Dynamics Analysis of a Stochastic Plant Disease Model with Continuous Cultural Control Strategy

Haisu Zhang,Tongqian Zhang,Ning Cai

doi:10.1155/2021/5550131

Haisu Zhang, Tongqian Zhang + Show 1 more

Open Access

https://doi.org/10.1155/2021/5550131

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Abstract

In this paper, a new stochastic plant disease model with continuous control strategy is proposed and analyzed. The dynamics of the system are explored under white noise disturbance. We prove that if R 1 > 1 , then the disease is persistent; moreover, if R 2 > 1 , then the solutions of the system have a stationary distribution. For the special case, we prove that if R 1 < 1 , then the disease will eventually disappear. Finally, some numerical simulations were implemented to illustrate the theoretical results.

Highlights

Plant disease is an important constraint on global crop production and severely damages the yield and quality of crops. e main sources of infections that cause crop disease are viruses, bacteria, fungi, nematodes, and plant disease caused by parasitic plants
Plant viruses have caused a large reduction in crop production
In the late 1940s, tobacco mosaic virus caused an average loss of approximately 40 million pounds of tobacco in the United States each year, accounting for 2%3% of tobacco production [2]

Summary

Introduction

Plant disease is an important constraint on global crop production and severely damages the yield and quality of crops. e main sources of infections that cause crop disease are viruses, bacteria, fungi, nematodes, and plant disease caused by parasitic plants. Because the occurrence, development, and spread of plant diseases is a very complex process, it will inevitably be disturbed by various unpredictable random factors, such as environmental conditions (temperature, moisture, and light), soil texture, pH value, and so on. On the basis of model (1), we assume that the environmental white noise is proportional to the variables S and I, respectively, and propose a simple plant disease model under stochastic perspective as follows: dS(t) Let Ze be the explosion time, and we claim that for any initial value (S(0), I(0)) ∈ R2+ there exists a unique local solution (S(t), I(t)) ∈ R2+ on t ∈ [0, Ze) a.s. it is easy to get from the local Lipschitz property of the coefficients of system (2). (η + ω)β is finishes the proof of eorem 2

Existence of a Stationary Distribution

Numerical Simulation

Findings

Discussion and Conclusion