| Citation: |
Kangkang Chang, Qimin Zhang, Huaimin Yuan. STATIONARY DISTRIBUTION AND CONTROL STRATEGY OF A STOCHASTIC DENGUE MODEL WITH SPATIAL DIFFUSION[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 153-178. doi: 10.11948/20210094
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STATIONARY DISTRIBUTION AND CONTROL STRATEGY OF A STOCHASTIC DENGUE MODEL WITH SPATIAL DIFFUSION
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Abstract
In this paper, we establish a dengue model, which is described by the spatial diffusion and Brownian motion, and discuss the stationary distribution and optimal control of the stochastic dengue model. At first, we show the existence of the global positive solution by constructing Lyapunov function. The sufficient conditions are given for the existence and uniqueness of stationary distribution of the positive solution. Subsequently, we introduce the control strategy, namely, decrease the infected individual and spray mosquito insecticides. The first order necessary conditions are derived for the existence of optimal control by applying Pontryagins maximum principle. Finally, numerical simulations are introduced to confirm the analytical results. The simulation results verified the existence of stationary distribution, and there are certain differences in the solutions of the stationary distribution in different spaces. The influence of different noise intensity on the stationary distribution and the effect of different control strategy for stochastic dengue fever.
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References
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Kangkang Chang, Qimin Zhang, Huaimin Yuan. STATIONARY DISTRIBUTION AND CONTROL STRATEGY OF A STOCHASTIC DENGUE MODEL WITH SPATIAL DIFFUSION[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 153-178. doi: 10.11948/20210094
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Figure 1. The solutions are observed in system (2.5) under initial conditions
$(S_{H, 0}(x), I_{H, 0}(x), R_{H, 0}(x), $ $S_{V, 0}(x), I_{V, 0}(x))=(33+\sin\frac{\pi x}{60}, 11+\sin\frac{\pi x}{60}, 0, 10+\sin\frac{\pi x}{60}, \sin\frac{\pi x}{60})$ -
Figure 2. The histograms of
$S_{H}, I_{H}, R_{H}, S_{V}, I_{V}$ -
Figure 3. The evolution of a single path of
$S_{H}, I_{H}, R_{H}, S_{V}, I_{V}$ for different noise intensity - Figure 4. The effects of treating infected individuals
- Figure 5. The effects of mosquito control
- Figure 6. The effects of both control measures
- Figure 7. The graph for the two controls