GLOBAL DYNAMICS, OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS FOR ANTHRAX TRANSMISSION MODEL IN ANIMAL POPULATIONS WITH VACCINATION AND SANITATION

Abstract

In this study, we propose a deterministic model describing the dynamics of anthrax transmission in animals. It is assumed in the model that anthrax is contracted when susceptible animal comes into contact with infected animals, infected carcasses or the spores of Bacillus anthracis. Conditions for disease-free and endemic equilibria are derived and the basic reproduction number ([Formula: see text]) is computed. The disease-free equilibrium is stable when [Formula: see text] and the disease will be eliminated. If [Formula: see text], the disease persists, therefore, the endemic equilibrium is globally stable. Further, we extend our model by applying optimal control problem in which vaccination for susceptible animals and sanitation are control variables to minimize the anthrax transmission. We study three strategies to investigate the impact of the controls. Our numerical results demonstrate that both vaccination and sanitation help minimizing the transmission although vaccination alone gives more significant impact than sanitation alone. However, the combination of both controls gives the best result in wiping out the anthrax transmission overall. Further, cost-effectiveness analysis shows that the most effective strategy to control anthrax disease is a combination of vaccination and sanitation of the infected areas, therefore these two interventions should be encouraged.