Stability analysis of Toxoplasma gondii propagation model

Abstract

Toxoplasma gondii as a typical zoonotic disease, because there is no suitable vaccine, its control is important in prevention, so it has been the subject of research by all scholars. in order to study the critical value of controlling its transmission and carry out relevant theoretical analysis, This paper establishes a mathematical model based on the life history and transmission route of Toxoplasma gondii, and analyzes the basic regeneration number that determines whether the disease continues to exist. When the basic reproduction number is less than 1, the disease died out finally. When the basic reproduction number is greater than 1, the model had a unique endemic equilibrium point, and the disease uniformly persisted. In addition, the sufficient conditions for the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium are given by establishing a suitable Lyapunov function. In this paper, a systematic and complete stability study of the established mathematical model can be provided to provide advice for controlling the spread of disease.

Keywords

• theory of stability
• Toxoplasma gondii
• final host
• basic reproduction number
• global stability
• Lyapunov function