Journal
APPLIED MATHEMATICS LETTERS
Volume 143, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.aml.2023.108690
Keywords
SEI epidemic model; Ornstein-Uhlenbeck process; Stationary distribution; Extinction
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In this paper, a stochastic SEI epidemic model with general transmission rates following a log-normal Ornstein-Uhlenbeck process is proposed. The existence of a unique positive global solution is theoretically proved. By constructing suitable Lyapunov functions, the condition Rs0 > 1 for the existence of a stationary distribution is established. The extinction of the disease is also investigated, and it is found that the disease will die out at an exponential rate when RE0 < 1.
In this paper, we propose a stochastic SEI epidemic model in which the trans-mission rates are general functions and satisfy the log-normal Ornstein-Uhlenbeck (OU) process. We first theoretically prove that there is a unique positive global solution of this stochastic model. By constructing several suitable Lyapunov functions, the sufficient condition Rs0 > 1 is established for the existence of stationary distribution. The extinction of disease is also investigated and we find that the disease will die out at an exponential rate when RE0 < 1.(c) 2023 Elsevier Ltd. All rights reserved.
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