Abstract

We formulate a delayed SIR epidemic model by introducing a latent period into susceptible, and infectious individuals in incidence rate. This new reformulation provides a reasonable role of incubation period on the dynamics of SIR epidemic model. We show that if the basic reproduction number, denoted, R0, is less than unity, the diseasefree equilibrium is locally asymptotically stable. Moreover, we prove that if R0 > 1, the endemic equilibrium is locally asymptotically stable. In the end some numerical simulations are given to compare our model with existing model.

Highlights

  • Introduction and mathematical modelsEpidemic models have been studied by many authors

  • In a recent paper [17], we considered a delayed SIR epidemic model with a saturated incidence rate as follows: dS dt

  • In the SIR model (1), the number of the new infective cases produced in the period

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Summary

Introduction and mathematical models

Epidemic models have been studied by many authors. Most of them are interesting in the formulation of the incidence rate, i.e., the infection rate of susceptible individuals through their contacts with infectious (see, for example, [1,2,3,4,5]). In order to model this disease transmission process several authors employ the following incidence functions: The first one is the bilinear incidence rate βSI, where S and I are respectively the number of susceptible and infective individuals in the population, and β is a positive constant [6,7,8,9,10]. In a recent paper [17], we considered a delayed SIR epidemic model with a saturated incidence rate as follows: dS dt. In the SIR model (1), the number of the new infective cases produced in the period In the end some numerical simulations are given to compare our model with existing model

Steady state and local stability analysis
Numerical application
Concluding remarks and future research

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