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 Infectious Model with Distributed Time Delay
Masaaki Ishikawa
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JOURNALS OPEN ACCESS

2018 Volume 31 Issue 4 Pages 129-136

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Abstract

This paper is concerned with the stability analysis of the stochastic infectious model with time delay. In the vector-borne diseases such as malaria and Japanese encephalitis, there exists time delay caused by an incubation period in the virus development in the vectors on the transmission of disease. Moreover, environmental change and individual difference cause some kinds of random fluctuations in the infection, recovery rates, etc. Hence, we propose the stochastic infectious model with time delay. The equilibrium solution with zero infected individuals is called the disease-free steady state. Since the stability of the disease-free steady state is related to whether or not the infectious disease spreads, we analyze stability of the disease-free steady state using the stochastic Lyapunov function. Moreover, we study the influence of the random noise on the stability based on the calculation of the Lyapunov exponent, and show results of numerical simulations.

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© 2018 The Institute of Systems, Control and Information Engineers
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