bstract
The problem of foot and mouth disease (FMD) is of serious concern to the livestock
sector in most nations, especially in developing countries. This paper presents the
formulation and analysis of a deterministic model for the transmission dynamics of
FMD through a contaminated environment. It is shown that the key parameters that
drive the transmission of FMD in a contaminated environment are the shedding,
transmission, and decay rates of the virus. Using numerical results, it is depicted that
the host-to-host route is more severe than the environmental-to-host route. The model
is then transformed into an optimal control problem. Using the Pontryagin's Maximum
Principle, the optimality system is determined. Utilizing a gradient type algorithm with
projection, the optimality system is solved for three control strategies: optimal use of
vaccination, environmental decontamination, and a combination of vaccination and
environmental decontamination. Results show that a combination of vaccination and
environmental decontamination is the most optimal strategy. These results indicate
that if vaccination and environmental decontamination are used optimally during an
outbreak, then FMD transmission can be controlled. Future studies focusing on the
control measures for the transmission of FMD in a contaminated environment should
aim at reducing the transmission and the shedding rates, while increasing the decay rate.