Abstract
or persistence of the infectious disease. When the infective part is forced to expire, the susceptible part converges weakly to an inverse-gamma distribution with explicit shape and scale parameters. In case of persistence, by new stochastic Lyapunov functions, we show the ergodic property and positive
recurrence of the stochastic model. We also derive an estimate for the mean of the stationary distribution. The analytical results are all verified by computer simulations, including examples based on experiments in laboratory populations of mice.
| Original language | English |
|---|---|
| Pages (from-to) | 1003-1025 |
| Number of pages | 23 |
| Journal | Mathematical Biosciences and Engineering |
| Volume | 11 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Mar 2014 |
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Keywords
- ergodic property
- positive recurrence
- stochastic Lyapunov functions
- stochastic SIRS models
- infectious diseases
- extinction
Cite this
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Stochastic dynamical behavior of SIRS epidemic models with random perturbation. / Yang, Qingshan; Mao, Xuerong.
In: Mathematical Biosciences and Engineering, Vol. 11, No. 4, 03.2014, p. 1003-1025.Research output: Contribution to journal › Article
TY - JOUR
T1 - Stochastic dynamical behavior of SIRS epidemic models with random perturbation
AU - Yang, Qingshan
AU - Mao, Xuerong
PY - 2014/3
Y1 - 2014/3
N2 - In this paper, we consider a stochastic SIRS model with parameter perturbation, which is a standard technique in modeling population dynamics. In our model, the disease transmission coefficient and the removal rates are all affected by noise. We show that the stochastic model has a unique positive solution as it is essential in any population model. Then we establish conditions for extinctionor persistence of the infectious disease. When the infective part is forced to expire, the susceptible part converges weakly to an inverse-gamma distribution with explicit shape and scale parameters. In case of persistence, by new stochastic Lyapunov functions, we show the ergodic property and positiverecurrence of the stochastic model. We also derive an estimate for the mean of the stationary distribution. The analytical results are all verified by computer simulations, including examples based on experiments in laboratory populations of mice.
AB - In this paper, we consider a stochastic SIRS model with parameter perturbation, which is a standard technique in modeling population dynamics. In our model, the disease transmission coefficient and the removal rates are all affected by noise. We show that the stochastic model has a unique positive solution as it is essential in any population model. Then we establish conditions for extinctionor persistence of the infectious disease. When the infective part is forced to expire, the susceptible part converges weakly to an inverse-gamma distribution with explicit shape and scale parameters. In case of persistence, by new stochastic Lyapunov functions, we show the ergodic property and positiverecurrence of the stochastic model. We also derive an estimate for the mean of the stationary distribution. The analytical results are all verified by computer simulations, including examples based on experiments in laboratory populations of mice.
KW - ergodic property
KW - positive recurrence
KW - stochastic Lyapunov functions
KW - stochastic SIRS models
KW - infectious diseases
KW - extinction
UR - http://aimsciences.org/journals/home.jsp?journalID=8
U2 - 10.3934/mbe.2014.11.1003
DO - 10.3934/mbe.2014.11.1003
M3 - Article
VL - 11
SP - 1003
EP - 1025
JO - Mathematical Biosciences and Engineering
JF - Mathematical Biosciences and Engineering
SN - 1547-1063
IS - 4
ER -