The Optimization Model of The Avian influenza Disease Control with Vaccination and Treatment

Nuning Nuraini, Tasmi Tasmi


In this study, a transmission model of the Avian influenza disease was developed and analyzedin view of optimization of vaccination and medical treatment. The model is a host-vector model. We focussed on control of Avian influenza, where a vaccination is given to susceptible poultry, while medical treatment is given to infected humans. In the model, the human population is divided into four compartments: susceptible humans, infected humans, recovered humans, and treated humans. Meanwhile, the poultry population is divided into three compartments: susceptible poultry, infected poultry, and vaccinated poultry. To analyze the dynamical behavior of the model, we obtained the disease-free equilibrium, the endemic equilibrium, and the basic reproduction ratio.Furthermore, a model of the optimal vaccination and medical treatment schedule was constructed to know the optimal strategy for controlling Avian influenza. The model can be used to determine the minimal cost of controlling the disease. The model is solved by a genetic algorithm method. Numerical simulations showed that effective control of Avian influenza can be achieved with a combination of vaccination and medical treatment. Likewise, the optimal schedule and strategy for controlling Avian influenza are shown.


genetic algorithm; host-vector model; medical treatment; optimization; vaccination;

Full Text:



Alexander, D.J., A Review of Avian Influenza in Different Bird Species, Veterinary Microbiology, 714(1-2), pp. 3-13, 2000.

Liu, S., Pang, L., Ruan, S. & Zhang, X., Global Dynamics of Avian Influenza Epidemic Model with Psychological Effect, Computational and Mathematical Methods in Medicine, 2015(913726), pp. 1-12, 2015.

Lim, S., J., Heo, C., Hwang, Y. & Yoon, T., Analyzing Patterns of Various Avian Influenza Virus by Decision Tree, International Journal of Computer Theory and Engineering, 7(4), pp. 302-305, 2015.

MMWR, Update: Isolation of Avian Influenza A(H5N1) Viruses From Humans-Hong Kong 1997-1998, American Medical Association, 279(5), pp. 347-352, 1998.

WHO, Cumulative Number of Confirmed Human Cases of Avian Influenza A/(H5N1) Reported to WHO, World Health Organization,, (August 9th, 2011).

Agusto, F.B. & Gumel, A.B., Theoretical Assessment of Avian Influenza Vaccine, Discrete and Continuous Dynamical Systems, 13(1), pp. 1-25, 2010.

Manach, A.L., Vergu, E., Grais, R.F., Smith, D.L. & Flahault, L., Key Strategies for Reducing Spread of Avian Influenza Among Commercial Poultry Holdings: Lessons for Transmission to Humans, Proceedings of Royal Society, pp. 2467-2475, 2006.

Iwami, S., Takeuchi, Y. & Liu, X., Avian-Human Influenza Epidemic Model, Mathematical Biosciences, 207(2007), pp. 1-25, 2007.

Gumel, A.B., Global Dynamics of A Two-Strain Avian Influenza Model, International Journal of Computer Mathematics, 86(1), pp. 85-108, 2009.

Jung, E., Iwami, S., Takeuchi, Y. & Jo, T.C., Optimal Control Strategy for Prevention of Avian Influenza Pandemic, Journal of Theoretical Biology, 260(2), pp. 220-229, 2009.

Vaidya, K.N., Wang, F.B. & Zou, X., Avian Influenza Dynamics in Wild Birds Mobility and Spatial Heterogeneous Environment, Discrete and Continuous Dynamical Systems Series B, 17(8), pp. 2829-2848, 2012.

Martcheva, M., Avian Flu: Modeling and Implications for Control, J. Biological Systems, 22(1), pp. 151-175, 2014.

Diekmann, O. & Heesterbeek, J.A.P., Mathematical Epidemiology of Infectious Diseases, Model Building, Analysis and Interpretation, John Wiley and Son, Chichester, pp. 73-95, 2000.

Hethcote, H.W. & Waltman, P., Optimal Vaccination Schedules in a Deterministic Epidemic Model, Mathematical Biosciences, 18(3-4), pp. 365-381, 1973.



  • There are currently no refbacks.

View my Stats

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.