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  4. Time delay and nonlinear incidence effects on the stochastic SIRC epidemic model

Time delay and nonlinear incidence effects on the stochastic SIRC epidemic model

MMC.
2024;
Volume 11, Number 1
: pp. 84–95
https://doi.org/10.23939/mmc2024.01.084
Received: June 28, 2023
Revised: January 29, 2024
Accepted: January 31, 2024

Ben Lahbib A., Azrar L. Time delay and nonlinear incidence effects on the stochastic SIRC epidemic model. Mathematical Modeling and Computing. Vol. 11, No. 1, pp. 84–95 (2024)

Authors:
  1. A. Ben Lahbib
  2. L. Azrar
1
Research Center STIS, M2CS, Department of Applied Mathematics and Informatics, ENSAM, Mohammed V University
2
Research Center STIS, M2CS, Department of Applied Mathematics and Informatics, ENSAM, Mohammed V University

This paper presents theoretical and numerical study of a stochastic SIRC epidemic model with time delay and nonlinear incidence.  The existence and uniqueness of a global positive solution is proved.  The Lyapunov analysis method is used to obtain sufficient conditions for the existence of a stationary distribution and the disease extinction under certain assumptions.  Numerical simulations are also elaborated for the considered stochastic model in order to corroborate the theoretical findings.

SIRC model
stochastic
time delay
Lyapunov function
nonlinear incidence
stationary distribution
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