Stability analysis of five-grade Leishmania epidemic model with harmonic mean-type incidence rate

[摘要] In this paper, we discuss the Anthroponotic Cutaneous Leishmania transmission. In addition, we develop a mathematical model for the Anthroponotic Cutaneous Leishmania transmission and consider its qualitative behavior. We derive the threshold number$R_{0}$ of the model using the next generation method. In the disease-free case, we carry out the local and global stability under the condition$R_{0}1$ . We also establish the global stability at the endemic equilibrium point with the help of a geometrical approach, which is a generalization of Lyapunov theory, by using a second additive compound matrix. Finally, we take into account the sensitivity analysis of the threshold number with other parameters. We also discuss several graphs of important parameters.

[学科分类] 航空航天科学

[关键词] Compound matrix;Sensitivity analysis;Geometric approach;Stability analysis