## Journal of Applied Mathematics

### Application of Optimal Control Theory to Newcastle Disease Dynamics in Village Chicken by Considering Wild Birds as Reservoir of Disease Virus

#### Abstract

In this study, an optimal control theory was applied to a nonautonomous model for Newcastle disease transmission in the village chicken population. A notable feature of this model is the inclusion of environment contamination and wild birds, which act as reservoirs of the disease virus. Vaccination, culling, and environmental hygiene and sanitation time dependent control strategies were adopted in the proposed model. This study proved the existence of an optimal control solution, and the necessary conditions for optimality were determined using Pontryagin’s Maximum Principle. The numerical simulations of the optimal control problem were performed using the forward–backward sweep method. The results showed that the use of only the environmental hygiene and sanitation control strategy has no significant effect on the transmission dynamics of the Newcastle disease. Additionally, the combination of vaccination and environmental hygiene and sanitation strategies reduces more number of infected chickens and the concentration of the Newcastle disease virus in the environment than any other combination of control strategies. Furthermore, a cost-effective analysis was performed using the incremental cost-effectiveness ratio method, and the results showed that the use of vaccination alone as the control measure is less costly compared to other control strategies. Hence, the most effective way to minimize the transmission rate of the Newcastle disease and the operational costs is concluded to be the timely vaccination of the entire population of the village chicken, improvement in the sanitation of facilities, and the maintenance of a hygienically clean environment.

#### Article information

Source
J. Appl. Math., Volume 2019 (2019), Article ID 3024965, 14 pages.

Dates
Revised: 14 January 2019
Accepted: 5 February 2019
First available in Project Euclid: 16 May 2019

https://projecteuclid.org/euclid.jam/1557972260

Digital Object Identifier
doi:10.1155/2019/3024965

#### Citation

Chuma, Furaha; Mwanga, Gasper Godson; Masanja, Verdiana Grace. Application of Optimal Control Theory to Newcastle Disease Dynamics in Village Chicken by Considering Wild Birds as Reservoir of Disease Virus. J. Appl. Math. 2019 (2019), Article ID 3024965, 14 pages. doi:10.1155/2019/3024965. https://projecteuclid.org/euclid.jam/1557972260

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