Mathematical model for the infectiology of brucellosis with some control strategies
Abstract
Brucellosis is a neglected zoonotic infection caused by gram-negative bacteria of genus brucella. In this paper, a
deterministic mathematical model for the infectiology of brucellosis with vaccination of ruminants, culling of seropositive animals
through slaughter, and proper environmental hygiene and sanitation is formulated and analyzed. A positive invariant region of the
formulated model is established using the Box Invariance method, the effective reproduction number, Re of the model is computed
using the standard next generation approach. We prove that the brucellosis free equilibrium exists, locally and globally asymptotically
stable if Re < 1 while the endemic equilibrium point exists, locally and globally asymptotically stable if Re > 1. Sensitivity analysis of
the effective reproductive number shows that, natural mortality rate of ruminants, recruitment rate, ruminant to ruminant transmission
rate, vaccination rate, and disease induced culling rate are the most sensitive parameters and should be targeted in designing of the
control strategies for the disease. Numerical simulation is done to show the variations of each subpopulation with respect to the
control parameters.