Mathematical analysis and passive control strategies for a fractional-order dog-to-human rabies model in danger zones

Abstract Rabies is an invariably fatal zoonosis and a serious public health problem among dogs and humans within the danger zones due to large concentrations of stray dog populations. In order to provide insights into the transmission dynamics of the disease between dogs and humans, we present in this paper a new fractional-order SEIVQRD compartmental model using Caputo derivative. While in most traditional SEIR models it is difficult to investigate the role of control interventions, we explicitly incorporate the roles of various passive control methods such as mass vaccination of dogs and human post and pre exposure prophylaxis. The use of fractional calculus allows one to account for the nonlocal properties and hereditary effects in the highly variable incubation period of the virus. We prove some important properties of the model such as positivity and boundedness of solutions and calculation of the basic reproduction number of the canine population ( $$R_{0d}$$ ). It is proved that the disease free equilibrium is globally asymptotically stable when $$R_{0d}<1$$ . Moreover, through normalization of sensitivity analysis, it is found that canine vaccination is the most dominant parameter for controlling the epidemic threshold and hence preventing human death. Lastly, numerical simulation through Adams Bashforth Moulton predictor corrector method has been done to prove the theoretical results.