Sensitivity analysis and optimal control for the dynamic mathematical model of cassava mosaic disease

Abstract

Cassava mosaic disease (CMD) is found in many countries around the world. This disease is caused by a mosaic virus carried by whitefly. It hurts the growth and yield of cassava, which in turn causes damage to farmers who grow cassava. In this paper, we present a model for the transmission of CMD dynamics by the ordinary differential equation system and recommend the optimal control for this model when controlling the disease by uprooting diseased cassava and spraying insecticides. For this model analysis, we are given the basic reproductive number R0, which is the threshold number for classifying the disease-free equilibrium point when R0 < 1 and the endemic equilibrium point when R0 > 1 by using the next-generation method. Disease-free equilibrium points and endemic equilibrium points have found conditions of stability. Sensitivity analysis of basic reproductive numbers reveals the impact of the parameters on disease outbreaks. Then, the model is modified to an optimal control problem with two optimal control parameters, in which the goal is to reduce cassava infections to a minimum. The necessary conditions for optimal control of disease were created by Pontryagin’s maximum principle. Numerical simulations are shown to demonstrate the effectiveness of the control system in the final section.