Optimising plant epidemic control: a mathematical model integrating susceptible and infectives plants, and herbivores with pesticide intervention

Abstract

This work presents and analyses a deterministic mathematical model incorporating herbivores and plant populations, with pesticide application as a control measure. There are three distinct populations under consideration: susceptible and infected plants, as well as herbivorous population. Our model's goal is to analyse the interactions and dynamics of these populations. By analysing their behaviour, we can gain insight into the ecological processes that regulate their growth and survival. The model administers pesticides as a control measure to both susceptible and infected plants. Furthermore, given that herbivores have the potential to consume pesticide-sprayed plants, we can observe an interaction between herbivores and pesticides. The primary goal of pesticide application is to mitigate disease transmission among plant populations. To verify the biological validity and precisely defined characteristics of the model, we assess the system's permanence and examine its positivity, boundedness, uniqueness, and existence of solutions. The determination of the infection's basic reproduction number (R₀) and observation of the disease-free equilibrium state reveal that it is locally asymptotically stable when R₀ is less than unity, but unstable otherwise. In addition, we conduct sensitivity analysis on the basic reproduction number and use Pontryagin's Minimum Principle to determine a necessary condition for the existence of optimal controls. Finally, we perform numerical simulations using the MATLAB software to compare the analytical results. In summation, the findings yielded by this analysis are innovative and substantial, thereby constituting a meaningful addition to the body of knowledge in theoretical ecology.