Volume 42 Issue 12
Dec.  2021
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HE Xueqing. Dynamics of a Class of Stochastic SIRS Infectious Disease Models With Both Logistic Birth and Markov Switching[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1327-1337. doi: 10.21656/1000-0887.420140
Citation: HE Xueqing. Dynamics of a Class of Stochastic SIRS Infectious Disease Models With Both Logistic Birth and Markov Switching[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1327-1337. doi: 10.21656/1000-0887.420140

Dynamics of a Class of Stochastic SIRS Infectious Disease Models With Both Logistic Birth and Markov Switching

doi: 10.21656/1000-0887.420140
Funds:

The National Natural Science Foundation of China(11961074)

  • Received Date: 2021-05-19
  • Rev Recd Date: 2021-06-23
  • Available Online: 2021-12-31
  • A class of stochastic SIRS infectious disease models with both logistic birth and Markov switching were investigated. The uniqueness of the existence of a globally positive solution to the stochastic infectious disease model was first analyzed through construction of suitable V functions and then by means of Itô’s formula. Afterwards, the results of the existence of an ergodic smooth distribution for the solution of the model and the sufficient conditions for the extinction of the disease were discussed. Finally, numerical examples were given to illustrate the conclusions.
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