RUNGE-KUTTA’S 4TH-ORDER DIFFERENTIAL EQUATION SYSTEM (RK4) BASED ON THE SIR (SUSCEPTIBLE-INFECTED-REMOVED) EPIDEMIOLOGICAL MODEL TO PREDICT THE DYNAMIC SPREAD OF COCOA SWOLLEN SHOOT VIRUS

Abstract

Swollen shoot disease (CSSV - Cocoa Swollen Shoot Virus) represents a major threat to cocoa plantations, causing significant economic losses in cocoa-producing regions. This paper proposes a differential equation system based on a Runge-Kutta 4th-order SIR (Susceptible-Infected-Removed) epidemiological model to analyze, predict and control the spread of Swollen Shoot disease in cocoa plantations. This model makes it possible to analyze epidemiological dynamics with stochastic variability, identifying effective strategies for limiting the impact of the disease. The aim of the SIR model is to provide a predictive tool to assess disease spread dynamics, identify critical parameters influencing the epidemic, such as transmission rate  and recovery rate  while developing optimal control strategies to minimize losses. The methodological technique will consist of compartmentalizing the tree population into three: susceptible trees  infected trees  and withdrawn (felled or immunized) trees  in a system of differential equations describing the flow between these compartments with the key parameters  and  Numerical results from simulations using the Runge-Kutta method make it possible to identify critical moments, such as the infection peak justifying optimization of intervention strategies, particularly in terms of biological vector management, rapid pruning to remove infected trees and long-term prevention of epidemic duration and the final number of trees infected or removed.

Received: February 7, 2025
Accepted: March 29, 2025