Open AccessA nonlinear population dynamics model of patient diagnosis and treatment involving in two level medical institutions and its qualitative analysis of positive singularity
Author(s) -
Xinhui Zhao,
AUTHOR_ID,
Lihong Jiang,
Kaihong Zhao,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022118
Subject(s) - correctness , singularity , nonlinear system , population , mathematics , government (linguistics) , computer science , calculus (dental) , mathematical analysis , medicine , algorithm , physics , linguistics , philosophy , environmental health , dentistry , quantum mechanics
In this article, we firstly establish a nonlinear population dynamical model to describe the changes and interaction of the density of patient population of China's primary medical institutions (PHCIs) and hospitals in China's medical system. Next we get some sufficient conditions of existence of positive singularity by utilising homotopy invariance theorem of topological degree. Meanwhile, we study the qualitative properties of positive singularity based on Perron's first theorem. Furthermore, we briefly analyze the significance and function of the mathematical results obtained in this paper in practical application. As verifications, some numerical examples are ultimately exploited the correctness of our main results. Combined with the numerical simulation results and practical application, we give some corresponding suggestions. Our research can provide a certain theoretical basis for government departments to formulate relevant policies.