Modeling plant disease with biological control of insect pests

Abstract

Introduction: This article discusses the problem of plant diseases that pose major threat to agriculture in several parts of the World. Herein, our focus is on viruses that are transmitted from one plant to another by insect vectors. We consider predators that prey on insect population leading to reduction in infection transmission of plant diseases. Methods: We formulate and analyze a deterministic model for plant disease by incorporating predators as biological control agents. Existence of equilibria and the stability of the model are discussed in-detail. Basic reproduction number R₀ of the proposed model is also computed and this helps in determining the impact of different key parameters on the transmission dynamics of disease. Additionally, the proposed model is extended to stochastic model and simulation results of both deterministic and stochastic models are compared and analyzed. Results: Our results of stochastic model show the less number of infected plants and insects compared to corresponding results for deterministic model. Also, our results analyze the impact of different key parameters on the equilibrium levels of infected plants and identify the key parameters. Discussion: Presented results are used to conclude and demonstrate that the biological control is effective in reducing the infection transmission of plant disease and there is a need to use plant-insect-specific predators to get desirable results.

Keywords:

• Plant disease model
• insects
• predators
• stability
• stochastic model

2010 Mathematics Subject Classification:

• 34D20
• 65C30
• 92C50

Disclosure statement

No potential conflict of interest was reported by the authors.