A delayed SIR epidemic model with a general incidence rate

1. IntroductionHistorically the mathematical modeling of epidemics has started since the time ofGraunt[1]. In fact, Kermackand Mckendric[2] describesome classicaldeterministicmathematical models of epidemiology by considering the total population into threeclasses namely susceptible (S) individuals, infected (I) individuals and recovered(R) individuals which is known to us as SIR epidemic model. This SIR epidemicmodel is very important in today’s analysis of diseases.In recent years, epidemiological models havebeen studied by a number of authors[3, 4, 5, 6]. The basic and important research subjects for these systems are theexistence of the threshold value which distinguishes whether the infectious diseasewill die out, the local and global stability of the disease-free equilibrium and theendemic equilibrium, the existence of periodic solutions, the persistence and extinc-tion of the disease, etc. Many models in the literature represent the dynamics ofdisease by systems of ordinary differential equations without time delay. In orderto reflect the real dynamical behaviors of models that depend on the past historyof systems, it is reasonable to incorporate time delays into the systems [7]. In fact,inclusion of delays in epidemic models makes them more realistic by allowing thedescription of the effects of disease latency or immunity [8, 9, 12]. Most of the de-lay differential mathematical models are concerned with local stability of equilibria.The papers that are concerned with global stability of delayed differential modelsare relatively few.Motivated by the worksofAbta et al. [13], in the present paper, we areconcernedwith the effect of generalized incidence rate. To this end, we consider the followingdelay differential equation model.

• Publication year

  2013

• Venue

  Electronic Journal of Qualitative Theory of Differential Equations

• Publication date

  Unknown publication date

• Fields of study

  Mathematics

• Identifiers
  DOI 10.14232/EJQTDE.2013.1.3
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  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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