A Mathematical Model For The Optimal Control Of Trypanosomiasis In A Cattle Population.

Abstract

Trypanosomiasis is a debilitating disease which is a major constraint to livestock production

in sub-Saharan Africa. It leads to loss of productivity in animals and without treatment it is

frequently fatal. The economic and social repercussions it causes in areas where it is endemic,

makes its control a priority operation. In this study we formulate three models; a basic model

to understand the transmission dynamics of the trypanosomiasis in a cattle population, a

model with treatment to evaluate the role of treatment and a model to assess the impact of

preventive and treatment control measures in a cattle population. The basic model and the

model with treatment show that the global dynamics of the disease are completely determined

by the threshold values: the basic reproduction number, R0, and the effective reproduction

number, Reff , respectively. The parameters that have the greatest influence on R0 are

the rate at which the vectors bite the wild animal population and the vector survival rate

which both increase endemicity of the disease while the vector death rate decreases disease

prevalence. Treatment of a proportion of the infected cattle decreases disease prevalence.

The proportion of cattle treated is an important parameter when treatment is used as an

intervention strategy. We show that treating 0.5 - 0.75 of the infected cattle population is

enough to eradicate the disease in the population. In the optimal control model, the existence

of the optimal control is established, it is characterized using the Maximum Principle and

solved numerically using a combination of forward and backward difference approximations.

Numerical simulations and optimal analysis of the model show that the preventive and

treatment control strategies help to reduce the number of infected cattle, however the net

effect on disease prevalence when both strategies are used is greater than when they are used

singly.