Optimal Control Theory Applied to Rabies Epidemiological Model with Time-dependent Vaccination in Davao City, Mindanao Island, Philippines

Abstract

Background and Objective. Rabies continues to be a challenge in Davao City despite the efforts of the city’s local government to vaccinate primarily the non-stray dog population. Meanwhile, studies have shown that time-dependent vaccination strategy is considered a prime factor for a cost-effective rabies control strategy. Hence, this study aims to provide information that will determine the optimal vaccination strategy targeted to the stray dog population that minimizes the rabies-infected dog population and vaccination costs using optimal control theory (OCT).

Methods. OCT is used to identify the optimal level of key rabies control, i.e., vaccination. Here, OCT was applied to a modified Susceptible-Exposed-Infectious-Vaccinated (SEIV) compartmental model. The study's key parameters were derived from published articles on rabies in Davao City and similar regions, along with the city's rabies reports.

Results. The findings revealed that while rabies remains endemic in the city, it is possible to reduce the number of cases through consistent implementation of vaccination programs to the exposed and susceptible dog populations. Nevertheless, the feasibility of these findings relies to the effective targeting of vaccine coverage for the dog population. From the simulations performed, the exposed dog population (i.e., pre-rabid dogs) was able to reach zero observation when the transmission rate (?) is 0.001 for all values of anti-rabies vaccine coverages for exposed (?) and susceptible (b) dog populations and ? = 0.01 only when ? = 0.7 and b = 0.7, ? = 0.7 and b = 0.5, and ? = 0.5 and b = 0.7. Consequently, the number of infectious dogs will thereby decrease. Moreover, a nonlinear correspondence was also observed in all scenarios between the vaccination rate and the number of rabies-exposed dogs such that the reduction in the incidence of rabies cases becomes apparent only when the vaccination rate is at least 0.9995.

Conclusion. In high rabies transmissibility scenarios, a time-dependent vaccination strategy demonstrated a reduction in the number of rabies-infected dogs. However, this approach involves a trade-off, limiting the period during which monthly vaccinations can be relaxed. Consequently, a robust and timely vaccination program for dogs is crucial to manage high rabies transmission rates. Lastly, the model simulation underscores the importance of initiating monthly vaccinations.