A mathematical model for the transmission dynamics and optimal control strategy of Coffee Wilt disease

Abstract

The main objective of this study was to formulate a mathematical model for the transmission dynamics and optimal control strategy of coffee wilt disease (CWD) in Uganda. A deterministic model for the transmission dynamics of CWD was formulated and analysed. Positivity and boundedness of the model variables were carried out. The basic reproduction number Ro was derived. Results from simulations show that, the key parameters that drive the transmission of CWD are, the contamination and transmission rates. Analysis of the model shows existence of two equilibria points, that is, the disease-free and endemic which are both locally and globally asymptotically stable when Ro is less and greater than unity, respectively. The model was transformed into a stochastic model and the probabilities of extinction and persistence of the disease were done. The probability of extinction of the disease was found to be P0=q1s*q2i*q3r*q4h and that of persistence was Pm = 1 - Po . The model was also modified ed by introducing two control functions, education of farmers, and uprooting and burning of infected coffee plants. Numerical results for the optimal control indicated that CWD can be best controlled by uprooting and burning of the infected coffee trees. Therefore, it is recommended that, the government facilitates the farmers such that they don't incur losses after uprooting infected coffee trees.