Impact of biosecurity and immunological memory in curtailing ratio-dependent transmission of anthrax in livestock.

Delineating the dynamics of highly lethal anthrax disease in a biosecured livestock farm and impact of anthrax vaccination is presented through a modified deterministic $SIRBV$ model incorporating nonlinear ratio-dependent disease transmission rate. The basic reproduction number $(R_{0})$ of the system is computed and employed to explore the existence and asymptotic stability around the steady states of the system. The system experiences transcritical bifurcation at the disease-free steady state for $R_{0} = 1$. Waning of recovery-derived immunity and vaccination-derived immunity trigger backward bifurcation causing reemergence of anthrax in livestock. The dynamical behaviors of the fractional order system express that increased immunological memory will benefit to cut down the eradication time of anthrax transmission from the system. Numerical simulations suggest that appropriate vaccination and comprehensive biosecurity protocols would help to prevent the anthrax transmission and control the disease-induced deaths of cattle.