Mathematical model of Anthrax disease dynamics incorporating Quarantine class.

Abstract

Anthrax disease is a zoonotic bacterial infection affecting human and animal populations. Consequences of infection can include respiratory failure, shock, inflammation of the brain membranes and death. That is, the Anthrax epidemic results in serious and fatal infections in both animals and humans globally. A mathematical model was proposed to study the transmission and control of Anthrax disease in farm animals and humans, incorporating the quarantine class. Both the reproduction number and the disease-free equilibrium (DFE) were calculated. For stability, the local stability of DFE was examined. Basic reproduction numbers were subjected to a sensitivity analysis concerning a few model parameters. The sensitive parameters with R0 are graphically displayed. If R0<1, then DFE's local stability is stable. According to the sensitivity analysis, the most sensitive parameter to increase the spread of the disease is the contact rate (α), while the most sensitive parameter to control the transmission of the disease is the quarantine rate (η).