The Curse of Black Sigatoka: A Backward Bifurcation Perspective

TL;DR

This paper models Black Sigatoka disease dynamics, revealing a backward bifurcation phenomenon that explains control challenges and emphasizing the importance of strategies beyond simple R0 reduction.

Contribution

It introduces a deterministic and stochastic model capturing the backward bifurcation in BSD, highlighting the need for comprehensive control strategies and analyzing variability factors.

Findings

Backward bifurcation explains persistence despite R0<1.

Control strategies should focus on leaf production and resistant varieties.

Stochastic analysis reveals key drivers of disease variability.

Abstract

Black Sigatoka disease (BSD), also known as black leaf streak disease, is an airborne fungal infection caused by \textit{Pseudocercospora fijiensis} that severely impacts global banana and plantain production. Its persistence and resistance to eradication make it one of the most challenging plant diseases to manage. In this paper, we propose a deterministic pathogen-host model to describe BSD dynamics. Due to dual transmission pathways (ascospores and conidia) and mate limitation in sexual reproduction, the model exhibits a backward bifurcation: a stable endemic equilibrium coexists with the disease-free equilibrium for certain parameter values in which the basic reproduction number, $\mathcal{R}_0$, is less than 1. This phenomenon explains why control strategies that solely reduce $\mathcal{R}_0$ below one may fail. For the backward bifurcation regime, we perform sensitivity analysis of the endemic equilibrium using normalized forward sensitivity indices, Latin Hypercube Sampling, and Partial Rank Correlation Coefficients. Results indicate that effective control must extend beyond $\mathcal{R}_0$ reduction and prioritize (1) limiting production of new susceptible leaves during high-risk periods and (2) developing and deploying disease-resistant plant varieties. To incorporate transmission variability, we also formulate a stochastic version of the model using the Stochastic Simulation Algorithm (SSA). Extensive numerical simulations compare stochastic realizations with deterministic predictions and quantify variability in disease dynamics. To identify the principal drivers of persistence and variability, we analyze the endemic equilibrium using Sobol's variance-based sensitivity method, which highlights the role of nonlinear parameter interactions in shaping variability.