# Mathematical Modeling of Dog Rabies Transmission Dynamics Using Optimal Control Analysis

## Authors

• Demsis Dejene Hailemichael Department of Mathematics, Wollega University, Nekemte, Ethiopia https://orcid.org/0000-0002-3950-1318
• Geremew Kenassa Edessa Department of Mathematics, Wollega University, Nekemte, Ethiopia
• Purnachandra Rao Koya Department of Mathematics, Wollega University, Nekemte, Ethiopia

## Keywords:

rabies, optimal control, vaccination, culling, sensitive index

## Abstract

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.

2023-05-22

## How to Cite

1.
Hailemichael DD, Edessa GK, Koya PR. Mathematical Modeling of Dog Rabies Transmission Dynamics Using Optimal Control Analysis. Contemp. Math. [Internet]. 2023 May 22 [cited 2024 May 25];4(2):296-319. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2347

Research Article