关键词: 霍乱模型, 基本再生数, 全局渐近稳定性, 鞍结点, 跨临界分岔

Abstract:

This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again. The threshold for determining disease prevalence is established, and the parameter conditions for

the existence of equilibria are discussed. The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.

By utilizing composite matrices and geometric techniques, the global dynamic behavior of the endemic equilibrium is investigated, and the sufficient conditions for its global asymptotic stability are derived. Furthermore, the disease-free equilibrium is a saddle-node when the basic reproductive number is 1, and tthe transcritical bifurcation in this case is discussed.

Key words: Cholera model , Basic reproductive number, Global asymptotic stability, Saddle-node, Transcritical bifurcation