An epidemic model for tick-borne disease with two delays
type: Item
instance of: scholarly article
title: An epidemic model for tick-borne disease with two delays
zbMATH Open document ID: 1397.92645
DOI: 10.1155/2013/427621
author: Dan Li
author: Wanbiao Ma
author: Zhichao Jiang
published in: Journal of Applied Mathematics
publication date: 2018-10-10T00:00:00Z
review text: Summary: We have considered an epidemic model of a tick-borne infection which has nonviraemic transmission in addition to the viremic transmission. The basic reproduction number \(\mathfrak R_0\), which is a threshold quantity for stability of equilibria, is calculated. If \(\mathfrak R_0 \leq 1\), then the infection-free equilibrium is globally asymptotically stable, and this is the only equilibrium. On the contrary, if \(\mathfrak R_0> 1\), then an infection equilibrium appears which is globally asymptotically stable, when one time delay is absent. By applying a permanence theorem for infinite dimensional systems, we obtain that the disease is always present when \(\mathfrak R_0>1\).
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 6950670
zbMATH Keywords: tick-borne disease
zbMATH Keywords: basic reproduction number
zbMATH Keywords: infection equilibrium
Wikidata QID: Q59005927
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/427621
OpenAlex ID: W2127318140
description: scientific article; zbMATH DE number 6950670