Nonstandard finite difference method of modelling zoonotic diseases

Abstract

Zoonotic diseases are mostly the leading causes of illness and deaths in Sub-Saharan Africa but efforts to combat the spread of these diseases has always been a challenge. Incidence of zoonotic diseases has reduced substantially in most parts of Africa as a result of rigorous vaccination campaigns. However, zoonotic diseases still remain a threat to developing nations. Zoonotic diseases can be contracted either by direct contact, food and water. In this paper, we developed and analysed a general model that explains the dynamics of zoonotic diseases and analysed it using nonstantard finite difference approach. This scheme was used for the model analysis. The disease free equilibrium of the scheme in its explicit form was determined and it was both locally and globally asymptotically stable. Bifurcation and multiple equilibria as well as the threshold value for disease transmission was determined. An analysis of the effects of contact between susceptible and infected animals as well susceptible and infected humans was conducted. It showed an increase in infected animals and humans whenever the contact rate increases and decreases otherwise. The epidemiological implication is that zoonotic disease can be controlled by ensuring that interactions between susceptible humans, infected animals and infected humans is reduced to the bearest minimum.