New Directions in Non-linear Mathematical Asymptotics

预测流行病或癌症建模等重大挑战依赖于我们对具有极其复杂解决方案的简单数学模型的理解。文献中第一个也是唯一一个重现HIV/AIDS免疫反应三阶段循环的模型是基于细胞自动机的。它的结果对参数的微小变化极其敏感。然而，没有技术存在，以研究这种变化的细胞自动机。该研究为此类模型的预测和分析提供了新的方法。

Major challenges such as predicting epidemics or modelling cancer rely on our understanding of simple mathematical models with extremely complicated solutions. The first and only model in the literature to reproduce the three-phase cycle of immune response in HIV/AIDS was based on cellular automata. Its results are extremely sensitive to infinitesimally small changes in parameters. Yet, no technique exists to study such variation in cellular automata. This research will provide new methods for prediction and analysis of such models.