A Mathematical Models to Study the effects of Biocontrol on the Dynamics of Tomato Bacterial Wilt Disease

Abstract

Tomato farmers are faced with many challenges such as the presence of Tomato bacterial wilt disease (TBWD) caused by Ralstonia solanacearum (RS) bacterium. The congeneric strain of this bacterium called Ralstonia pickettii (RP) is harmless to tomatoes and is known to compete with RS for space and resources. We formulated models to investigate the conditions under which TBWD can be controlled by incorporating RS and the populations of RP as biocontrol using both ordinary and stochastic differential equations, assuming that the model parameters depend on climatic conditions. We investigated the basic properties of the model and the existence and stability of steady states. We find that biocontrol alone can only suppress TBWD but cannot eradicate it; RS and RP can coexist even when the reproduction number is less than unity, implying that the disease will persist. Sensitivity analysis conducted indicates that the rate at which RP consumes the resources of RS is the most sensitive parameter affecting the reproduction number. Increasing the value of this parameter will have more meaningful impacts in reducing the menace of TBWD. The numerical simula tions conducted indicate that the reproduction number alone cannot be used to establish the condition for eradication of the disease.