Numerical techniques for stochastic foot and mouth disease epidemic model with the impact of vaccination

The spread of an epidemic diseases is stochastic in nature. It is more realistic to include this stochasticity when modelling the dynamics of a communicable disease. In this paper, a stochastic model for foot and mouth disease dynamics in animals is constructed from its corresponding deterministic model. Like the deterministic model, the dynamics of the stochastic model is also governed by a threshold parameter $A^{\ast }$, called FMD generation number. If we are able to make $A^{\ast }<1$, then the disease will completely die out from the animal population. If $A^{\ast }>1$, the disease will become endemic in animals. A competitive structure preserving numerical analysis of the stochastic model in comparison with its deterministic part is presented. The proposed numerical analysis is also compared with already existing numerical techniques which may not be reliable in certain situations. Numerical experiments are performed and their results are plotted to show the strength of the proposed technique.