Modeling rabies evolution with vaccination: A fractional calculus perspective

In Africa and elsewhere in the world, Rabies poses a severe public health hazard. The number of human and canine rabies cases has significantly increased over the past years, and this rise can be linked to a lack of knowledge about the dynamics of the disease’s transmission and practical management strategies. The current work considers both humans and dogs, with distinct compartments of susceptible, exposed, infected, and vaccinated. To better reflect the dynamics of the epidemic, a fractional order derivative is used to account for the cumulative memory and non-local interaction involved in Rabies propagation. We analyze the model mathematically to assess its stability and an effective strategy for reducing the menace of the disease. The fundamental reproduction number, which represents the probability of the disease spreading in the population, is determined using the next-generation matrix technique. Sensitivity analysis of the model parameters is carried out to determine significant factors influencing the spread of disease in order to address the effective control strategy. This sensitivity analysis demonstrated that postexposure prophylaxis has a greater effect than preexposure prophylaxis on the contagious population. Using the framework fde12, numerical simulations of the fractional order model are carried out using MATLAB Software, and the outcomes indicate how successful the suggested techniques are in reducing the expansion of rabies.