Mathematical Modelling of Host-Pest Interaction in the Presence of Insecticides and Resistance: A Case of Fall Armyworm

Abstract

Several pest management programs have been developed to control rising agricultural pest populations. However, the challenge of rapid evolution and pest resistance towards 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 barely incorporated the effect of insecticide resistance. Models with resistance would help predict the dynamics of the FAW population, thus mitigating losses. The main objectives of this work were to develop, analyze, 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. Their local stability is conducted using either the eigenvalue or the Routh–Hurwitz stability criteria, and their global stability is analyzed using either the Castillo–Chavez, Perron eigenvector, or the Lyapunov methods. An expression for the basic reproduction number $R_0$, together with the sensitivity analysis of its parameter values, is provided. Numerical analysis is conducted on various model parameter values. The results established all the model steady states to be locally and globally asymptotically stable at $R_0\le 1$. Also, resistance $\omega$ increased the infection rates by increasing the FAW larvae survival rate $\lambda$ and reducing the insecticidal efficacy ${\delta }_R$ and ${\delta }_N$. This work informs the agriculturists and policymakers 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 to minimize FAW-host interaction, thus reducing crop damage.