A mathematical model for the dynamics and cost effectiveness of the current controls of cassava brown streak disease in Uganda

Abstract

In this paper, Cassava brown streak disease (CBSD), transmitted from white fly vector to the host plant and vice versa, is a major threat to cassava production in Uganda and other cassava growing countries in Africa, e.g. Kenya, Tanzania, Malawi, Mozambique, e.t.c. The seriousness of the situation is that almost all varieties of cassava resistant to cassava mosaic disease (CMD) are susceptible to the new strain of CBSD. Numerous control measures are practiced by farmers, however, the cost effectiveness of these control measures have not been quantified. Therefore it is imperative that we formulate a mathematical model to investigate the transmission dynamics of CBSD and the cost-effectiveness of the control measures. In the analysis of the model we derived the basic reproduction number which helps us in establishing the stability of disease free and endemic equilibrium points. The model is then modified as an optimal control problem with an aim of minimizing the number of infected plants while keeping the cost low. Two time dependent controls are used in the model and an objective function which is a combination of the actual and relative costs associated with the controls is designed. Pontryagins Maximum Principle (PMP) is used to establish the necessary conditions for optimal control of the disease. The incremental cost-effectiveness ratio (ICER) is also computed and used to analyse the cost-effectiveness of the control strategies. Numerical results show that strategy B (uprooting and burning of infected plants) is cost effective, however if the government intervenes with massive spraying, strategy C (spraying with chemicals and uprooting and burning of infected plants) gives the farmer more yield.