https://doi.org/10.1140/epjp/s13360-020-00535-0
Regular Article
Stability analysis of leishmania epidemic model with harmonic mean type incidence rate
1
Department of Mathematics and Statistics, University of Swat, Swat, Khyber Pakhtunkhawa, Pakistan
2
Department of Mathematics, Science Faculty, Firat University, Elazig, Turkey
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
4
Department of Mathematics, University of Malakand, Chakdara Dir, Khyber Pakhtunkhawa, Pakistan
5
Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia
Received:
28
April
2020
Accepted:
13
June
2020
Published online:
26
June
2020
We discussed anthroponotic cutaneous leishmania transmission in this article, due to its large effect on the community in the recent years. The mathematical model is developed for anthroponotic cutaneous leishmania transmission, and its qualitative behavior is taken under consideration. The threshold number 
of the model is derived using the next-generation method. In the disease-free case, local and global stability is carried out with the condition that will be less than one. The global stability at the disease-free equilibrium point has been derived by utilizing the Castillo–Chavez method. On the other hand, at the endemic equilibrium point, the local and global stability holds with some conditions, and is greater than unity. The global stability at the endemic equilibrium point is established with the help of a geometrical approach which is the generalization of Lyapunov theory, by using the third additive compound matrix. The sensitivity analysis of the threshold number with other parameters is also taken into account. Several graphs of important parameters are discussed in the last section.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
