Mathematical assessment of the optimal intervention strategy for Cercospora fungal disease in orange plants

Cercospora fragariae is a fungal plant pathogen. Citrus trees and shrubs are particularly vulnerable to Cercospora infections, which can result in significant crop losses. This paper presented a new mathematical model of Cercospora fungal disease transmission dynamics in orange plants, which incorporates two control interventions – plant inoculation or immunization for resistance to the disease, ν, and quarantine of infective orange plants, α. The model was qualitatively analysed to establish the disease-free and endemic equilibria associated with it. The next generation matrix method was used to compute the effective reproduction number, Re, of the model. The model was later extended to an optimal control model by considering the two interventions as time-dependent control functions ν(t) and α(t), respectively. These time-dependent controls were characterized using Pontryagin’s maximum principle. Qualitative analysis of the autonomous model reveals that the disease-free equilibrium is both locally and globally asymptotically stable if Re<1, and unstable otherwise, whereas the endemic equilibrium is globally asymptotically stable in the absence of re-infection whenever Re>1. Under the situation of no re-infection, additional analysis of the model establishes the existence of forward bifurcation. Simulations of the autonomous model show that the constant control rate α is more sensitive than the constant control rate ν as small increase in α value influences the dynamics of the disease transmission as compared to high increase in ν value. Simulated results of the optimal control model suggest that the use of only optimal quarantine of infective orange plants, α(t), is as good as the combination of the two optimal controls as an intervention strategy when compared to the use of only optimal inoculation of orange plant for resistance to disease, ν(t). A cost analysis was conducted to identify the most cost-effective strategy for the prevention and control of disease spread with limited resources.