Abstract
Salmonellosis is an extremely contagious disease caused by bacteria of the genus Salmonella which affects both humans and animals. Salmonella is a cause for concern in the cattle business because it is a zoonotic disease that can cause serious invasive infections in people and besides, infected herds suffer economic and welfare losses. Consequently, a SIRB (Susceptible - Infected - Recovered-Bacteria) model is being constructed to study the transmission process of the Salmonella Dublin disease in a diary calf. The associated basic reproduction number and stability theory are used to investigate the stability analysis of the model equilibrium points. Numerical simulations was carried out to investigate the effect of the sensitive parameters on the basic reproduction number R 0. Also, the impact of environmental bacteria on Salmonella transmisssion dynamics and the eradication threshold was shown to help reduce the spread of the disease.
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