MATHEMATICAL MODEL OF FUNGICIDES AND ROGUING FOR OPTIMAL CONTROL OF COMMON RUST (Puccinia sorghi) IN RICE PLANTS WITH DISCRETE RECRUITMENT

OPTIMAL CONTROL OF COMMON RUST.

Abstract

Rice faces significant yield losses from Common Rust (*Puccinia sorghi*). This paper presents a mathematical model for managing Common Rust using optimal control strategies that incorporate realistic discrete recruitment patterns reflecting actual agricultural practices. We develop a SEIRP (Susceptible-Exposed-Infectious-Recovered-Protected) compartmental model with periodic replanting events and two time-dependent controls: protective measures (fungicide application) and quarantine or roguing of infectious plants. Unlike conventional models assuming unrealistic continuous recruitment, ours models recruitment as discrete events at specific agricultural intervals. Qualitative analysis establishes the disease-free equilibrium and derives the basic reproduction number ($R_0$). An optimal control problem formulated using Pontryagin's Maximum Principle minimizes infectious plant numbers and control costs. Numerical simulations compare constant versus optimal dynamic controls, demonstrating superior performance of the latter. Cost-effectiveness analysis using the Incremental Cost-Effectiveness Ratio evaluates three strategies: protection only, quarantine only, and combined approaches. Results reveal that discrete recruitment patterns significantly affect disease dynamics, with recruitment timing critically influencing optimal strategies.