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Analysis of a Sub-Optimal Immune Reaction EpidemiologicalModel with Saturation Incidence(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2016年01期
Page:
48-
Research Field:
数学
Publishing date:

Info

Title:
Analysis of a Sub-Optimal Immune Reaction EpidemiologicalModel with Saturation Incidence
Author(s):
Wei Chunmiao; Pang Jianhua; Lu Shuangyang; Hui Jing
School of Science，Guangxi Universty of Science and Technology，Liuzhou 545006，China
Keywords:
Sub-optimal immune reaction; epidemiological model; reproduction number; global stability
PACS:
O129
DOI:
-
Abstract:
In this paper，an epidemiological model with saturation incidence rate which can reflect sub-optimal immune reaction propagation mechanism is investigated. This model corresponds to a transition between SIR and SIS model frameworks by a parameter. It shows that saturation incidence rate leads to rich dynamic behaviors，and the threshold of the existence of various equilibria are found. By means of constructing Dulac function and combing with the local stability of the corresponding linear system，we can obtain the conditions of global stability of equilibria. Furthermore，we are pleasantly surprised to find that between the SIS and SIR models there are very similar dynamics with saturation incidence rate，but it is obviously discriminate that the date when the endemic equilibrium becomes and the number of individuals will be infected between SIS and SIRS models.

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Last Update: 2016-03-30