Improving Stability Conditions for Equilibria of SIR Epidemic Model with Delay under Stochastic Perturbations
Abstract
:1. Introduction
2. Some Auxiliary Definitions and Statements
- -
- mean square stable if for each there exists a such that , , provided that ;
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- asymptotically mean square stable if it is mean square stable and for each initial function ϕ the solution of the system (12) satisfies the condition ;
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- exponentially mean square stable if it is mean square stable and there exists such that for each initial function ϕ there exists (which may depend on ϕ) such that for .
3. Stability of Equilibria
3.1. The First Stability Condition
3.2. The Second Stability Condition
3.3. The Third Stability Condition
3.4. Numerical Simulations
4. Conclusions
Funding
Conflicts of Interest
References
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Shaikhet, L. Improving Stability Conditions for Equilibria of SIR Epidemic Model with Delay under Stochastic Perturbations. Mathematics 2020, 8, 1302. https://doi.org/10.3390/math8081302
Shaikhet L. Improving Stability Conditions for Equilibria of SIR Epidemic Model with Delay under Stochastic Perturbations. Mathematics. 2020; 8(8):1302. https://doi.org/10.3390/math8081302
Chicago/Turabian StyleShaikhet, Leonid. 2020. "Improving Stability Conditions for Equilibria of SIR Epidemic Model with Delay under Stochastic Perturbations" Mathematics 8, no. 8: 1302. https://doi.org/10.3390/math8081302