Mathematical model for the infectiology of Brucellosis with some control strategies
Date
2019
Authors
Nyerere, Nkuba
Luboobi, Livingstone
Mpeshe, Saul
Shirima, Gabriel
Journal Title
Journal ISSN
Volume Title
Publisher
Strathmore University
Abstract
Brucellosis is a 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 proved 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 mortality rate
are the most sensitive parameters and should be targeted in design of the control
strategies for the disease. Numerical simulation shows that the combination of
more than two control strategies reduces/eliminates the disease from the livestock
population.
Description
Paper presented at the 5th Strathmore International Mathematics Conference (SIMC 2019), 12 - 16 August 2019, Strathmore University, Nairobi, Kenya
Keywords
Brucellosis, Mathematical model, Infectiology, Control Strategies