Mathematical Modelling of Host-Pest Interaction in the Presence of Insecticides and Resistance

Abstract

Several pest management programs have been developed to control the rising agricultural pest populations. However, the challenge of rapid evolution and pest resistance towards the control measures continues to cause high production losses to maize farmers in Africa. Few models have attempted to address the issue of Fall Armyworm (FAW) but have not incorporated the effect of insecticides resistance. The knowledge on the effect of insecticides resistance is still scanty. Models with resistance would help predict the dynamics of FAW population thus mitigate loses. The main objectives of this work were to develop, analyse, and numerically simulate a susceptible- infected deterministic mathematical model expressing the FAW-maize interaction and population dynamics under insecticidal sprays and resistance FAW larvae. Three model steady states are established and their local stability conducted using either the eigenvalue or the Routh- Hurwitz stability criterions and the global stability analyzed using Castillo Chavez, Perron eigen vector, and the Lyapunov methods. An expression for the Basic reproduction number, 𝑅0, and the sensitivity analysis of its parameter values is provided. Numerical analysis is conducted to various model parameter values. The results established all the model steady states to be locally and globally asymptotically stable at 𝑅0≤1. Also, resistance 𝜔 increased the infection rates by increasing the FAW larvae survival rate 𝜆 and reducing the insecticidal efficacy 𝛿𝑅 and 𝛿𝑁. This work informs the agriculture sector and policy makers on pest control with the best ways to use insecticides to minimize pest resistance and enhance efficacy in production. Pest control measures should be modified to lower the FAW survival rate and all model parameters contributing to resistance formation by FAW larvae in order to minimize FAW- host interaction thus reducing crop damage.