一类基于非线性传染率与出生率的传染病模型

A Class of Infectious Disease Models Based on Nonlinear Incidence and Birth Rates

摘要: 本文研究了具有非线性出生率和非线性感染率的传染病模型。考虑疾病发生时，医院的医疗能力有限，本文在模型中加入医院容纳量进行讨论。第一，证明解的非负性和有界性；第二，计算模型的无病平衡点和基本再生数并证明无病平衡点的局部渐近稳定性；第三，讨论地方病平衡点的存在条件并给出发生后向分支的参数要求。

Abstract: In this paper, we investigate a class of epidemic models incorporating both a nonlinear birth rate and a nonlinear incidence rate. To account for the limited medical capacity of hospitals during disease outbreaks, a hospital admission capacity is introduced into the models. First, the nonnegativity and boundedness of solutions of the models are established. Second, the disease-free equilibrium and the basic reproduction number are derived, and the local asymptotic stability of the disease-free equilibrium is analyzed. Third, the conditions for the existence of the endemic equilibrium are discussed, together with the parameter requirements under which backward bifurcation may occur.