Stability and Hopf Bifurcation of a Generalized Chikungunya Virus Infection Model with Two Modes of Transmission and Delays

Hajar Besbassi,Noura Yousfi,Khalid Hattaf,Abdul Qadeer Khan

doi:10.1155/2020/5908976

Hajar Besbassi, Noura Yousfi + Show 2 more

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https://doi.org/10.1155/2020/5908976

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Abstract

A generalized chikungunya virus (CHIKV) infection model with nonlinear incidence functions and two time delays is proposed and investigated. The model takes into account both modes of transmission that are virus-to-cell infection and cell-to-cell transmission. Furthermore, the local and global stabilities of the disease-free equilibrium and the chronic infection equilibrium are established by using the linearization and Lyapunov functional methods. Moreover, the existence of Hopf bifurcation is also analyzed. Finally, an application is presented in order to support the analytical results.

Highlights

Introduction echikungunya virus (CHIKV) belongs to the family Togaviridae, a term built from the Roman toga, to describe the draped appearance of their envelope [1]
C+ is the Banach space of continuous functions mapping the interval [− τ, 0] into IR4+ with the topology of uniform convergence. It follows from the fundamental theory of functional differential equations [18] that there exists a unique solution of system (1) with initial condition (φ1, φ2, φ3, φ4) ∈ C+
From LaSalle’s invariance principle, we deduce that the chronic infection equilibrium Q∗ is globally asymptotically stable when R0 > 1

Summary

Introduction

Introduction eCHIKV belongs to the family Togaviridae, a term built from the Roman toga, to describe the draped appearance of their envelope [1]. It follows from the fundamental theory of functional differential equations [18] that there exists a unique solution of system (1) with initial condition (φ1, φ2, φ3, φ4) ∈ C+.

Results

Conclusion