Mathematical Modeling of Culling and Vaccination for Dog Rabies Disease Transmission with Optimal Control and Sensitivity Analysis Approach

Source abstract

Objective: In this work, a five-compartment mathematical model is developed to investigate the transmission dynamics of rabies infection in dog populations, incorporating vaccination and culling as control interventions. The study also includes an optimal control analysis and a cost-effectiveness evaluation of the proposed interventions. Methods: Local and global stability analyses of the disease-free equilibrium (E₀) and the endemic equilibrium (E*) are established through Jacobian and Lyapunov function techniques, alongside the calculation of the effective reproductive number (Re). A sensitivity analysis is conducted by normalized forward index method to identify key parameters influencing Re. Optimal control and cost-effectiveness techniques were employed to find the optimal and suitable control strategies for the disease control. Results: The study findings indicate that, vaccination rate η1 and force of infection β are the most influential parameters negatively and positively for reducing and increasing Re by -0.8197 and +1.0000 respectively. Also, the work identifies that, combined strategy of vaccination and culling is the most effective approach for controlling rabies within short time, just within 3y, while implementation by using single intervention takes control profile of 4.5y to eliminate the disease. Moreover, the cost-effectiveness analysis shows that, control strategy B is more economically best choice with less incremental cost-effectiveness ratio (ICER) compared to strategies A and C. Conclusion: Therefore, it is recommended that vaccination and culling be implemented simultaneously to significantly reduce the population of exposed and infected dogs, leading to better control of rabies transmission.