Modeling rabies transmission dynamics with fractional order analysis: Examining stability, susceptibility, and vaccination impact

The transmission of rabies continues to be a major worldwide problem, involving all segments of society and necessitating concerted efforts towards control. In this research, we introduce a fractional-order mathematical model to study the spread of rabies, taking into account the effect of infected individuals at different phases of their lives and their interactions with humans and dogs. The model particularly focuses on rabies dynamics in dogs, individuals bitten by rabid dogs, and those who have undergone treatment or vaccination. To capture this transmission process, we constructed an eight-equation system. The basic reproduction number was calculated using the next-generation matrix method. Moreover, the existence, uniqueness, and stability of solutions to the model were proved using the Ulam–Hyers theorem, Banach contraction principle, and Krasnoselskii fixed-point theorem. Numerical simulations reveal a positive correlation between the increase in susceptible individuals and the prevalence of rabies among specific groups of people. The persistence of rabies represents a major impediment to eradication since the difficulties, be they logistical or personal, may deter people from accessing treatment or vaccination, thus raising exposure risk. To curb the spread of rabies among various susceptible populations, it is necessary to increase public education and adopt comprehensive anti-rabies measures in every sphere of society.