An optimal control model for rabies transmission with pre-exposure vaccination and post-exposure treatment of domestic and stray dogs

Abstract

In this paper, we formulate and analyze a mathematical model to study the effect of pre-exposure vaccination and post-exposure treatment on the spread of rabies in domestic and stray dogs. The effective reproduction number (R_e) was calculated using the next-generation matrix approach. Using the Castillo-Chavez method, the disease-free equilibrium (DFE) point is proven to be locally asymptotically stable if R_e<1. Using the quadratic Lyapunov function, the endemic equilibrium (EE) point is determined to be globally asymptotically stable if R_e>1. In addition, sensitivity analysis of model parameters on R_e was carried out using the normalized forward sensitivity index method. Optimal control analysis using Pontryagin's minimal principle was carried out to minimize the number of exposed and infected individuals as well as the control costs of vaccinating susceptible individuals and treating exposed individuals. Numerical simulations were carried out to verify the analytical results using MATLAB software. The results of the sensitivity analysis show that the transmission rate in stray dogs and the vaccination rate of stray dogs are the most sensitive parameters and are key factors in reducing the prevalence of rabies. The implementation of a combination of two optimal controls (pre-exposure vaccination and post-exposure treatment) results in a significant reduction in the number of cases in infected individuals, as demonstrated numerically by optimal control analysis.