Global stability properties for a delayed virus dynamics model with humoral immunity response and absorption effect

2017 International Conference on Electrical Engineering (ICEE) Pub Date : 2017-03-02 DOI:10.1109/ICEE.2017.7893424

B. Sampath, A. Pradeep, Hazrat Ali

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引用次数: 1

Abstract

A model for virus infection with absorption effect and humoral immunity response consisting of system of delay differential equations has been investigated. By direct calculations, the basic number of reproduction and humoral immune-activated reproduction numbers which are also known as threshold values have been obtained. The equilibria of the proposed model, the infection free equilibrium, humoral immune-inactivated equilibrium and humoral immune-activated equilibrium which are completely based on the basic number of reproduction, and humoral immune-activated reproduction number have been found by directly solving the system. Results obtained for Lyapunov functionals and using LaSalle's invariance principle with sufficient conditions, are: (i) the infection free equilibrium satisfied the global asymptotic stability criteria if the basic reproduction number is below unity or equal to unity. (ii) the humoral immune-inactivated equilibrium is globally asymptotically stable, provided that the humoral immune-activated reproduction number is below unit or equal to unity and the basic reproduction number exceeds unity, and (iii) the humoral immune-activated equilibrium satisfies the global asymptotic stability criteria for the case when humoral immune-activated reproduction number exceeds unity.

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具有体液免疫反应和吸收效应的延迟病毒动力学模型的全局稳定性

研究了由时滞微分方程组组成的病毒感染吸收效应和体液免疫反应模型。通过直接计算，获得了基本繁殖数和体液免疫激活繁殖数，也称为阈值。通过对系统的直接求解，得到了模型的无感染平衡、体液免疫灭活平衡和体液免疫激活平衡，这三种平衡完全基于基本繁殖数和体液免疫激活繁殖数。对于Lyapunov泛函，在充分条件下，利用LaSalle不变性原理，得到:(i)当基本繁殖数小于或等于单位时，无感染平衡点满足全局渐近稳定性判据。(ii)体液免疫灭活平衡是全局渐近稳定的，前提是体液免疫激活繁殖数低于单位或等于单位，且基本繁殖数超过单位;(iii)体液免疫激活平衡在体液免疫激活繁殖数超过单位的情况下满足全局渐近稳定标准。

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2017 International Conference on Electrical Engineering (ICEE)

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