Qualitative Analysis Of Two Biomathematical Models

With the progress of medical treatment,people have higher requirements for the prevention and treatment of the disease.Many biomathematical models can well fit the mechanism of disease and its dynamic development.This paper studies two mathematical models with biological backgrounds and we rigorously proves the existence of its global solution.The first is the treatment of chronic wound healing.It not only seriously affects the patient's life,but also poses a huge challenge to the development of the medical level.The second is the exploration of synthetic genetic oscillators.Hes1 oscillator is beneficial for cancer and can promote the regulation of life.The first chapter is the introduction,we mainly introduces the research status of the topic and some of the symbols and lemmas.In the second chapter,we study a mathematical model of hyperbaric oxygen therapy for chronic wound healing.The model contains coupled partial differential equations and ordinary differential equations.In this paper,the mathematical models of oxygen diffusion concentration,capillary tip density and blood vessel density are discussed.Applying the hyperbolic equation theory,Banach Fixed Point Theorem and Ho&lder-estimate,we prove the problem exists a global solution.In the third chapter,we study a mathematical model of the Hes1 gene oscillator.This model contains partial differential equations with discontinuous coefficients.Polishing the discontinuous function and then using the fixed point theorem and ~pL-estimate,we prove the approximation problem exists a global solution.In the end,we prove that the original problem exists a global solution.