally, optimal lag lengths are inconsistent across individuals because of the domain shift occurrence. Therefore, in bespoke analysis, either optimal lag values should be found for each individual separately or a globally suboptimal lag value should be used for all. The former approach degenerates the analysis’s congruency and imposes extra perplexity. With the latter, the fine-tunned lag is not necessarily the optimum option for all individuals. To cope with this challenge, this work suggests an interconnected lag fusion framework based on nested meta-learning analysis that improves the accuracy and precision of predictions for personalised blood glucose level forecasting. The proposed framework is leveraged to generate blood glucose prediction models for patients with type 1 diabetes by scrutinising two well-established publicly available Ohio type 1 diabetes datasets. The models developed undergo vigorous evaluation and statistical analysis from mathematical and clinical perspectives. The results achieved underpin the efficacy of the proposed method in blood glucose level time-series prediction analysis.
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