Lyapunov approach and global stability of Ebola virus infection model of an individual cells population

Nurudeen Oluwasola Lasisi

doi:10.21595/msea.2021.21977

Abstract

Ebola virus is among the most dangerous and devastating threats to human health, causing a large number of fatalities. In this paper, a mathematical modelling for the dynamics of Ebola virus infectious of an individual is presented as a system of nonlinear differential equations. The model has two equilibrium states namely, virus free equilibrium (VFE) and virus persistence equilibrium (VPE) states. The Effective reproduction number was obtained. The conditions under which the virus-free-equilibrium is globally asymptotically stable with the approach of linear Lyapunov function are shown when the effective reproduction numbers is less than unity. The nonlinear Lyapunov approach is employed to show the global stability of the endemic equilibrium only when the effective reproduction number is greater than unity. It was found that VFE is globally asymptotically stable if effective reproduction numbers is less than unity and VPE is globally asymptotically stable if M<N, otherwise unstable if M>N.

Highlights

The virus is known to cause damage to large variety of cell types including monocytes, macrophages, dendritic cells, endothelial cells, fibroblasts, hepatocytes, and several types of epithelial cells
The dendritic cells alert the body for any foreign antigen and serve as potent Antigen Presenting Cells (APC) that capture foreign antigen for uptake and processing to target secondary lymphoid tissues for the simulation of T-cell and B-cells [4]
Macrophages are susceptible to the virus [3], macrophages encounter APC and release a protein called interlenkin-1 (IL-1) that acts as a chemical alarm signal; Helper T-cells respond to interlekin-1 and release interlenkin-2 (IL-2) by simultaneously initiating two parallel lines of immune system defense: the cell-mediated response carried out by T-cells, and humoral response carried out by B-cells [5]

Summary

Introduction

The virus is known to cause damage to large variety of cell types including monocytes, macrophages, dendritic cells, endothelial cells, fibroblasts, hepatocytes, and several types of epithelial cells. The primary targets of the virus are dendritic, monocytes and macrophage cells [1]. The incubation period of Ebola virus ranges from 2 to 21 days and infectious period ranges from 4 to 10 days [6]. It takes an approximation of 31 days to quarantine a patient under investigation of the Ebola virus. The spread of the virus and eventual death of infected patients was largely contained (reduced) through early detection and effective contact tracing [8]. The aim of this paper is to analysis Lyapunov function and global stability of Ebola virus infection model

Model description

Equilibrium state of the model equations

Conclusions