Research Article Open Access

Application of Optimal Control to the Epidemiology of Fowl Pox Transmission Dynamics in Poultry

Udofia Ekere Sunday1 and Inyama Simeon Chioma1
  • 1 Federal University of Technology Owerri, Nigeria

Abstract

Problem statement: In this study, we present the mathematical model of the transmission dynamics of fowl pox infection in poultry. Approach: It describes the interaction between the susceptible and the infected birds which results in a system of ordinary differential equation. Introducing the control which represents the effort in applying chemoprophylaxis control u1 and treatment control u2 in birds with fowl pox, the system becomes a system of ordinary differential equations with control. Results: Our optimal control problem involves that in which the number of birds with latent and active fowl pox infections and the cost of treatment controls u1 (t) and u2 (t) were minimized subject to the differential Eq. 5-8. This involves the number of birds with active and latent fowl pox respectively as well as the cost of applying chemoprophylaxis control u1 and treatment u2 in birds with fowl pox. Conclusion: Analysing the model using Pontryagin’s Maximum Principle and optimality conditions, optimal effort necessary to reduce the transmission rate of fowl pox in the poultry has been determined. Hence, it is possible to reduce to reduce the rate of transmission.

Journal of Mathematics and Statistics
Volume 8 No. 2, 2012, 248-252

DOI: https://doi.org/10.3844/jmssp.2012.248.252

Submitted On: 21 November 2011 Published On: 13 June 2012

How to Cite: Sunday, U. E. & Chioma, I. S. (2012). Application of Optimal Control to the Epidemiology of Fowl Pox Transmission Dynamics in Poultry. Journal of Mathematics and Statistics, 8(2), 248-252. https://doi.org/10.3844/jmssp.2012.248.252

  • 2,830 Views
  • 2,502 Downloads
  • 5 Citations

Download

Keywords

  • Optimal control
  • fowl pox
  • optimality condition
  • caseous deposits
  • mosquitoes remain infected
  • numerical solution setting
  • disease transmission