Modelling Of Health State System On Given Public And Its Analysis

Taking into account the sort of given public health status, in this dissertation, proposes a mathematical model with time for all types of health status and their conversion among the types.In this dissertation, one aspect of the public health problem-the status of healthy distribution is studied. According to a particular region or a particular state of health of the crowd under consideration, the people are divided into crowd-four types: healthful group; sub-healthful group; insignificant illness group and serious illness group. With these separated groups, it discusses the conversion of all types of relations among the crowd group, and establishes a mathematical model for this system under certain assumptions, which is described by coupled equations of ordinary and partial differential equations. Using linear operator semigroup theory, the dissertation shows that this system denoted by the model established is well-posed and associates with a positive C₀ semigroup in a Hilbert sate space. Hence the positive solution of system exists.The dissertation analyzes the stability of this system and conservatism of its solution. According to the theory of Banach lattice and semigroup, and shows that the stable solution of system exists and give the expression of it, and the dynamic solution to system converges asymptotically to the stable one under some conditions.The dissertation studies the stable solution to the system. First of all, it gives process of calculating the solution to system. Then from mathematical theorems, it analyzes the state of the system with the changes of parameters so as to obtain the probability distribution of these four crowds given above, as well as the relationship between the distribution of crowds and the various parameters.Finally, the dissertation indicates some examples (officers' crowd and workers' crowd) and have an analysis about them so as to study the specific conditions in our life. By analyzing some correlative data, it gets some conclusion of them and gives some advices in order to improve the status of these crowds. Furthermore, the dissertation shows that these advices can be effective to improving them.