MODEL FOR TRANSMISSION AND OPTIMAL CONTROL OF ANTHRAX INVOLVING HUMAN AND ANIMAL POPULATION

Abstract

Anthrax is a disease caused by Bacillus anthracis, commonly affects animals as well as humans health. In this paper, a nonlinear deterministic anthrax model involving human and animal is proposed and analyzed. The reproduction number [Formula: see text] and equilibrium points are explored to study the dynamic behavior of the disease. The existence and stability of equilibrium points are discussed. For [Formula: see text], the disease-free equilibrium [Formula: see text] is globally stable. However, it is unstable when [Formula: see text] and a locally stable endemic equilibrium point [Formula: see text] exists. The model is then extended to optimal control model considering human vaccination, animal vaccination and proper removal of carcass. The vaccination class of human and animal population appears separately in a model. The existence and characterization of optimal control are discussed. The numerical simulations are carried out for the choice of parametric values and initial conditions. These illustrate scavengers in the suspected area which eat infected dead body of animals contributing to the effort of reducing the expansion of disease. In addition, numerical comparison analysis with four distinct control strategies is carried out. Our findings show that each control technique has its own influence on reducing the total number of infections in the human and animal populations. The cumulative impact of all control measures is found to be extremely effective in lowering the prevalence of the disease.