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

Marsudi -, Wuryansari M. Kusumawinahyu, Darmajid -, Ahmad Fitri

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 (Re) 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 Re<1. Using the quadratic Lyapunov function, the endemic equilibrium (EE) point is determined to be globally asymptotically stable if Re>1. In addition, sensitivity analysis of model parameters on Re 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.

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Published: 2024-01-29

How to Cite this Article:

Marsudi -, Wuryansari M. Kusumawinahyu, Darmajid -, Ahmad Fitri, An optimal control model for rabies transmission with pre-exposure vaccination and post-exposure treatment of domestic and stray dogs, Commun. Math. Biol. Neurosci., 2024 (2024), Article ID 12

Copyright © 2024 Marsudi -, Wuryansari M. Kusumawinahyu, Darmajid -, Ahmad Fitri. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

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