BIFURCATION OF NONTRIVIAL PERIODIC SOLUTIONS FOR LEISHMANIASIS DISEASE MODEL

Facta Universitatis. Series Mathematics and Informatics

Fatima Boukhalfa¹  Abdelkader Lakmeche²  Mohamed Helal³ 

[1] Laboratory of Biomathematics, Univ Sidi Bel-Abbes, Algeria;Laboratory of Biomathematics, Univ. Sidi Bel-Abbes, Algeria;laboratory of Biomathematics, Univ Sidi Bel-Abbes, Algeria

关键词: Leishmanias model;    Exponential stability;    Bifurcation;    Impulsive differential equations;   

DOI  :  10.22190/FUMI1705583B

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Nishu / University of Nis

【 摘 要 】

We develop an impulsive model for zoonotic visceral leishmaniasis disease on a population of dogs. The disease infects a population D of dogs. We determine the basic reproduction number R0, which depends on the vectorial capacity C. Our analysis focuses on the values of C which give either stability or instability of the disease-free equilibrium (DFE). If the vectorial capacity C is less than some threshold, we obtain the stability of DFE, which means that the disease is eradicated for any period of culling dogs. Otherwise, for C greater than the threshold, the period of culling must be in a limited interval. For the particular case, when the period of culling is equal to the threshold, we observe bifurcation phenomena, which means that the disease is installed. In our study of the exponential stability of the DFE we use the fixed point method, and for the bifurcation we use the Lyapunov-Schmidt method.

【 授权许可】

Unknown