| Citation: |
Bin Liu, Jing Hu, Libo Liu. FINITE TIME STABILITY AND OPTIMAL CONTROL OF A STOCHASTIC REACTION DIFFUSION ECHINOCOCCOSIS MODEL WITH IMPULSE AND TIME-VARYING DELAY[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 160-197. doi: 10.11948/20240021
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FINITE TIME STABILITY AND OPTIMAL CONTROL OF A STOCHASTIC REACTION DIFFUSION ECHINOCOCCOSIS MODEL WITH IMPULSE AND TIME-VARYING DELAY
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Abstract
This paper presents a model for echinococcosis which incorporates stochastic reaction diffusion, impulse, and time-varying delay. First, the existence and uniqueness of global positive solution is proved through the construction of a Lyapunov function. Then, by applying the bounded impulse interval method, several sufficient conditions for finite time stability (FTS) are obtained. Finally, from the angle of cost-benefit, the issue of optimal control of echinococcosis is presented with the aim of minimizing infection and controlling costs. The validity of the analytical results is verified by numerical simulations.
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Keywords:
- Finite-time stability /
- Lyapunov functional /
- optimal control /
- time-varying delay
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References
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Bin Liu, Jing Hu, Libo Liu. FINITE TIME STABILITY AND OPTIMAL CONTROL OF A STOCHASTIC REACTION DIFFUSION ECHINOCOCCOSIS MODEL WITH IMPULSE AND TIME-VARYING DELAY[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 160-197. doi: 10.11948/20240021
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Figure 1.
The state trajectories of
$ y(x,t)=(S_1(x,t),E_1(x,t),I_1(x,t),S_2(x,t),E_2(x,t),I_2(x,t)) $ $ y(x,0)=(1.405\times10^4,1.3\times10^4,3.3\times10^3,2.78\times10^5,1.23\times10^5,4.16\times10^4) $ -
Figure 2.
The System (2.5) displays state trajectories for
$ y(t,x)=(S_1(t,x), E_1(t,x),I_1(t,x), S_2(t,x), E_2(t,x), I_2(t,x)) $ $ y(0,x)=(1.405\times10^4, 1.3\times10^4, 3.3\times10^3, 2.78\times10^5, 1.23\times10^5, 4.16\times10^4) $ -
Figure 3.
The System (2.5) displays state trajectories for
$ y(t,x)=(S_1(t,x), E_1(t,x), I_1(t,x), S_2(t,x), E_2(t,x), I_2(t,x)) $ $ y(0,x)=(1.405\times10^4, 1.3\times10^4, 3.3\times10^3, 2.78\times10^5, 1.23\times10^5, 4.16\times10^4) $ -
Figure 4.
The System (2.5) displays state trajectories for
$ y(t,x)=(S_1(t,x), E_1(t,x), I_1(t,x), S_2(t,x), E_2(t,x), I_2(t,x)) $ $ y(0,x)=(1.405\times10^4, 1.3\times10^4, 3.3\times10^3, 2.78\times10^5, 1.23\times10^5, 4.16\times10^4) $ $ \tau(t)=2.5 $ -
Figure 5.
The trajectories of
$ v_1(t,x),v_2(t,x) $ $ x=6 $ $ y(0,x)=(1.405\times10^4,1.3\times10^4,3.3\times10^3,2.78\times10^5,1.23\times10^5,4.16\times10^4) $ -
Figure 6.
The paths of
$ (S_1(t,x),E_1(t,x),I_1(t,x),S_2(t,x),E_2(t,x),I_2(t,x)) $ $ x=6 $ $ y(0,x)=(1.405\times10^4,1.3\times10^4,3.3\times10^3,2.78\times10^5,1.23\times10^5,4.16\times10^4) $