Mathematical Modeling of Dog Rabies Transmission Dynamics Using Optimal Control Analysis (Contemporary Mathematics, 2023)
An ideal control method for the dynamics of dog rabies transmission is provided in this study. Given the nature of the disease and the fact that contact behavior varies, we divided the infected compartment into prodromal and furious compartments in the current updated model, which is an extension of the previous SEIR model. Vaccination and culling are two disease-controlling strategies used in the current model, and their effects are examined. It is possible to compute the basic reproduction number using the next-generation matrix. We study the stability, sensitivity analysis, endemic equilibrium, disease-free equilibrium, and stability of the optimal control model. According to the numerical simulation, which utilizes approximations for parameter values, the most efficient strategy to prevent the spread of rabies is a combination of vaccination and the culling of infected dogs. Using ode45 from MATLAB, this numerical simulation investigation was carried out. According to our research, the annual dog birth rate is a factor that influences the incidence of rabies. The state equations, adjoint equations, and the optimal condition that sets the controls by Pontryagin's Maximum/Minimum principle can all be used to construct the optimal control system. The body of the article contains the findings and discussions in an ordered manner.
Keywords: rabies, optimal control, vaccination, culling, sensitive index