Mathematical Modeling towards the Dynamical Interaction of Leptospirosis

Authors

Muhammad Altaf Khan, Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, Pakistan
Saeed Islam
Sher Afzal Khan

Author Country (or Countries)

Pakistan

Abstract

In this work, we extend the mathematical model of leptospirosis disease by taking into account the exposed individuals, the related death rate and the transmission coefficients between susceptible human and infected vector. Initially, we present the local asymptotical stability of both the disease-free and endemic equilibrium. We use the Lyapunov function theory with some sufficient conditions. This shows the global stability of both the disease-free and endemic equilibrium. Further, we present the bifurcation of the model and exhibit that the local asymptotical stability of the disease-free and endemic equilibrium co-exists with the threshold quantity. Finally, we discuss the numerical results.

Suggested Reviewers

N/A

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/080314

Recommended Citation

Altaf Khan, Muhammad; Islam, Saeed; and Afzal Khan, Sher (2014) "Mathematical Modeling towards the Dynamical Interaction of Leptospirosis," Applied Mathematics & Information Sciences: Vol. 08: Iss. 3, Article 14.
DOI: http://dx.doi.org/10.12785/amis/080314
Available at: https://digitalcommons.aaru.edu.jo/amis/vol08/iss3/14