ZHAO Yingying, HU Hua. Dynamic Behaviors of Stochastically Delayed SIRS Epidemic Models With Standard Incidence Rates Under Information Intervention[J]. Applied Mathematics and Mechanics, 2019, 40(12): 1373-1388. doi: 10.21656/1000-0887.400031
Citation: ZHAO Yingying, HU Hua. Dynamic Behaviors of Stochastically Delayed SIRS Epidemic Models With Standard Incidence Rates Under Information Intervention[J]. Applied Mathematics and Mechanics, 2019, 40(12): 1373-1388. doi: 10.21656/1000-0887.400031

Dynamic Behaviors of Stochastically Delayed SIRS Epidemic Models With Standard Incidence Rates Under Information Intervention

doi: 10.21656/1000-0887.400031
Funds:  The National Natural Science Foundation of China(11361044)
  • Received Date: 2019-01-14
  • Rev Recd Date: 2019-05-16
  • Publish Date: 2019-12-01
  • A class of stochastic-time-delay SIRS infectious disease models with standard incidence under information intervention were considered. A stopping time was defined. Then the existence of a unique global positive solution was proved through construction of a suitable Lyapunov function to prove the stopping time is infinite. The asymptotic behaviors of the model solution around the disease-free equilibrium point and the endemic equilibrium point of the deterministic model were studied with suitable Lyapunov functions respectively. The results show that, the solution of the stochastic system involves random vibration around the 2 equilibrium points under certain conditions respectively.
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