GLOBAL STABILITY OF HOST-VECTOR MODEL FOR VECTOR-BORN DISEASE

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Muhammad Gul
Muhammad Usman
Nawab Ali
Muhammad Ilyas
Sayyida Aiza Bukhari
Muhammad Haidar Zaman
Muhammad Abubakar

Keywords

Biological model, Stability theory, Routh-Hurwitz Criteria, Endemic equilibrium

Abstract

The purpose of this research is to examine a biological model of vector-borne disease. The paper’s research demonstrates that its dynamics are solely dependent on the basic reproduction number R0. Our investigation is consisted on stability theory and numerical simulations. The Routh-Hurwitz Criteria and the Lyapunov approach are used to determine the local and global asymptotic stability of the disease-free equilibrium. In this paper, we use the work of McCluskey and van den Driessche to show that endemic equilibrium is stable locally. We also use the geometric approach method developed by Li and Muldowney to show that endemic equilibrium is stable at the global level, where the disease stays latent if it already exists. If R0 ≤1, the disease-free equilibrium is globally asymptotically stable, and the disease will vanish, and a unique endemic equilibrium exists if R0 >1.


 

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