An optimal control model for Coffee Berry Disease and Coffee Leaf Rust co-infection

Abstract

In the 1980s, coffee production in Kenya was peaking at an average of 1.7 million bags annually. Since then, this production has been declining to the current production of below 0.9 million bags annually. Coffee berry disease (CBD) and Coffee leaf rust (CLR) are some of the causes of this decline. This is due to a lack of sufficient knowledge on optimal control strategies for co-infection of CBD and CLR. In this research, we derive a system of ODEs from the mathematical model for co-infection of CBD and CLR with prevention of CBD infection, prevention of CLR infection, the treatment of CBD-infected coffee plants, the treatment of CLR-infected coffee plants, the treatment of CBD-CLR Co-infected coffee plants, elimination of Colletotrichum kahawae pathogens and elimination of Hemileia vastatrix pathogens to perform optimal control analysis. An optimal control problem is formulated andsolved using Pontryagin’s maximum principle. The outcomes of the model’s numerical simulations indicate that combining all controls would be the best strategy for slowing the spread of the CBD-CLR co-infection.