Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
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On the Stability Analysis of the Stochastic SIR Model with Time Delay
Masaaki Ishikawa
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JOURNALS OPEN ACCESS

2017 Volume 30 Issue 4 Pages 115-121

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Abstract

The purpose of this paper is to propose the stochastic infectious model with time delay and to study the stability of the disease-free steady state. In the realistic spread of the infectious disease, environmental change and individual difference cause some kinds of random fluctuations in the model parameters. Moreover, in the vector-borne diseases such as malaria and dengue fever, there exists time delay caused by an incubation period in the virus development in the vectors (mosquitoes) on the transmission of disease. Taking these facts into consideration, we propose a stochastic SIR(susceptible-infected-recovered) model with time delay. We analyze stability of the disease-free steady state, and study the influence of time delay and the random noise on the stability by numerical simulations.

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© 2017 The Institute of Systems, Control and Information Engineers
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